Stan Math Library  2.14.0
reverse mode automatic differentiation
Namespaces | Classes | Typedefs | Functions | Variables
stan::math Namespace Reference

Matrices and templated mathematical functions. More...

Namespaces

 detail
 

Classes

class  accumulator
 Class to accumulate values and eventually return their sum. More...
 
struct  acos_fun
 Structure to wrap acos() so it can be vectorized. More...
 
struct  acosh_fun
 Structure to wrap acosh() so it can be vectorized. More...
 
struct  ad_promotable
 Template traits metaprogram to determine if a variable of one template type can be promoted to a second target template type. More...
 
struct  ad_promotable< bool, double >
 A blool may be promoted to a double. More...
 
struct  ad_promotable< char, double >
 A char may be promoted to a double. More...
 
struct  ad_promotable< double, double >
 A double may be promoted to a double. More...
 
struct  ad_promotable< float, double >
 A float may be promoted to a double. More...
 
struct  ad_promotable< int, double >
 An int may be promoted to a double. More...
 
struct  ad_promotable< long double, double >
 A long double may be promoted to a double. More...
 
struct  ad_promotable< long, double >
 A long may be promoted to a double. More...
 
struct  ad_promotable< short, double >
 A short may be promoted to a double. More...
 
struct  ad_promotable< T, T >
 Any type may be promoted to itself. More...
 
struct  ad_promotable< T, var >
 
struct  ad_promotable< unsigned char, double >
 An unsigned char may be promoted to a double. More...
 
struct  ad_promotable< unsigned int, double >
 An unsigned int may be promoted to a double. More...
 
struct  ad_promotable< unsigned long, double >
 An unsigned long may be promoted to a double. More...
 
struct  ad_promotable< unsigned short, double >
 An unsigned short may be promoted to a double. More...
 
struct  ad_promotable< V, fvar< T > >
 
struct  ad_promotable< var, var >
 
struct  apply_scalar_unary
 Base template class for vectorization of unary scalar functions defined by a template class F to a scalar, standard library vector, or Eigen dense matrix expression template. More...
 
struct  apply_scalar_unary< F, double >
 Template specialization for vectorized functions applying to double arguments. More...
 
struct  apply_scalar_unary< F, fvar< T > >
 Template specialization to fvar for vectorizing a unary scalar function. More...
 
struct  apply_scalar_unary< F, int >
 Template specialization for vectorized functions applying to integer arguments. More...
 
struct  apply_scalar_unary< F, std::vector< T > >
 Template specialization for vectorized functions applying to standard vector containers. More...
 
struct  apply_scalar_unary< F, var >
 Template specialization to var for vectorizing a unary scalar function. More...
 
struct  array_builder
 Structure for building up arrays in an expression (rather than in statements) using an argumentchaining add() method and a getter method array() to return the result. More...
 
struct  asin_fun
 Structure to wrap asin() so it can be vectorized. More...
 
struct  asinh_fun
 Structure to wrap asinh() so it can be vectorized. More...
 
struct  atan_fun
 Structure to wrap atan() so it can be vectorized. More...
 
struct  atanh_fun
 Structure to wrap atanh() so it can be vectorized. More...
 
struct  AutodiffStackStorage
 
struct  cbrt_fun
 Structure to wrap cbrt() so it can be vectorized. More...
 
struct  ceil_fun
 Structure to wrap ceil() so it can be vectorized. More...
 
class  chainable_alloc
 A chainable_alloc is an object which is constructed and destructed normally but the memory lifespan is managed along with the arena allocator for the gradient calculation. More...
 
struct  child_type
 Primary template class for metaprogram to compute child type of T. More...
 
struct  child_type< T_struct< T_child > >
 Specialization for template classes / structs. More...
 
class  cholesky_decompose_v_vari
 
struct  common_type
 
struct  common_type< Eigen::Matrix< T1, R, C >, Eigen::Matrix< T2, R, C > >
 
struct  common_type< std::vector< T1 >, std::vector< T2 > >
 
class  container_view
 Primary template class for container view of array y with same structure as T1 and size as x. More...
 
class  container_view< dummy, T2 >
 Dummy type specialization, used in conjunction with struct dummy as described above. More...
 
class  container_view< Eigen::Matrix< T1, R, C >, Eigen::Matrix< T2, R, C > >
 Template specialization for Eigen::Map view of array with scalar type T2 with size inferred from input Eigen::Matrix. More...
 
class  container_view< Eigen::Matrix< T1, R, C >, T2 >
 Template specialization for scalar view of array y with scalar type T2. More...
 
class  container_view< std::vector< Eigen::Matrix< T1, R, C > >, Eigen::Matrix< T2, R, C > >
 Template specialization for matrix view of array y with scalar type T2 with shape equal to x. More...
 
class  container_view< std::vector< T1 >, T2 >
 Template specialization for scalar view of array y with scalar type T2 with proper indexing inferred from input vector x of scalar type T1. More...
 
struct  cos_fun
 Structure to wrap cos() so it can be vectorized. More...
 
struct  cosh_fun
 Structure to wrap cosh() so it can be vectorized. More...
 
struct  coupled_ode_observer
 Observer for the coupled states. More...
 
struct  coupled_ode_system
 Base template class for a coupled ordinary differential equation system, which adds sensitivities to the base system. More...
 
class  coupled_ode_system< F, double, double >
 The coupled ode system for known initial values and known parameters. More...
 
struct  coupled_ode_system< F, double, var >
 The coupled ODE system for known initial values and unknown parameters. More...
 
struct  coupled_ode_system< F, var, double >
 The coupled ODE system for unknown initial values and known parameters. More...
 
struct  coupled_ode_system< F, var, stan::math::var >
 The coupled ode system for unknown intial values and unknown parameters. More...
 
class  cov_exp_quad_vari
 This is a subclass of the vari class for precomputed gradients of cov_exp_quad. More...
 
class  cov_exp_quad_vari< T_x, double, T_l >
 This is a subclass of the vari class for precomputed gradients of cov_exp_quad. More...
 
class  cvodes_ode_data
 CVODES ode data holder object which is used during CVODES integration for CVODES callbacks. More...
 
struct  digamma_fun
 Structure to wrap digamma() so it can be vectorized. More...
 
struct  dummy
 Empty struct for use in boost::condtional<is_constant_struct<T1>::value, T1, dummy>::type as false condtion for safe indexing. More...
 
struct  erf_fun
 Structure to wrap erf() so it can be vectorized. More...
 
struct  erfc_fun
 Structure to wrap erfc() so that it can be vectorized. More...
 
struct  exp2_fun
 Structure to wrap exp2() so it can be vectorized. More...
 
struct  exp_fun
 Structure to wrap exp() so that it can be vectorized. More...
 
struct  expm1_fun
 Structure to wrap expm1() so that it can be vectorized. More...
 
struct  fabs_fun
 Structure to wrap fabs() so that it can be vectorized. More...
 
struct  floor_fun
 Structure to wrap floor() so that it can be vectorized. More...
 
struct  fvar
 
class  gevv_vvv_vari
 
struct  include_summand
 Template metaprogram to calculate whether a summand needs to be included in a proportional (log) probability calculation. More...
 
struct  index_type
 Primary template class for the metaprogram to compute the index type of a container. More...
 
struct  index_type< const T >
 Template class for metaprogram to compute the type of indexes used in a constant container type. More...
 
struct  index_type< Eigen::Matrix< T, R, C > >
 Template metaprogram defining typedef for the type of index for an Eigen matrix, vector, or row vector. More...
 
struct  index_type< std::vector< T > >
 Template metaprogram class to compute the type of index for a standard vector. More...
 
struct  inv_cloglog_fun
 Structure to wrap inv_cloglog() so that it can be vectorized. More...
 
struct  inv_fun
 Structure to wrap inv() so that it can be vectorized. More...
 
struct  inv_logit_fun
 Structure to wrap inv_logit() so that it can be vectorized. More...
 
struct  inv_Phi_fun
 Structure to wrap inv_Phi() so it can be vectorized. More...
 
struct  inv_sqrt_fun
 Structure to wrap inv_sqrt() so that it can be vectorized. More...
 
struct  inv_square_fun
 Structure to wrap inv_square() so that it can be vectorized. More...
 
class  LDLT_alloc
 This object stores the actual (double typed) LDLT factorization of an Eigen::Matrix<var> along with pointers to its vari's which allow the *ldlt_ functions to save memory. More...
 
class  LDLT_factor
 
class  LDLT_factor< T, R, C >
 LDLT_factor is a thin wrapper on Eigen::LDLT to allow for reusing factorizations and efficient autodiff of things like log determinants and solutions to linear systems. More...
 
class  LDLT_factor< var, R, C >
 A template specialization of src/stan/math/matrix/LDLT_factor.hpp for var which can be used with all the *_ldlt functions. More...
 
struct  lgamma_fun
 Structure to wrap lgamma() so that it can be vectorized. More...
 
struct  log10_fun
 Structure to wrap log10() so it can be vectorized. More...
 
struct  log1m_exp_fun
 Structure to wrap log1m_exp() so it can be vectorized. More...
 
struct  log1m_fun
 Structure to wrap log1m() so it can be vectorized. More...
 
struct  log1m_inv_logit_fun
 Structure to wrap log1m_inv_logit() so it can be vectorized. More...
 
struct  log1p_exp_fun
 Structure to wrap log1m_exp() so that it can be vectorized. More...
 
struct  log1p_fun
 Structure to wrap log1p() so it can be vectorized. More...
 
struct  log2_fun
 Structure to wrap log2() so it can be vectorized. More...
 
struct  log_fun
 Structure to wrap log() so that it can be vectorized. More...
 
struct  log_inv_logit_fun
 Structure to wrap log_inv_logit() so it can be vectorized. More...
 
struct  logit_fun
 Structure to wrap logit() so it can be vectorized. More...
 
class  multiply_mat_vari
 This is a subclass of the vari class for matrix multiplication A * B where A is N by M and B is M by K. More...
 
class  multiply_mat_vari< double, 1, CA, TB, 1 >
 This is a subclass of the vari class for matrix multiplication A * B where A is a double row vector of length M and B is a vector of length M. More...
 
class  multiply_mat_vari< double, RA, CA, TB, CB >
 This is a subclass of the vari class for matrix multiplication A * B where A is an N by M matrix of double and B is M by K. More...
 
class  multiply_mat_vari< TA, 1, CA, double, 1 >
 This is a subclass of the vari class for matrix multiplication A * B where A is a row vector of length M and B is a vector of length M of doubles. More...
 
class  multiply_mat_vari< TA, 1, CA, TB, 1 >
 This is a subclass of the vari class for matrix multiplication A * B where A is 1 by M and B is M by 1. More...
 
class  multiply_mat_vari< TA, RA, CA, double, CB >
 This is a subclass of the vari class for matrix multiplication A * B where A is N by M and B is an M by K matrix of doubles. More...
 
class  ode_system
 Internal representation of an ODE model object which provides convenient Jacobian functions to obtain gradients wrt to states and parameters. More...
 
class  op_ddv_vari
 
class  op_dv_vari
 
class  op_dvd_vari
 
class  op_dvv_vari
 
class  op_matrix_vari
 
class  op_v_vari
 
class  op_vd_vari
 
class  op_vdd_vari
 
class  op_vdv_vari
 
class  op_vector_vari
 
class  op_vv_vari
 
class  op_vvd_vari
 
class  op_vvv_vari
 
struct  OperandsAndPartials
 This class builds partial derivatives with respect to a set of operands. More...
 
struct  OperandsAndPartials< T1, T2, T3, T4, T5, T6, fvar< T_partials_return > >
 This class builds partial derivatives with respect to a set of operands. More...
 
struct  OperandsAndPartials< T1, T2, T3, T4, T5, T6, stan::math::var >
 This class builds partial derivatives with respect to a set of operands. More...
 
struct  pass_type
 
struct  pass_type< double >
 
struct  pass_type< int >
 
struct  Phi_approx_fun
 Structure to wrap Phi_approx() so it can be vectorized. More...
 
struct  Phi_fun
 Structure to wrap Phi() so it can be vectorized. More...
 
class  precomp_v_vari
 
class  precomp_vv_vari
 
class  precomp_vvv_vari
 
class  precomputed_gradients_vari
 A variable implementation taking a sequence of operands and partial derivatives with respect to the operands. More...
 
struct  promote_scalar_struct
 General struct to hold static function for promoting underlying scalar types. More...
 
struct  promote_scalar_struct< T, Eigen::Matrix< S, -1, -1 > >
 Struct to hold static function for promoting underlying scalar types. More...
 
struct  promote_scalar_struct< T, Eigen::Matrix< S, -1, 1 > >
 Struct to hold static function for promoting underlying scalar types. More...
 
struct  promote_scalar_struct< T, Eigen::Matrix< S, 1, -1 > >
 Struct to hold static function for promoting underlying scalar types. More...
 
struct  promote_scalar_struct< T, std::vector< S > >
 Struct to hold static function for promoting underlying scalar types. More...
 
struct  promote_scalar_struct< T, T >
 Struct to hold static function for promoting underlying scalar types. More...
 
struct  promote_scalar_type
 Template metaprogram to calculate a type for converting a convertible type. More...
 
struct  promote_scalar_type< T, Eigen::Matrix< S, 1, Eigen::Dynamic > >
 Template metaprogram to calculate a type for a row vector whose underlying scalar is converted from the second template parameter type to the first. More...
 
struct  promote_scalar_type< T, Eigen::Matrix< S, Eigen::Dynamic, 1 > >
 Template metaprogram to calculate a type for a vector whose underlying scalar is converted from the second template parameter type to the first. More...
 
struct  promote_scalar_type< T, Eigen::Matrix< S, Eigen::Dynamic, Eigen::Dynamic > >
 Template metaprogram to calculate a type for a matrix whose underlying scalar is converted from the second template parameter type to the first. More...
 
struct  promote_scalar_type< T, std::vector< S > >
 Template metaprogram to calculate a type for a container whose underlying scalar is converted from the second template parameter type to the first. More...
 
struct  promoter
 
struct  promoter< Eigen::Matrix< F, R, C >, Eigen::Matrix< T, R, C > >
 
struct  promoter< Eigen::Matrix< T, R, C >, Eigen::Matrix< T, R, C > >
 
struct  promoter< std::vector< F >, std::vector< T > >
 
struct  promoter< std::vector< T >, std::vector< T > >
 
struct  promoter< T, T >
 
struct  round_fun
 Structure to wrap round() so it can be vectorized. More...
 
class  scal_squared_distance_dv_vari
 
class  scal_squared_distance_vd_vari
 
class  scal_squared_distance_vv_vari
 
class  seq_view
 
class  seq_view< double, std::vector< int > >
 
class  seq_view< T, Eigen::Matrix< S, 1, Eigen::Dynamic > >
 
class  seq_view< T, Eigen::Matrix< S, Eigen::Dynamic, 1 > >
 
class  seq_view< T, Eigen::Matrix< S, Eigen::Dynamic, Eigen::Dynamic > >
 
class  seq_view< T, std::vector< S > >
 
class  seq_view< T, std::vector< std::vector< T > > >
 
class  seq_view< T, std::vector< T > >
 
struct  sin_fun
 Structure to wrap sin() so it can be vectorized. More...
 
struct  sinh_fun
 Structure to wrap sinh() so that it can be vectorized. More...
 
struct  sqrt_fun
 Structure to wrap sqrt() so that it can be vectorized. More...
 
struct  square_fun
 Structure to wrap square() so that it can be vectorized. More...
 
class  stack_alloc
 An instance of this class provides a memory pool through which blocks of raw memory may be allocated and then collected simultaneously. More...
 
struct  store_type
 
struct  store_type< double >
 
struct  store_type< int >
 
class  stored_gradient_vari
 A var implementation that stores the daughter variable implementation pointers and the partial derivative with respect to the result explicitly in arrays constructed on the auto-diff memory stack. More...
 
class  sum_eigen_v_vari
 Class for representing sums with constructors for Eigen. More...
 
class  sum_v_vari
 Class for sums of variables constructed with standard vectors. More...
 
struct  tan_fun
 Structure to wrap tan() so that it can be vectorized. More...
 
struct  tanh_fun
 Structure to wrap tanh() so that it can be vectorized. More...
 
struct  tgamma_fun
 Structure to wrap tgamma() so that it can be vectorized. More...
 
struct  trigamma_fun
 Structure to wrap trigamma() so it can be vectorized. More...
 
struct  trunc_fun
 Structure to wrap trunc() so it can be vectorized. More...
 
struct  value_type
 Primary template class for metaprogram to compute the type of values stored in a container. More...
 
struct  value_type< const T >
 Template class for metaprogram to compute the type of values stored in a constant container. More...
 
struct  value_type< Eigen::Matrix< T, R, C > >
 Template metaprogram defining the type of values stored in an Eigen matrix, vector, or row vector. More...
 
struct  value_type< std::vector< T > >
 Template metaprogram class to compute the type of values stored in a standard vector. More...
 
class  var
 Independent (input) and dependent (output) variables for gradients. More...
 
class  vari
 The variable implementation base class. More...
 
class  welford_covar_estimator
 
class  welford_var_estimator
 

Typedefs

typedef Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic >::Index size_type
 Type for sizes and indexes in an Eigen matrix with double e. More...
 
typedef Eigen::Matrix< fvar< double >, Eigen::Dynamic, Eigen::Dynamic > matrix_fd
 
typedef Eigen::Matrix< fvar< fvar< double > >, Eigen::Dynamic, Eigen::Dynamic > matrix_ffd
 
typedef Eigen::Matrix< fvar< double >, Eigen::Dynamic, 1 > vector_fd
 
typedef Eigen::Matrix< fvar< fvar< double > >, Eigen::Dynamic, 1 > vector_ffd
 
typedef Eigen::Matrix< fvar< double >, 1, Eigen::Dynamic > row_vector_fd
 
typedef Eigen::Matrix< fvar< fvar< double > >, 1, Eigen::Dynamic > row_vector_ffd
 
typedef Eigen::Matrix< fvar< var >, Eigen::Dynamic, Eigen::Dynamic > matrix_fv
 
typedef Eigen::Matrix< fvar< fvar< var > >, Eigen::Dynamic, Eigen::Dynamic > matrix_ffv
 
typedef Eigen::Matrix< fvar< var >, Eigen::Dynamic, 1 > vector_fv
 
typedef Eigen::Matrix< fvar< fvar< var > >, Eigen::Dynamic, 1 > vector_ffv
 
typedef Eigen::Matrix< fvar< var >, 1, Eigen::Dynamic > row_vector_fv
 
typedef Eigen::Matrix< fvar< fvar< var > >, 1, Eigen::Dynamic > row_vector_ffv
 
typedef Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > matrix_d
 Type for matrix of double values. More...
 
typedef Eigen::Matrix< double, Eigen::Dynamic, 1 > vector_d
 Type for (column) vector of double values. More...
 
typedef Eigen::Matrix< double, 1, Eigen::Dynamic > row_vector_d
 Type for (row) vector of double values. More...
 
typedef boost::math::policies::policy< boost::math::policies::overflow_error< boost::math::policies::errno_on_error >, boost::math::policies::pole_error< boost::math::policies::errno_on_error > > boost_policy_t
 Boost policy that overrides the defaults to match the built-in C++ standard library functions. More...
 
typedef AutodiffStackStorage< vari, chainable_allocChainableStack
 
typedef Eigen::Matrix< var, Eigen::Dynamic, Eigen::Dynamic > matrix_v
 The type of a matrix holding var values. More...
 
typedef Eigen::Matrix< var, Eigen::Dynamic, 1 > vector_v
 The type of a (column) vector holding var values. More...
 
typedef Eigen::Matrix< var, 1, Eigen::Dynamic > row_vector_v
 The type of a row vector holding var values. More...
 

Functions

template<typename T >
fvar< T > log_sum_exp (const std::vector< fvar< T > > &v)
 
template<typename T >
fvar< T > sum (const std::vector< fvar< T > > &m)
 Return the sum of the entries of the specified standard vector. More...
 
template<typename T >
std::vector< fvar< T > > to_fvar (const std::vector< T > &v)
 
template<typename T >
std::vector< fvar< T > > to_fvar (const std::vector< T > &v, const std::vector< T > &d)
 
template<typename T >
std::vector< fvar< T > > to_fvar (const std::vector< fvar< T > > &v)
 
template<typename T >
fvar< T > operator+ (const fvar< T > &x1, const fvar< T > &x2)
 
template<typename T >
fvar< T > operator+ (double x1, const fvar< T > &x2)
 
template<typename T >
fvar< T > operator+ (const fvar< T > &x1, double x2)
 
template<typename T >
fvar< T > operator/ (const fvar< T > &x1, const fvar< T > &x2)
 
template<typename T >
fvar< T > operator/ (const fvar< T > &x1, double x2)
 
template<typename T >
fvar< T > operator/ (double x1, const fvar< T > &x2)
 
template<typename T >
bool operator== (const fvar< T > &x, const fvar< T > &y)
 
template<typename T >
bool operator== (const fvar< T > &x, double y)
 
template<typename T >
bool operator== (double x, const fvar< T > &y)
 
template<typename T >
bool operator> (const fvar< T > &x, const fvar< T > &y)
 
template<typename T >
bool operator> (const fvar< T > &x, double y)
 
template<typename T >
bool operator> (double x, const fvar< T > &y)
 
template<typename T >
bool operator>= (const fvar< T > &x, const fvar< T > &y)
 
template<typename T >
bool operator>= (const fvar< T > &x, double y)
 
template<typename T >
bool operator>= (double x, const fvar< T > &y)
 
template<typename T >
bool operator< (const fvar< T > &x, double y)
 
template<typename T >
bool operator< (double x, const fvar< T > &y)
 
template<typename T >
bool operator< (const fvar< T > &x, const fvar< T > &y)
 
template<typename T >
bool operator<= (const fvar< T > &x, const fvar< T > &y)
 
template<typename T >
bool operator<= (const fvar< T > &x, double y)
 
template<typename T >
bool operator<= (double x, const fvar< T > &y)
 
template<typename T >
fvar< T > operator* (const fvar< T > &x1, const fvar< T > &x2)
 
template<typename T >
fvar< T > operator* (double x1, const fvar< T > &x2)
 
template<typename T >
fvar< T > operator* (const fvar< T > &x1, double x2)
 
template<typename T >
bool operator!= (const fvar< T > &x, const fvar< T > &y)
 
template<typename T >
bool operator!= (const fvar< T > &x, double y)
 
template<typename T >
bool operator!= (double x, const fvar< T > &y)
 
template<typename T >
fvar< T > operator- (const fvar< T > &x1, const fvar< T > &x2)
 
template<typename T >
fvar< T > operator- (double x1, const fvar< T > &x2)
 
template<typename T >
fvar< T > operator- (const fvar< T > &x1, double x2)
 
template<typename T >
fvar< T > operator- (const fvar< T > &x)
 
template<typename T , int R1, int C1, int R2, int C2>
Eigen::Matrix< fvar< T >, 1, C1 > columns_dot_product (const Eigen::Matrix< fvar< T >, R1, C1 > &v1, const Eigen::Matrix< fvar< T >, R2, C2 > &v2)
 
template<typename T , int R1, int C1, int R2, int C2>
Eigen::Matrix< fvar< T >, 1, C1 > columns_dot_product (const Eigen::Matrix< fvar< T >, R1, C1 > &v1, const Eigen::Matrix< double, R2, C2 > &v2)
 
template<typename T , int R1, int C1, int R2, int C2>
Eigen::Matrix< fvar< T >, 1, C1 > columns_dot_product (const Eigen::Matrix< double, R1, C1 > &v1, const Eigen::Matrix< fvar< T >, R2, C2 > &v2)
 
template<typename T , int R, int C>
Eigen::Matrix< fvar< T >, 1, C > columns_dot_self (const Eigen::Matrix< fvar< T >, R, C > &x)
 
template<typename T , int R, int C>
Eigen::Matrix< fvar< T >, C, C > crossprod (const Eigen::Matrix< fvar< T >, R, C > &m)
 
template<typename T , int R, int C>
fvar< T > determinant (const Eigen::Matrix< fvar< T >, R, C > &m)
 
template<typename T , int R, int C>
Eigen::Matrix< fvar< T >, R, C > divide (const Eigen::Matrix< fvar< T >, R, C > &v, const fvar< T > &c)
 
template<typename T , int R, int C>
Eigen::Matrix< fvar< T >, R, C > divide (const Eigen::Matrix< fvar< T >, R, C > &v, double c)
 
template<typename T , int R, int C>
Eigen::Matrix< fvar< T >, R, C > divide (const Eigen::Matrix< double, R, C > &v, const fvar< T > &c)
 
template<typename T , int R, int C>
Eigen::Matrix< fvar< T >, R, C > operator/ (const Eigen::Matrix< fvar< T >, R, C > &v, const fvar< T > &c)
 
template<typename T , int R, int C>
Eigen::Matrix< fvar< T >, R, C > operator/ (const Eigen::Matrix< fvar< T >, R, C > &v, double c)
 
template<typename T , int R, int C>
Eigen::Matrix< fvar< T >, R, C > operator/ (const Eigen::Matrix< double, R, C > &v, const fvar< T > &c)
 
template<typename T , int R1, int C1, int R2, int C2>
fvar< T > dot_product (const Eigen::Matrix< fvar< T >, R1, C1 > &v1, const Eigen::Matrix< fvar< T >, R2, C2 > &v2)
 
template<typename T , int R1, int C1, int R2, int C2>
fvar< T > dot_product (const Eigen::Matrix< fvar< T >, R1, C1 > &v1, const Eigen::Matrix< double, R2, C2 > &v2)
 
template<typename T , int R1, int C1, int R2, int C2>
fvar< T > dot_product (const Eigen::Matrix< double, R1, C1 > &v1, const Eigen::Matrix< fvar< T >, R2, C2 > &v2)
 
template<typename T , int R1, int C1, int R2, int C2>
fvar< T > dot_product (const Eigen::Matrix< fvar< T >, R1, C1 > &v1, const Eigen::Matrix< fvar< T >, R2, C2 > &v2, size_type &length)
 
template<typename T , int R1, int C1, int R2, int C2>
fvar< T > dot_product (const Eigen::Matrix< fvar< T >, R1, C1 > &v1, const Eigen::Matrix< double, R2, C2 > &v2, size_type &length)
 
template<typename T , int R1, int C1, int R2, int C2>
fvar< T > dot_product (const Eigen::Matrix< double, R1, C1 > &v1, const Eigen::Matrix< fvar< T >, R2, C2 > &v2, size_type &length)
 
template<typename T >
fvar< T > dot_product (const std::vector< fvar< T > > &v1, const std::vector< fvar< T > > &v2)
 
template<typename T >
fvar< T > dot_product (const std::vector< double > &v1, const std::vector< fvar< T > > &v2)
 
template<typename T >
fvar< T > dot_product (const std::vector< fvar< T > > &v1, const std::vector< double > &v2)
 
template<typename T >
fvar< T > dot_product (const std::vector< fvar< T > > &v1, const std::vector< fvar< T > > &v2, size_type &length)
 
template<typename T >
fvar< T > dot_product (const std::vector< double > &v1, const std::vector< fvar< T > > &v2, size_type &length)
 
template<typename T >
fvar< T > dot_product (const std::vector< fvar< T > > &v1, const std::vector< double > &v2, size_type &length)
 
template<typename T , int R, int C>
fvar< T > dot_self (const Eigen::Matrix< fvar< T >, R, C > &v)
 
template<typename T , int R, int C>
Eigen::Matrix< fvar< T >, R, C > inverse (const Eigen::Matrix< fvar< T >, R, C > &m)
 
template<typename T , int R, int C>
fvar< T > log_determinant (const Eigen::Matrix< fvar< T >, R, C > &m)
 
template<typename T >
Eigen::Matrix< fvar< T >, Eigen::Dynamic, 1 > log_softmax (const Eigen::Matrix< fvar< T >, Eigen::Dynamic, 1 > &alpha)
 
template<typename T , int R, int C>
fvar< T > log_sum_exp (const Eigen::Matrix< fvar< T >, R, C > &v)
 
template<typename T , int R1, int C1, int R2, int C2>
Eigen::Matrix< fvar< T >, R1, C2 > mdivide_left (const Eigen::Matrix< fvar< T >, R1, C1 > &A, const Eigen::Matrix< fvar< T >, R2, C2 > &b)
 
template<typename T , int R1, int C1, int R2, int C2>
Eigen::Matrix< fvar< T >, R1, C2 > mdivide_left (const Eigen::Matrix< double, R1, C1 > &A, const Eigen::Matrix< fvar< T >, R2, C2 > &b)
 
template<typename T , int R1, int C1, int R2, int C2>
Eigen::Matrix< fvar< T >, R1, C2 > mdivide_left (const Eigen::Matrix< fvar< T >, R1, C1 > &A, const Eigen::Matrix< double, R2, C2 > &b)
 
template<int R1, int C1, int R2, int C2, typename T2 >
Eigen::Matrix< fvar< T2 >, R1, C2 > mdivide_left_ldlt (const LDLT_factor< double, R1, C1 > &A, const Eigen::Matrix< fvar< T2 >, R2, C2 > &b)
 Returns the solution of the system Ax=b given an LDLT_factor of A. More...
 
template<typename T , int R1, int C1, int R2, int C2>
Eigen::Matrix< fvar< T >, R1, C1 > mdivide_left_tri_low (const Eigen::Matrix< fvar< T >, R1, C1 > &A, const Eigen::Matrix< fvar< T >, R2, C2 > &b)
 
template<typename T , int R1, int C1, int R2, int C2>
Eigen::Matrix< fvar< T >, R1, C1 > mdivide_left_tri_low (const Eigen::Matrix< double, R1, C1 > &A, const Eigen::Matrix< fvar< T >, R2, C2 > &b)
 
template<typename T , int R1, int C1, int R2, int C2>
Eigen::Matrix< fvar< T >, R1, C1 > mdivide_left_tri_low (const Eigen::Matrix< fvar< T >, R1, C1 > &A, const Eigen::Matrix< double, R2, C2 > &b)
 
template<typename T , int R1, int C1, int R2, int C2>
Eigen::Matrix< fvar< T >, R1, C2 > mdivide_right (const Eigen::Matrix< fvar< T >, R1, C1 > &A, const Eigen::Matrix< fvar< T >, R2, C2 > &b)
 
template<typename T , int R1, int C1, int R2, int C2>
Eigen::Matrix< fvar< T >, R1, C2 > mdivide_right (const Eigen::Matrix< fvar< T >, R1, C1 > &A, const Eigen::Matrix< double, R2, C2 > &b)
 
template<typename T , int R1, int C1, int R2, int C2>
Eigen::Matrix< fvar< T >, R1, C2 > mdivide_right (const Eigen::Matrix< double, R1, C1 > &A, const Eigen::Matrix< fvar< T >, R2, C2 > &b)
 
template<typename T , int R1, int C1, int R2, int C2>
Eigen::Matrix< fvar< T >, R1, C1 > mdivide_right_tri_low (const Eigen::Matrix< fvar< T >, R1, C1 > &A, const Eigen::Matrix< fvar< T >, R2, C2 > &b)
 
template<typename T , int R1, int C1, int R2, int C2>
Eigen::Matrix< fvar< T >, R1, C2 > mdivide_right_tri_low (const Eigen::Matrix< fvar< T >, R1, C1 > &A, const Eigen::Matrix< double, R2, C2 > &b)
 
template<typename T , int R1, int C1, int R2, int C2>
Eigen::Matrix< fvar< T >, R1, C2 > mdivide_right_tri_low (const Eigen::Matrix< double, R1, C1 > &A, const Eigen::Matrix< fvar< T >, R2, C2 > &b)
 
template<typename T , int R1, int C1>
Eigen::Matrix< fvar< T >, R1, C1 > multiply (const Eigen::Matrix< fvar< T >, R1, C1 > &m, const fvar< T > &c)
 
template<typename T , int R2, int C2>
Eigen::Matrix< fvar< T >, R2, C2 > multiply (const Eigen::Matrix< fvar< T >, R2, C2 > &m, double c)
 
template<typename T , int R1, int C1>
Eigen::Matrix< fvar< T >, R1, C1 > multiply (const Eigen::Matrix< double, R1, C1 > &m, const fvar< T > &c)
 
template<typename T , int R1, int C1>
Eigen::Matrix< fvar< T >, R1, C1 > multiply (const fvar< T > &c, const Eigen::Matrix< fvar< T >, R1, C1 > &m)
 
template<typename T , int R1, int C1>
Eigen::Matrix< fvar< T >, R1, C1 > multiply (double c, const Eigen::Matrix< fvar< T >, R1, C1 > &m)
 
template<typename T , int R1, int C1>
Eigen::Matrix< fvar< T >, R1, C1 > multiply (const fvar< T > &c, const Eigen::Matrix< double, R1, C1 > &m)
 
template<typename T , int R1, int C1, int R2, int C2>
Eigen::Matrix< fvar< T >, R1, C2 > multiply (const Eigen::Matrix< fvar< T >, R1, C1 > &m1, const Eigen::Matrix< fvar< T >, R2, C2 > &m2)
 
template<typename T , int R1, int C1, int R2, int C2>
Eigen::Matrix< fvar< T >, R1, C2 > multiply (const Eigen::Matrix< fvar< T >, R1, C1 > &m1, const Eigen::Matrix< double, R2, C2 > &m2)
 
template<typename T , int R1, int C1, int R2, int C2>
Eigen::Matrix< fvar< T >, R1, C2 > multiply (const Eigen::Matrix< double, R1, C1 > &m1, const Eigen::Matrix< fvar< T >, R2, C2 > &m2)
 
template<typename T , int C1, int R2>
fvar< T > multiply (const Eigen::Matrix< fvar< T >, 1, C1 > &rv, const Eigen::Matrix< fvar< T >, R2, 1 > &v)
 
template<typename T , int C1, int R2>
fvar< T > multiply (const Eigen::Matrix< fvar< T >, 1, C1 > &rv, const Eigen::Matrix< double, R2, 1 > &v)
 
template<typename T , int C1, int R2>
fvar< T > multiply (const Eigen::Matrix< double, 1, C1 > &rv, const Eigen::Matrix< fvar< T >, R2, 1 > &v)
 
template<typename T , int R, int C>
Eigen::Matrix< fvar< T >, R, R > multiply_lower_tri_self_transpose (const Eigen::Matrix< fvar< T >, R, C > &m)
 
template<typename T >
Eigen::Matrix< fvar< T >, Eigen::Dynamic, Eigen::Dynamic > qr_Q (const Eigen::Matrix< fvar< T >, Eigen::Dynamic, Eigen::Dynamic > &m)
 
template<typename T >
Eigen::Matrix< fvar< T >, Eigen::Dynamic, Eigen::Dynamic > qr_R (const Eigen::Matrix< fvar< T >, Eigen::Dynamic, Eigen::Dynamic > &m)
 
template<int RA, int CA, int RB, int CB, typename T >
Eigen::Matrix< fvar< T >, CB, CB > quad_form_sym (const Eigen::Matrix< fvar< T >, RA, CA > &A, const Eigen::Matrix< double, RB, CB > &B)
 
template<int RA, int CA, int RB, typename T >
fvar< T > quad_form_sym (const Eigen::Matrix< fvar< T >, RA, CA > &A, const Eigen::Matrix< double, RB, 1 > &B)
 
template<int RA, int CA, int RB, int CB, typename T >
Eigen::Matrix< fvar< T >, CB, CB > quad_form_sym (const Eigen::Matrix< double, RA, CA > &A, const Eigen::Matrix< fvar< T >, RB, CB > &B)
 
template<int RA, int CA, int RB, typename T >
fvar< T > quad_form_sym (const Eigen::Matrix< double, RA, CA > &A, const Eigen::Matrix< fvar< T >, RB, 1 > &B)
 
template<typename T , int R1, int C1, int R2, int C2>
Eigen::Matrix< fvar< T >, R1, 1 > rows_dot_product (const Eigen::Matrix< fvar< T >, R1, C1 > &v1, const Eigen::Matrix< fvar< T >, R2, C2 > &v2)
 
template<typename T , int R1, int C1, int R2, int C2>
Eigen::Matrix< fvar< T >, R1, 1 > rows_dot_product (const Eigen::Matrix< double, R1, C1 > &v1, const Eigen::Matrix< fvar< T >, R2, C2 > &v2)
 
template<typename T , int R1, int C1, int R2, int C2>
Eigen::Matrix< fvar< T >, R1, 1 > rows_dot_product (const Eigen::Matrix< fvar< T >, R1, C1 > &v1, const Eigen::Matrix< double, R2, C2 > &v2)
 
template<typename T , int R, int C>
Eigen::Matrix< fvar< T >, R, 1 > rows_dot_self (const Eigen::Matrix< fvar< T >, R, C > &x)
 
template<typename T >
Eigen::Matrix< fvar< T >, Eigen::Dynamic, 1 > softmax (const Eigen::Matrix< fvar< T >, Eigen::Dynamic, 1 > &alpha)
 
template<typename T , int R, int C>
fvar< T > squared_distance (const Eigen::Matrix< fvar< T >, R, C > &v1, const Eigen::Matrix< double, R, C > &v2)
 Returns the squared distance between the specified vectors of the same dimensions. More...
 
template<typename T , int R1, int C1, int R2, int C2>
fvar< T > squared_distance (const Eigen::Matrix< fvar< T >, R1, C1 > &v1, const Eigen::Matrix< double, R2, C2 > &v2)
 Returns the squared distance between the specified vectors of the same dimensions. More...
 
template<typename T , int R, int C>
fvar< T > squared_distance (const Eigen::Matrix< double, R, C > &v1, const Eigen::Matrix< fvar< T >, R, C > &v2)
 Returns the squared distance between the specified vectors of the same dimensions. More...
 
template<typename T , int R1, int C1, int R2, int C2>
fvar< T > squared_distance (const Eigen::Matrix< double, R1, C1 > &v1, const Eigen::Matrix< fvar< T >, R2, C2 > &v2)
 Returns the squared distance between the specified vectors of the same dimensions. More...
 
template<typename T , int R, int C>
fvar< T > squared_distance (const Eigen::Matrix< fvar< T >, R, C > &v1, const Eigen::Matrix< fvar< T >, R, C > &v2)
 Returns the squared distance between the specified vectors of the same dimensions. More...
 
template<typename T , int R1, int C1, int R2, int C2>
fvar< T > squared_distance (const Eigen::Matrix< fvar< T >, R1, C1 > &v1, const Eigen::Matrix< fvar< T >, R2, C2 > &v2)
 Returns the squared distance between the specified vectors of the same dimensions. More...
 
template<typename T , int R, int C>
fvar< T > sum (const Eigen::Matrix< fvar< T >, R, C > &m)
 Return the sum of the entries of the specified matrix. More...
 
template<typename T , int R, int C>
Eigen::Matrix< fvar< T >, R, R > tcrossprod (const Eigen::Matrix< fvar< T >, R, C > &m)
 
template<int R, int C, typename T >
Eigen::Matrix< T, R, C > to_fvar (const Eigen::Matrix< T, R, C > &m)
 
template<int R, int C>
Eigen::Matrix< fvar< double >, R, C > to_fvar (const Eigen::Matrix< double, R, C > &m)
 
template<typename T , int R, int C>
Eigen::Matrix< fvar< T >, R, C > to_fvar (const Eigen::Matrix< T, R, C > &val, const Eigen::Matrix< T, R, C > &deriv)
 
template<int RD, int CD, int RA, int CA, int RB, int CB, typename T >
fvar< T > trace_gen_quad_form (const Eigen::Matrix< fvar< T >, RD, CD > &D, const Eigen::Matrix< fvar< T >, RA, CA > &A, const Eigen::Matrix< fvar< T >, RB, CB > &B)
 
template<int RA, int CA, int RB, int CB, typename T >
fvar< T > trace_quad_form (const Eigen::Matrix< fvar< T >, RA, CA > &A, const Eigen::Matrix< fvar< T >, RB, CB > &B)
 
template<int RA, int CA, int RB, int CB, typename T >
fvar< T > trace_quad_form (const Eigen::Matrix< fvar< T >, RA, CA > &A, const Eigen::Matrix< double, RB, CB > &B)
 
template<int RA, int CA, int RB, int CB, typename T >
fvar< T > trace_quad_form (const Eigen::Matrix< double, RA, CA > &A, const Eigen::Matrix< fvar< T >, RB, CB > &B)
 
template<typename T , int R, int C>
Eigen::Matrix< fvar< T >, R, C > unit_vector_constrain (const Eigen::Matrix< fvar< T >, R, C > &y)
 
template<typename T , int R, int C>
Eigen::Matrix< fvar< T >, R, C > unit_vector_constrain (const Eigen::Matrix< fvar< T >, R, C > &y, fvar< T > &lp)
 
template<typename T , typename F >
void gradient (const F &f, const Eigen::Matrix< T, Eigen::Dynamic, 1 > &x, T &fx, Eigen::Matrix< T, Eigen::Dynamic, 1 > &grad_fx)
 Calculate the value and the gradient of the specified function at the specified argument. More...
 
template<typename T , typename F >
void jacobian (const F &f, const Eigen::Matrix< T, Eigen::Dynamic, 1 > &x, Eigen::Matrix< T, Eigen::Dynamic, 1 > &fx, Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &J)
 
template<typename T >
fvar< T > abs (const fvar< T > &x)
 
template<typename T >
fvar< T > acos (const fvar< T > &x)
 
template<typename T >
fvar< T > acosh (const fvar< T > &x)
 
template<typename T >
fvar< T > asin (const fvar< T > &x)
 
template<typename T >
fvar< T > asinh (const fvar< T > &x)
 
template<typename T >
fvar< T > atan (const fvar< T > &x)
 
template<typename T >
fvar< T > atan2 (const fvar< T > &x1, const fvar< T > &x2)
 
template<typename T >
fvar< T > atan2 (double x1, const fvar< T > &x2)
 
template<typename T >
fvar< T > atan2 (const fvar< T > &x1, double x2)
 
template<typename T >
fvar< T > atanh (const fvar< T > &x)
 Return inverse hyperbolic tangent of specified value. More...
 
template<typename T >
fvar< T > bessel_first_kind (int v, const fvar< T > &z)
 
template<typename T >
fvar< T > bessel_second_kind (int v, const fvar< T > &z)
 
template<typename T >
fvar< T > binary_log_loss (int y, const fvar< T > &y_hat)
 
template<typename T >
fvar< T > binomial_coefficient_log (const fvar< T > &x1, const fvar< T > &x2)
 
template<typename T >
fvar< T > binomial_coefficient_log (const fvar< T > &x1, double x2)
 
template<typename T >
fvar< T > binomial_coefficient_log (double x1, const fvar< T > &x2)
 
template<typename T >
fvar< T > cbrt (const fvar< T > &x)
 Return cube root of specified argument. More...
 
template<typename T >
fvar< T > ceil (const fvar< T > &x)
 
template<typename T >
fvar< T > cos (const fvar< T > &x)
 
template<typename T >
fvar< T > cosh (const fvar< T > &x)
 
template<typename T >
fvar< T > digamma (const fvar< T > &x)
 Return the derivative of the log gamma function at the specified argument. More...
 
template<typename T >
fvar< T > erf (const fvar< T > &x)
 
template<typename T >
fvar< T > erfc (const fvar< T > &x)
 
template<typename T >
fvar< T > exp (const fvar< T > &x)
 
template<typename T >
fvar< T > exp2 (const fvar< T > &x)
 
template<typename T >
fvar< T > expm1 (const fvar< T > &x)
 
template<typename T >
fvar< T > fabs (const fvar< T > &x)
 
template<typename T >
fvar< T > falling_factorial (const fvar< T > &x, const fvar< T > &n)
 
template<typename T >
fvar< T > falling_factorial (const fvar< T > &x, double n)
 
template<typename T >
fvar< T > falling_factorial (double x, const fvar< T > &n)
 
template<typename T >
fvar< T > fdim (const fvar< T > &x, const fvar< T > &y)
 Return the positive difference of the specified values (C++11). More...
 
template<typename T >
fvar< T > fdim (const fvar< T > &x, double y)
 Return the positive difference of the specified values (C++11). More...
 
template<typename T >
fvar< T > fdim (double x, const fvar< T > &y)
 Return the positive difference of the specified values (C++11). More...
 
template<typename T >
fvar< T > floor (const fvar< T > &x)
 
template<typename T1 , typename T2 , typename T3 >
fvar< typename stan::return_type< T1, T2, T3 >::type > fma (const fvar< T1 > &x1, const fvar< T2 > &x2, const fvar< T3 > &x3)
 The fused multiply-add operation (C99). More...
 
template<typename T1 , typename T2 , typename T3 >
fvar< typename stan::return_type< T1, T2, T3 >::type > fma (const T1 &x1, const fvar< T2 > &x2, const fvar< T3 > &x3)
 See all-var input signature for details on the function and derivatives. More...
 
template<typename T1 , typename T2 , typename T3 >
fvar< typename stan::return_type< T1, T2, T3 >::type > fma (const fvar< T1 > &x1, const T2 &x2, const fvar< T3 > &x3)
 See all-var input signature for details on the function and derivatives. More...
 
template<typename T1 , typename T2 , typename T3 >
fvar< typename stan::return_type< T1, T2, T3 >::type > fma (const fvar< T1 > &x1, const fvar< T2 > &x2, const T3 &x3)
 See all-var input signature for details on the function and derivatives. More...
 
template<typename T1 , typename T2 , typename T3 >
fvar< typename stan::return_type< T1, T2, T3 >::type > fma (const T1 &x1, const T2 &x2, const fvar< T3 > &x3)
 See all-var input signature for details on the function and derivatives. More...
 
template<typename T1 , typename T2 , typename T3 >
fvar< typename stan::return_type< T1, T2, T3 >::type > fma (const fvar< T1 > &x1, const T2 &x2, const T3 &x3)
 See all-var input signature for details on the function and derivatives. More...
 
template<typename T1 , typename T2 , typename T3 >
fvar< typename stan::return_type< T1, T2, T3 >::type > fma (const T1 &x1, const fvar< T2 > &x2, const T3 &x3)
 See all-var input signature for details on the function and derivatives. More...
 
template<typename T >
fvar< T > fmax (const fvar< T > &x1, const fvar< T > &x2)
 Return the greater of the two specified arguments. More...
 
template<typename T >
fvar< T > fmax (double x1, const fvar< T > &x2)
 Return the greater of the two specified arguments. More...
 
template<typename T >
fvar< T > fmax (const fvar< T > &x1, double x2)
 Return the greater of the two specified arguments. More...
 
template<typename T >
fvar< T > fmin (const fvar< T > &x1, const fvar< T > &x2)
 
template<typename T >
fvar< T > fmin (double x1, const fvar< T > &x2)
 
template<typename T >
fvar< T > fmin (const fvar< T > &x1, double x2)
 
template<typename T >
fvar< T > fmod (const fvar< T > &x1, const fvar< T > &x2)
 
template<typename T >
fvar< T > fmod (const fvar< T > &x1, double x2)
 
template<typename T >
fvar< T > fmod (double x1, const fvar< T > &x2)
 
template<typename T >
fvar< T > gamma_p (const fvar< T > &x1, const fvar< T > &x2)
 
template<typename T >
fvar< T > gamma_p (const fvar< T > &x1, double x2)
 
template<typename T >
fvar< T > gamma_p (double x1, const fvar< T > &x2)
 
template<typename T >
fvar< T > gamma_q (const fvar< T > &x1, const fvar< T > &x2)
 
template<typename T >
fvar< T > gamma_q (const fvar< T > &x1, double x2)
 
template<typename T >
fvar< T > gamma_q (double x1, const fvar< T > &x2)
 
template<typename T >
void grad_inc_beta (fvar< T > &g1, fvar< T > &g2, fvar< T > a, fvar< T > b, fvar< T > z)
 Gradient of the incomplete beta function beta(a, b, z) with respect to the first two arguments. More...
 
template<typename T >
fvar< T > hypot (const fvar< T > &x1, const fvar< T > &x2)
 Return the length of the hypoteneuse of a right triangle with opposite and adjacent side lengths given by the specified arguments (C++11). More...
 
template<typename T >
fvar< T > hypot (const fvar< T > &x1, double x2)
 Return the length of the hypoteneuse of a right triangle with opposite and adjacent side lengths given by the specified arguments (C++11). More...
 
template<typename T >
fvar< T > hypot (double x1, const fvar< T > &x2)
 Return the length of the hypoteneuse of a right triangle with opposite and adjacent side lengths given by the specified arguments (C++11). More...
 
template<typename T >
fvar< T > inc_beta (const fvar< T > &a, const fvar< T > &b, const fvar< T > &x)
 
template<typename T >
fvar< T > inv (const fvar< T > &x)
 
template<typename T >
fvar< T > inv_cloglog (const fvar< T > &x)
 
template<typename T >
fvar< T > inv_logit (const fvar< T > &x)
 Returns the inverse logit function applied to the argument. More...
 
template<typename T >
fvar< T > inv_Phi (const fvar< T > &p)
 
template<typename T >
fvar< T > inv_sqrt (const fvar< T > &x)
 
template<typename T >
fvar< T > inv_square (const fvar< T > &x)
 
template<typename T >
int is_inf (const fvar< T > &x)
 Returns 1 if the input's value is infinite and 0 otherwise. More...
 
template<typename T >
int is_nan (const fvar< T > &x)
 Returns 1 if the input's value is NaN and 0 otherwise. More...
 
template<typename T >
fvar< T > lbeta (const fvar< T > &x1, const fvar< T > &x2)
 
template<typename T >
fvar< T > lbeta (double x1, const fvar< T > &x2)
 
template<typename T >
fvar< T > lbeta (const fvar< T > &x1, double x2)
 
template<typename T >
fvar< T > lgamma (const fvar< T > &x)
 Return the natural logarithm of the gamma function applied to the specified argument. More...
 
template<typename T >
fvar< typename stan::return_type< T, int >::type > lmgamma (int x1, const fvar< T > &x2)
 
template<typename T >
fvar< T > log (const fvar< T > &x)
 
template<typename T >
fvar< T > log10 (const fvar< T > &x)
 
template<typename T >
fvar< T > log1m (const fvar< T > &x)
 
template<typename T >
fvar< T > log1m_exp (const fvar< T > &x)
 Return the natural logarithm of one minus the exponentiation of the specified argument. More...
 
template<typename T >
fvar< T > log1m_inv_logit (const fvar< T > &x)
 Return the natural logarithm of one minus the inverse logit of the specified argument. More...
 
template<typename T >
fvar< T > log1p (const fvar< T > &x)
 
template<typename T >
fvar< T > log1p_exp (const fvar< T > &x)
 
template<typename T >
fvar< T > log2 (const fvar< T > &x)
 Return the base two logarithm of the specified argument. More...
 
template<typename T >
fvar< T > log_diff_exp (const fvar< T > &x1, const fvar< T > &x2)
 
template<typename T1 , typename T2 >
fvar< T2 > log_diff_exp (const T1 &x1, const fvar< T2 > &x2)
 
template<typename T1 , typename T2 >
fvar< T1 > log_diff_exp (const fvar< T1 > &x1, const T2 &x2)
 
template<typename T >
fvar< T > log_falling_factorial (const fvar< T > &x, const fvar< T > &n)
 
template<typename T >
fvar< T > log_falling_factorial (double x, const fvar< T > &n)
 
template<typename T >
fvar< T > log_falling_factorial (const fvar< T > &x, double n)
 
template<typename T >
fvar< T > log_inv_logit (const fvar< T > &x)
 
template<typename T_theta , typename T_lambda1 , typename T_lambda2 , int N>
void log_mix_partial_helper (const T_theta &theta, const T_lambda1 &lambda1, const T_lambda2 &lambda2, typename boost::math::tools::promote_args< T_theta, T_lambda1, T_lambda2 >::type(&partials_array)[N])
 
template<typename T >
fvar< T > log_mix (const fvar< T > &theta, const fvar< T > &lambda1, const fvar< T > &lambda2)
 Return the log mixture density with specified mixing proportion and log densities and its derivative at each. More...
 
template<typename T >
fvar< T > log_mix (const fvar< T > &theta, const fvar< T > &lambda1, double lambda2)
 
template<typename T >
fvar< T > log_mix (const fvar< T > &theta, double lambda1, const fvar< T > &lambda2)
 
template<typename T >
fvar< T > log_mix (double theta, const fvar< T > &lambda1, const fvar< T > &lambda2)
 
template<typename T >
fvar< T > log_mix (const fvar< T > &theta, double lambda1, double lambda2)
 
template<typename T >
fvar< T > log_mix (double theta, const fvar< T > &lambda1, double lambda2)
 
template<typename T >
fvar< T > log_mix (double theta, double lambda1, const fvar< T > &lambda2)
 
template<typename T >
fvar< T > log_rising_factorial (const fvar< T > &x, const fvar< T > &n)
 
template<typename T >
fvar< T > log_rising_factorial (const fvar< T > &x, double n)
 
template<typename T >
fvar< T > log_rising_factorial (double x, const fvar< T > &n)
 
template<typename T >
fvar< T > log_sum_exp (const fvar< T > &x1, const fvar< T > &x2)
 
template<typename T >
fvar< T > log_sum_exp (double x1, const fvar< T > &x2)
 
template<typename T >
fvar< T > log_sum_exp (const fvar< T > &x1, double x2)
 
template<typename T >
fvar< T > logit (const fvar< T > &x)
 
template<typename T >
fvar< T > modified_bessel_first_kind (int v, const fvar< T > &z)
 
template<typename T >
fvar< T > modified_bessel_second_kind (int v, const fvar< T > &z)
 
template<typename T >
fvar< T > multiply_log (const fvar< T > &x1, const fvar< T > &x2)
 
template<typename T >
fvar< T > multiply_log (double x1, const fvar< T > &x2)
 
template<typename T >
fvar< T > multiply_log (const fvar< T > &x1, double x2)
 
template<typename T >
fvar< T > owens_t (const fvar< T > &x1, const fvar< T > &x2)
 Return Owen's T function applied to the specified arguments. More...
 
template<typename T >
fvar< T > owens_t (double x1, const fvar< T > &x2)
 Return Owen's T function applied to the specified arguments. More...
 
template<typename T >
fvar< T > owens_t (const fvar< T > &x1, double x2)
 Return Owen's T function applied to the specified arguments. More...
 
template<typename T >
fvar< T > Phi (const fvar< T > &x)
 
template<typename T >
fvar< T > Phi_approx (const fvar< T > &x)
 Return an approximation of the unit normal cumulative distribution function (CDF). More...
 
template<typename T >
fvar< T > pow (const fvar< T > &x1, const fvar< T > &x2)
 
template<typename T >
fvar< T > pow (double x1, const fvar< T > &x2)
 
template<typename T >
fvar< T > pow (const fvar< T > &x1, double x2)
 
template<typename T >
double primitive_value (const fvar< T > &v)
 Return the primitive value of the specified forward-mode autodiff variable. More...
 
template<typename T >
fvar< T > rising_factorial (const fvar< T > &x, const fvar< T > &n)
 
template<typename T >
fvar< T > rising_factorial (const fvar< T > &x, double n)
 
template<typename T >
fvar< T > rising_factorial (double x, const fvar< T > &n)
 
template<typename T >
fvar< T > round (const fvar< T > &x)
 Return the closest integer to the specified argument, with halfway cases rounded away from zero. More...
 
template<typename T >
fvar< T > sin (const fvar< T > &x)
 
template<typename T >
fvar< T > sinh (const fvar< T > &x)
 
template<typename T >
fvar< T > sqrt (const fvar< T > &x)
 
template<typename T >
fvar< T > square (const fvar< T > &x)
 
template<typename T >
fvar< T > tan (const fvar< T > &x)
 
template<typename T >
fvar< T > tanh (const fvar< T > &x)
 
template<typename T >
fvar< T > tgamma (const fvar< T > &x)
 Return the result of applying the gamma function to the specified argument. More...
 
template<typename T >
fvar< T > to_fvar (const T &x)
 
template<typename T >
fvar< T > to_fvar (const fvar< T > &x)
 
template<typename T >
fvar< T > trigamma (const fvar< T > &u)
 Return the value of the trigamma function at the specified argument (i.e., the second derivative of the log Gamma function at the specified argument). More...
 
template<typename T >
fvar< T > trunc (const fvar< T > &x)
 Return the nearest integral value that is not larger in magnitude than the specified argument. More...
 
template<typename T >
value_of (const fvar< T > &v)
 Return the value of the specified variable. More...
 
template<typename T >
double value_of_rec (const fvar< T > &v)
 Return the value of the specified variable. More...
 
template<typename T >
bool is_aligned (T *ptr, unsigned int bytes_aligned)
 Return true if the specified pointer is aligned on the number of bytes. More...
 
template<typename T , typename F >
void derivative (const F &f, const T &x, T &fx, T &dfx_dx)
 Return the derivative of the specified univariate function at the specified argument. More...
 
template<typename F >
void finite_diff_grad_hessian (const F &f, const Eigen::Matrix< double, -1, 1 > &x, double &fx, Eigen::Matrix< double, -1, -1 > &hess, std::vector< Eigen::Matrix< double, -1, -1 > > &grad_hess_fx, double epsilon=1e-04)
 Calculate the value and the gradient of the hessian of the specified function at the specified argument using second-order autodiff and first-order finite difference. More...
 
template<typename F >
void grad_hessian (const F &f, const Eigen::Matrix< double, Eigen::Dynamic, 1 > &x, double &fx, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > &H, std::vector< Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > > &grad_H)
 Calculate the value, the Hessian, and the gradient of the Hessian of the specified function at the specified argument. More...
 
template<typename F >
void grad_tr_mat_times_hessian (const F &f, const Eigen::Matrix< double, Eigen::Dynamic, 1 > &x, const Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > &M, Eigen::Matrix< double, Eigen::Dynamic, 1 > &grad_tr_MH)
 
template<typename T1 , typename T2 , typename F >
void gradient_dot_vector (const F &f, const Eigen::Matrix< T1, Eigen::Dynamic, 1 > &x, const Eigen::Matrix< T2, Eigen::Dynamic, 1 > &v, T1 &fx, T1 &grad_fx_dot_v)
 
template<typename F >
void hessian (const F &f, const Eigen::Matrix< double, Eigen::Dynamic, 1 > &x, double &fx, Eigen::Matrix< double, Eigen::Dynamic, 1 > &grad, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > &H)
 Calculate the value, the gradient, and the Hessian, of the specified function at the specified argument in O(N^2) time and O(N^2) space. More...
 
template<typename T , typename F >
void hessian (const F &f, const Eigen::Matrix< T, Eigen::Dynamic, 1 > &x, T &fx, Eigen::Matrix< T, Eigen::Dynamic, 1 > &grad, Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &H)
 
template<typename F >
void hessian_times_vector (const F &f, const Eigen::Matrix< double, Eigen::Dynamic, 1 > &x, const Eigen::Matrix< double, Eigen::Dynamic, 1 > &v, double &fx, Eigen::Matrix< double, Eigen::Dynamic, 1 > &Hv)
 
template<typename T , typename F >
void hessian_times_vector (const F &f, const Eigen::Matrix< T, Eigen::Dynamic, 1 > &x, const Eigen::Matrix< T, Eigen::Dynamic, 1 > &v, T &fx, Eigen::Matrix< T, Eigen::Dynamic, 1 > &Hv)
 
template<typename T , typename F >
void partial_derivative (const F &f, const Eigen::Matrix< T, Eigen::Dynamic, 1 > &x, int n, T &fx, T &dfx_dxn)
 Return the partial derivative of the specified multiivariate function at the specified argument. More...
 
template<typename T_y1 , typename T_y2 >
void check_matching_sizes (const char *function, const char *name1, const T_y1 &y1, const char *name2, const T_y2 &y2)
 Check if two structures at the same size. More...
 
template<typename T_y >
void check_nonzero_size (const char *function, const char *name, const T_y &y)
 Check if the specified matrix/vector is of non-zero size. More...
 
template<typename T_y >
void check_ordered (const char *function, const char *name, const std::vector< T_y > &y)
 Check if the specified vector is sorted into strictly increasing order. More...
 
double dot (const std::vector< double > &x, const std::vector< double > &y)
 
double dot_self (const std::vector< double > &x)
 
template<typename T , typename S >
void fill (std::vector< T > &x, const S &y)
 Fill the specified container with the specified value. More...
 
template<typename Vector >
void inverse_softmax (const Vector &simplex, Vector &y)
 Writes the inverse softmax of the simplex argument into the second argument. More...
 
double log_sum_exp (const std::vector< double > &x)
 Return the log of the sum of the exponentiated values of the specified sequence of values. More...
 
template<typename T >
std::vector< T > rep_array (const T &x, int n)
 
template<typename T >
std::vector< std::vector< T > > rep_array (const T &x, int m, int n)
 
template<typename T >
std::vector< std::vector< std::vector< T > > > rep_array (const T &x, int k, int m, int n)
 
void scaled_add (std::vector< double > &x, const std::vector< double > &y, double lambda)
 
template<typename T >
std::vector< T > sort_asc (std::vector< T > xs)
 Return the specified standard vector in ascending order. More...
 
template<typename T >
std::vector< T > sort_desc (std::vector< T > xs)
 Return the specified standard vector in descending order. More...
 
void sub (std::vector< double > &x, std::vector< double > &y, std::vector< double > &result)
 
template<typename T >
sum (const std::vector< T > &xs)
 Return the sum of the values in the specified standard vector. More...
 
template<typename T >
std::vector< typename child_type< T >::type > value_of (const std::vector< T > &x)
 Convert a std::vector of type T to a std::vector of child_type<T>::type. More...
 
template<>
std::vector< double > value_of (const std::vector< double > &x)
 Return the specified argument. More...
 
template<typename T >
std::vector< double > value_of_rec (const std::vector< T > &x)
 Convert a std::vector of type T to a std::vector of doubles. More...
 
template<>
std::vector< double > value_of_rec (const std::vector< double > &x)
 Return the specified argument. More...
 
template<typename F , typename T1 , typename T2 >
std::vector< std::vector< typename stan::return_type< T1, T2 >::type > > integrate_ode_rk45 (const F &f, const std::vector< T1 > y0, double t0, const std::vector< double > &ts, const std::vector< T2 > &theta, const std::vector< double > &x, const std::vector< int > &x_int, std::ostream *msgs=0, double relative_tolerance=1e-6, double absolute_tolerance=1e-6, int max_num_steps=1E6)
 Return the solutions for the specified system of ordinary differential equations given the specified initial state, initial times, times of desired solution, and parameters and data, writing error and warning messages to the specified stream. More...
 
template<typename T_y >
void check_cholesky_factor (const char *function, const char *name, const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y)
 Check if the specified matrix is a valid Cholesky factor. More...
 
template<typename T_y >
void check_cholesky_factor_corr (const char *function, const char *name, const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y)
 Check if the specified matrix is a valid Cholesky factor of a correlation matrix. More...
 
template<typename T_y , int R, int C>
void check_column_index (const char *function, const char *name, const Eigen::Matrix< T_y, R, C > &y, size_t i)
 Check if the specified index is a valid column of the matrix. More...
 
template<typename T_y >
void check_corr_matrix (const char *function, const char *name, const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y)
 Check if the specified matrix is a valid correlation matrix. More...
 
template<typename T_y >
void check_cov_matrix (const char *function, const char *name, const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y)
 Check if the specified matrix is a valid covariance matrix. More...
 
template<typename T , int R, int C>
void check_ldlt_factor (const char *function, const char *name, LDLT_factor< T, R, C > &A)
 Check if the argument is a valid LDLT_factor. More...
 
template<typename T_y >
void check_lower_triangular (const char *function, const char *name, const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y)
 Check if the specified matrix is lower triangular. More...
 
template<typename T1 , typename T2 , int R1, int C1, int R2, int C2>
void check_matching_dims (const char *function, const char *name1, const Eigen::Matrix< T1, R1, C1 > &y1, const char *name2, const Eigen::Matrix< T2, R2, C2 > &y2)
 Check if the two matrices are of the same size. More...
 
template<typename T1 , typename T2 >
void check_multiplicable (const char *function, const char *name1, const T1 &y1, const char *name2, const T2 &y2)
 Check if the matrices can be multiplied. More...
 
template<typename T_y >
void check_ordered (const char *function, const char *name, const Eigen::Matrix< T_y, Eigen::Dynamic, 1 > &y)
 Check if the specified vector is sorted into strictly increasing order. More...
 
template<typename T_y >
void check_pos_definite (const char *function, const char *name, const Eigen::Matrix< T_y, -1, -1 > &y)
 Check if the specified square, symmetric matrix is positive definite. More...
 
template<typename Derived >
void check_pos_definite (const char *function, const char *name, const Eigen::LDLT< Derived > &cholesky)
 Check if the specified LDLT transform of a matrix is positive definite. More...
 
template<typename Derived >
void check_pos_definite (const char *function, const char *name, const Eigen::LLT< Derived > &cholesky)
 Check if the specified LLT decomposition transform resulted in Eigen::Success More...
 
template<typename T_y >
void check_pos_semidefinite (const char *function, const char *name, const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y)
 Check if the specified matrix is positive definite. More...
 
template<typename T_y >
void check_positive_ordered (const char *function, const char *name, const Eigen::Matrix< T_y, Eigen::Dynamic, 1 > &y)
 Check if the specified vector contains non-negative values and is sorted into strictly increasing order. More...
 
void check_range (const char *function, const char *name, int max, int index, int nested_level, const char *error_msg)
 Check if specified index is within range. More...
 
void check_range (const char *function, const char *name, int max, int index, const char *error_msg)
 Check if specified index is within range. More...
 
void check_range (const char *function, const char *name, int max, int index)
 Check if specified index is within range. More...
 
template<typename T_y , int R, int C>
void check_row_index (const char *function, const char *name, const Eigen::Matrix< T_y, R, C > &y, size_t i)
 Check if the specified index is a valid row of the matrix. More...
 
template<typename T_prob >
void check_simplex (const char *function, const char *name, const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &theta)
 Check if the specified vector is simplex. More...
 
template<typename T_y >
void check_spsd_matrix (const char *function, const char *name, const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y)
 Check if the specified matrix is a square, symmetric, and positive semi-definite. More...
 
template<typename T_y >
void check_square (const char *function, const char *name, const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y)
 Check if the specified matrix is square. More...
 
template<typename T >
void check_std_vector_index (const char *function, const char *name, const std::vector< T > &y, int i)
 Check if the specified index is valid in std vector. More...
 
template<typename T_y >
void check_symmetric (const char *function, const char *name, const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y)
 Check if the specified matrix is symmetric. More...
 
template<typename T_prob >
void check_unit_vector (const char *function, const char *name, const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &theta)
 Check if the specified vector is unit vector. More...
 
template<typename T , int R, int C>
void check_vector (const char *function, const char *name, const Eigen::Matrix< T, R, C > &x)
 Check if the matrix is either a row vector or column vector. More...
 
void validate_non_negative_index (const char *var_name, const char *expr, int val)
 
template<typename T >
apply_scalar_unary< acos_fun, T >::return_t acos (const T &x)
 Vectorized version of acos(). More...
 
template<typename T >
apply_scalar_unary< acosh_fun, T >::return_t acosh (const T &x)
 Return the elementwise application of acosh() to specified argument container. More...
 
template<typename T1 , typename T2 , int R, int C>
Eigen::Matrix< typename boost::math::tools::promote_args< T1, T2 >::type, R, C > add (const Eigen::Matrix< T1, R, C > &m1, const Eigen::Matrix< T2, R, C > &m2)
 Return the sum of the specified matrices. More...
 
template<typename T1 , typename T2 , int R, int C>
Eigen::Matrix< typename boost::math::tools::promote_args< T1, T2 >::type, R, C > add (const Eigen::Matrix< T1, R, C > &m, const T2 &c)
 Return the sum of the specified matrix and specified scalar. More...
 
template<typename T1 , typename T2 , int R, int C>
Eigen::Matrix< typename boost::math::tools::promote_args< T1, T2 >::type, R, C > add (const T1 &c, const Eigen::Matrix< T2, R, C > &m)
 Return the sum of the specified scalar and specified matrix. More...
 
template<typename T1 , typename T2 , int R1, int C1, int R2, int C2>
Eigen::Matrix< typename return_type< T1, T2 >::type, Eigen::Dynamic, Eigen::Dynamic > append_col (const Eigen::Matrix< T1, R1, C1 > &A, const Eigen::Matrix< T2, R2, C2 > &B)
 Return the result of appending the second argument matrix after the first argument matrix, that is, putting them side by side, with the first matrix followed by the second matrix. More...
 
template<typename T1 , typename T2 , int C1, int C2>
Eigen::Matrix< typename return_type< T1, T2 >::type, 1, Eigen::Dynamic > append_col (const Eigen::Matrix< T1, 1, C1 > &A, const Eigen::Matrix< T2, 1, C2 > &B)
 Return the result of concatenaing the first row vector followed by the second row vector side by side, with the result being a row vector. More...
 
template<typename T , int R1, int C1, int R2, int C2>
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > append_col (const Eigen::Matrix< T, R1, C1 > &A, const Eigen::Matrix< T, R2, C2 > &B)
 Return the result of appending the second argument matrix after the first argument matrix, that is, putting them side by side, with the first matrix followed by the second matrix. More...
 
template<typename T , int C1, int C2>
Eigen::Matrix< T, 1, Eigen::Dynamic > append_col (const Eigen::Matrix< T, 1, C1 > &A, const Eigen::Matrix< T, 1, C2 > &B)
 Return the result of concatenaing the first row vector followed by the second row vector side by side, with the result being a row vector. More...
 
template<typename T1 , typename T2 , int R, int C>
Eigen::Matrix< typename return_type< T1, T2 >::type, 1, Eigen::Dynamic > append_col (const T1 &A, const Eigen::Matrix< T2, R, C > &B)
 Return the result of stacking an scalar on top of the a row vector, with the result being a row vector. More...
 
template<typename T1 , typename T2 , int R, int C>
Eigen::Matrix< typename return_type< T1, T2 >::type, 1, Eigen::Dynamic > append_col (const Eigen::Matrix< T1, R, C > &A, const T2 &B)
 Return the result of stacking a row vector on top of the an scalar, with the result being a row vector. More...
 
template<typename T1 , typename T2 , int R1, int C1, int R2, int C2>
Eigen::Matrix< typename return_type< T1, T2 >::type, Eigen::Dynamic, Eigen::Dynamic > append_row (const Eigen::Matrix< T1, R1, C1 > &A, const Eigen::Matrix< T2, R2, C2 > &B)
 Return the result of stacking the rows of the first argument matrix on top of the second argument matrix. More...
 
template<typename T1 , typename T2 , int R1, int R2>
Eigen::Matrix< typename return_type< T1, T2 >::type, Eigen::Dynamic, 1 > append_row (const Eigen::Matrix< T1, R1, 1 > &A, const Eigen::Matrix< T2, R2, 1 > &B)
 Return the result of stacking the first vector on top of the second vector, with the result being a vector. More...
 
template<typename T , int R1, int C1, int R2, int C2>
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > append_row (const Eigen::Matrix< T, R1, C1 > &A, const Eigen::Matrix< T, R2, C2 > &B)
 Return the result of stacking the rows of the first argument matrix on top of the second argument matrix. More...
 
template<typename T , int R1, int R2>
Eigen::Matrix< T, Eigen::Dynamic, 1 > append_row (const Eigen::Matrix< T, R1, 1 > &A, const Eigen::Matrix< T, R2, 1 > &B)
 Return the result of stacking the first vector on top of the second vector, with the result being a vector. More...
 
template<typename T1 , typename T2 , int R, int C>
Eigen::Matrix< typename return_type< T1, T2 >::type, Eigen::Dynamic, 1 > append_row (const T1 &A, const Eigen::Matrix< T2, R, C > &B)
 Return the result of stacking an scalar on top of the a vector, with the result being a vector. More...
 
template<typename T1 , typename T2 , int R, int C>
Eigen::Matrix< typename return_type< T1, T2 >::type, Eigen::Dynamic, 1 > append_row (const Eigen::Matrix< T1, R, C > &A, const T2 &B)
 Return the result of stacking a vector on top of the an scalar, with the result being a vector. More...
 
template<typename T >
apply_scalar_unary< asin_fun, T >::return_t asin (const T &x)
 Vectorized version of asin(). More...
 
template<typename T >
apply_scalar_unary< asinh_fun, T >::return_t asinh (const T &x)
 Vectorized version of asinh(). More...
 
void print_mat_size (int n, std::ostream &o)
 Helper function to return the matrix size as either "dynamic" or "1". More...
 
template<typename LHS , typename RHS >
void assign (LHS &lhs, const RHS &rhs)
 Copy the right-hand side's value to the left-hand side variable. More...
 
template<typename LHS , typename RHS , int R1, int C1, int R2, int C2>
void assign (Eigen::Matrix< LHS, R1, C1 > &x, const Eigen::Matrix< RHS, R2, C2 > &y)
 Copy the right-hand side's value to the left-hand side variable. More...
 
template<typename LHS , typename RHS , int R, int C>
void assign (Eigen::Matrix< LHS, R, C > &x, const Eigen::Matrix< RHS, R, C > &y)
 Copy the right-hand side's value to the left-hand side variable. More...
 
template<typename LHS , typename RHS , int R, int C>
void assign (Eigen::Block< LHS > x, const Eigen::Matrix< RHS, R, C > &y)
 Copy the right-hand side's value to the left-hand side variable. More...
 
template<typename LHS , typename RHS >
void assign (std::vector< LHS > &x, const std::vector< RHS > &y)
 Copy the right-hand side's value to the left-hand side variable. More...
 
template<typename T >
apply_scalar_unary< atan_fun, T >::return_t atan (const T &x)
 Vectorized version of asinh(). More...
 
template<typename T >
apply_scalar_unary< atanh_fun, T >::return_t atanh (const T &x)
 Return the elementwise application of atanh() to specified argument container. More...
 
template<typename T >
void autocorrelation (const std::vector< T > &y, std::vector< T > &ac, Eigen::FFT< T > &fft)
 Write autocorrelation estimates for every lag for the specified input sequence into the specified result using the specified FFT engine. More...
 
template<typename T >
void autocorrelation (const std::vector< T > &y, std::vector< T > &ac)
 Write autocorrelation estimates for every lag for the specified input sequence into the specified result. More...
 
template<typename T >
void autocovariance (const std::vector< T > &y, std::vector< T > &acov, Eigen::FFT< T > &fft)
 Write autocovariance estimates for every lag for the specified input sequence into the specified result using the specified FFT engine. More...
 
template<typename T >
void autocovariance (const std::vector< T > &y, std::vector< T > &acov)
 Write autocovariance estimates for every lag for the specified input sequence into the specified result. More...
 
template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > block (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &m, size_t i, size_t j, size_t nrows, size_t ncols)
 Return a nrows x ncols submatrix starting at (i-1, j-1). More...
 
template<typename T >
apply_scalar_unary< cbrt_fun, T >::return_t cbrt (const T &x)
 Vectorized version of cbrt(). More...
 
template<typename T >
apply_scalar_unary< ceil_fun, T >::return_t ceil (const T &x)
 Vectorized version of ceil(). More...
 
template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > cholesky_corr_constrain (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &y, int K)
 
template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > cholesky_corr_constrain (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &y, int K, T &lp)
 
template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, 1 > cholesky_corr_free (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &x)
 
template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > cholesky_decompose (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &m)
 Return the lower-triangular Cholesky factor (i.e., matrix square root) of the specified square, symmetric matrix. More...
 
template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > cholesky_factor_constrain (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &x, int M, int N)
 Return the Cholesky factor of the specified size read from the specified vector. More...
 
template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > cholesky_factor_constrain (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &x, int M, int N, T &lp)
 Return the Cholesky factor of the specified size read from the specified vector and increment the specified log probability reference with the log Jacobian adjustment of the transform. More...
 
template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, 1 > cholesky_factor_free (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &y)
 Return the unconstrained vector of parameters correspdonding to the specified Cholesky factor. More...
 
template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, 1 > col (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &m, size_t j)
 Return the specified column of the specified matrix using start-at-1 indexing. More...
 
template<typename T , int R, int C>
int cols (const Eigen::Matrix< T, R, C > &m)
 Return the number of columns in the specified matrix, vector, or row vector. More...
 
template<int R1, int C1, int R2, int C2>
Eigen::Matrix< double, 1, C1 > columns_dot_product (const Eigen::Matrix< double, R1, C1 > &v1, const Eigen::Matrix< double, R2, C2 > &v2)
 Returns the dot product of the specified vectors. More...
 
template<typename T , int R, int C>
Eigen::Matrix< T, 1, C > columns_dot_self (const Eigen::Matrix< T, R, C > &x)
 Returns the dot product of each column of a matrix with itself. More...
 
template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > corr_matrix_constrain (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &x, typename math::index_type< Eigen::Matrix< T, Eigen::Dynamic, 1 > >::type k)
 Return the correlation matrix of the specified dimensionality derived from the specified vector of unconstrained values. More...
 
template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > corr_matrix_constrain (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &x, typename math::index_type< Eigen::Matrix< T, Eigen::Dynamic, 1 > >::type k, T &lp)
 Return the correlation matrix of the specified dimensionality derived from the specified vector of unconstrained values. More...
 
template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, 1 > corr_matrix_free (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &y)
 Return the vector of unconstrained partial correlations that define the specified correlation matrix when transformed. More...
 
template<typename T >
apply_scalar_unary< cos_fun, T >::return_t cos (const T &x)
 Vectorized version of cos(). More...
 
template<typename T >
apply_scalar_unary< cosh_fun, T >::return_t cosh (const T &x)
 Vectorized version of cosh(). More...
 
template<typename T_x , typename T_sigma , typename T_l >
Eigen::Matrix< typename stan::return_type< T_x, T_sigma, T_l >::type, Eigen::Dynamic, Eigen::Dynamic > cov_exp_quad (const std::vector< T_x > &x, const T_sigma &sigma, const T_l &l)
 Returns a squared exponential kernel. More...
 
template<typename T_x1 , typename T_x2 , typename T_sigma , typename T_l >
Eigen::Matrix< typename stan::return_type< T_x1, T_x2, T_sigma, T_l >::type, Eigen::Dynamic, Eigen::Dynamic > cov_exp_quad (const std::vector< T_x1 > &x1, const std::vector< T_x2 > &x2, const T_sigma &sigma, const T_l &l)
 Returns a squared exponential kernel. More...
 
template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > cov_matrix_constrain (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &x, typename math::index_type< Eigen::Matrix< T, Eigen::Dynamic, 1 > >::type K)
 Return the symmetric, positive-definite matrix of dimensions K by K resulting from transforming the specified finite vector of size K plus (K choose 2). More...
 
template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > cov_matrix_constrain (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &x, typename math::index_type< Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > >::type K, T &lp)
 Return the symmetric, positive-definite matrix of dimensions K by K resulting from transforming the specified finite vector of size K plus (K choose 2). More...
 
template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > cov_matrix_constrain_lkj (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &x, size_t k)
 Return the covariance matrix of the specified dimensionality derived from constraining the specified vector of unconstrained values. More...
 
template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > cov_matrix_constrain_lkj (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &x, size_t k, T &lp)
 Return the covariance matrix of the specified dimensionality derived from constraining the specified vector of unconstrained values and increment the specified log probability reference with the log absolute Jacobian determinant. More...
 
template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, 1 > cov_matrix_free (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &y)
 The covariance matrix derived from the symmetric view of the lower-triangular view of the K by K specified matrix is freed to return a vector of size K + (K choose 2). More...
 
template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, 1 > cov_matrix_free_lkj (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &y)
 Return the vector of unconstrained partial correlations and deviations that transform to the specified covariance matrix. More...
 
matrix_d crossprod (const matrix_d &M)
 Returns the result of pre-multiplying a matrix by its own transpose. More...
 
template<typename T >
const std::vector< int > csr_extract_u (const Eigen::SparseMatrix< T, Eigen::RowMajor > &A)
 Extract the NZE index for each entry from a sparse matrix. More...
 
template<typename T , int R, int C>
const std::vector< int > csr_extract_u (const Eigen::Matrix< T, R, C > &A)
 Extract the NZE index for each entry from a sparse matrix. More...
 
template<typename T >
const std::vector< int > csr_extract_v (const Eigen::SparseMatrix< T, Eigen::RowMajor > &A)
 Extract the column indexes for non-zero value from a sparse matrix. More...
 
template<typename T , int R, int C>
const std::vector< int > csr_extract_v (const Eigen::Matrix< T, R, C > &A)
 Extract the column indexes for non-zero values from a dense matrix by converting to sparse and calling the sparse matrix extractor. More...
 
template<typename T >
const Eigen::Matrix< T, Eigen::Dynamic, 1 > csr_extract_w (const Eigen::SparseMatrix< T, Eigen::RowMajor > &A)
 
template<typename T , int R, int C>
const Eigen::Matrix< T, Eigen::Dynamic, 1 > csr_extract_w (const Eigen::Matrix< T, R, C > &A)
 
template<typename T1 , typename T2 >
Eigen::Matrix< typename boost::math::tools::promote_args< T1, T2 >::type, Eigen::Dynamic, 1 > csr_matrix_times_vector (int m, int n, const Eigen::Matrix< T1, Eigen::Dynamic, 1 > &w, const std::vector< int > &v, const std::vector< int > &u, const Eigen::Matrix< T2, Eigen::Dynamic, 1 > &b)
 
template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > csr_to_dense_matrix (int m, int n, const Eigen::Matrix< T, Eigen::Dynamic, 1 > &w, const std::vector< int > &v, const std::vector< int > &u)
 Construct a dense Eigen matrix from the CSR format components. More...
 
int csr_u_to_z (const std::vector< int > &u, int i)
 Return the z vector computed from the specified u vector at the index for the z vector. More...
 
template<typename T >
std::vector< T > cumulative_sum (const std::vector< T > &x)
 Return the cumulative sum of the specified vector. More...
 
template<typename T , int R, int C>
Eigen::Matrix< T, R, C > cumulative_sum (const Eigen::Matrix< T, R, C > &m)
 Return the cumulative sum of the specified matrix. More...
 
template<typename T , int R, int C>
determinant (const Eigen::Matrix< T, R, C > &m)
 Returns the determinant of the specified square matrix. More...
 
template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > diag_matrix (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &v)
 Return a square diagonal matrix with the specified vector of coefficients as the diagonal values. More...
 
template<typename T1 , typename T2 , int R1, int C1, int R2, int C2>
Eigen::Matrix< typename boost::math::tools::promote_args< T1, T2 >::type, R1, C1 > diag_post_multiply (const Eigen::Matrix< T1, R1, C1 > &m1, const Eigen::Matrix< T2, R2, C2 > &m2)
 
template<typename T1 , typename T2 , int R1, int C1, int R2, int C2>
Eigen::Matrix< typename boost::math::tools::promote_args< T1, T2 >::type, R2, C2 > diag_pre_multiply (const Eigen::Matrix< T1, R1, C1 > &m1, const Eigen::Matrix< T2, R2, C2 > &m2)
 
template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, 1 > diagonal (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &m)
 Return a column vector of the diagonal elements of the specified matrix. More...
 
template<typename T >
apply_scalar_unary< digamma_fun, T >::return_t digamma (const T &x)
 Vectorized version of digamma(). More...
 
template<typename T >
void dims (const T &x, std::vector< int > &result)
 
template<typename T , int R, int C>
void dims (const Eigen::Matrix< T, R, C > &x, std::vector< int > &result)
 
template<typename T >
void dims (const std::vector< T > &x, std::vector< int > &result)
 
template<typename T >
std::vector< int > dims (const T &x)
 
template<typename T1 , int R1, int C1, typename T2 , int R2, int C2>
boost::math::tools::promote_args< T1, T2 >::type distance (const Eigen::Matrix< T1, R1, C1 > &v1, const Eigen::Matrix< T2, R2, C2 > &v2)
 Returns the distance between the specified vectors. More...
 
template<int R, int C, typename T >
boost::enable_if_c< boost::is_arithmetic< T >::value, Eigen::Matrix< double, R, C > >::type divide (const Eigen::Matrix< double, R, C > &m, T c)
 Return specified matrix divided by specified scalar. More...
 
template<int R1, int C1, int R2, int C2>
double dot_product (const Eigen::Matrix< double, R1, C1 > &v1, const Eigen::Matrix< double, R2, C2 > &v2)
 Returns the dot product of the specified vectors. More...
 
double dot_product (const double *v1, const double *v2, size_t length)
 Returns the dot product of the specified arrays of doubles. More...
 
double dot_product (const std::vector< double > &v1, const std::vector< double > &v2)
 Returns the dot product of the specified arrays of doubles. More...
 
template<int R, int C>
double dot_self (const Eigen::Matrix< double, R, C > &v)
 Returns the dot product of the specified vector with itself. More...
 
template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, 1 > eigenvalues_sym (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &m)
 Return the eigenvalues of the specified symmetric matrix in descending order of magnitude. More...
 
template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > eigenvectors_sym (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &m)
 
template<typename T1 , typename T2 , int R, int C>
Eigen::Matrix< typename boost::math::tools::promote_args< T1, T2 >::type, R, C > elt_divide (const Eigen::Matrix< T1, R, C > &m1, const Eigen::Matrix< T2, R, C > &m2)
 Return the elementwise division of the specified matrices. More...
 
template<typename T1 , typename T2 , int R, int C>
Eigen::Matrix< typename boost::math::tools::promote_args< T1, T2 >::type, R, C > elt_divide (const Eigen::Matrix< T1, R, C > &m, T2 s)
 Return the elementwise division of the specified matrix by the specified scalar. More...
 
template<typename T1 , typename T2 , int R, int C>
Eigen::Matrix< typename boost::math::tools::promote_args< T1, T2 >::type, R, C > elt_divide (T1 s, const Eigen::Matrix< T2, R, C > &m)
 Return the elementwise division of the specified scalar by the specified matrix. More...
 
template<typename T1 , typename T2 , int R, int C>
Eigen::Matrix< typename boost::math::tools::promote_args< T1, T2 >::type, R, C > elt_multiply (const Eigen::Matrix< T1, R, C > &m1, const Eigen::Matrix< T2, R, C > &m2)
 Return the elementwise multiplication of the specified matrices. More...
 
template<typename T >
apply_scalar_unary< erf_fun, T >::return_t erf (const T &x)
 Vectorized version of erf(). More...
 
template<typename T >
apply_scalar_unary< erfc_fun, T >::return_t erfc (const T &x)
 Vectorized version of erfc(). More...
 
template<typename T >
apply_scalar_unary< exp_fun, T >::return_t exp (const T &x)
 Return the elementwise exponentiation of the specified argument, which may be a scalar or any Stan container of numeric scalars. More...
 
template<typename T >
apply_scalar_unary< exp2_fun, T >::return_t exp2 (const T &x)
 Return the elementwise application of exp2() to specified argument container. More...
 
template<typename T >
apply_scalar_unary< expm1_fun, T >::return_t expm1 (const T &x)
 Vectorized version of expm1(). More...
 
template<typename T >
apply_scalar_unary< fabs_fun, T >::return_t fabs (const T &x)
 Vectorized version of fabs(). More...
 
template<typename T >
bool factor_cov_matrix (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &Sigma, Eigen::Array< T, Eigen::Dynamic, 1 > &CPCs, Eigen::Array< T, Eigen::Dynamic, 1 > &sds)
 This function is intended to make starting values, given a covariance matrix Sigma. More...
 
template<typename T >
void factor_U (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &U, Eigen::Array< T, Eigen::Dynamic, 1 > &CPCs)
 This function is intended to make starting values, given a unit upper-triangular matrix U such that U'DU is a correlation matrix. More...
 
template<typename T , int R, int C, typename S >
void fill (Eigen::Matrix< T, R, C > &x, const S &y)
 Fill the specified container with the specified value. More...
 
template<typename T >
apply_scalar_unary< floor_fun, T >::return_t floor (const T &x)
 Vectorized version of floor(). More...
 
template<typename T >
const T & get_base1 (const std::vector< T > &x, size_t i, const char *error_msg, size_t idx)
 Return a reference to the value of the specified vector at the specified base-one index. More...
 
template<typename T >
const T & get_base1 (const std::vector< std::vector< T > > &x, size_t i1, size_t i2, const char *error_msg, size_t idx)
 Return a reference to the value of the specified vector at the specified base-one indexes. More...
 
template<typename T >
const T & get_base1 (const std::vector< std::vector< std::vector< T > > > &x, size_t i1, size_t i2, size_t i3, const char *error_msg, size_t idx)
 Return a reference to the value of the specified vector at the specified base-one indexes. More...
 
template<typename T >
const T & get_base1 (const std::vector< std::vector< std::vector< std::vector< T > > > > &x, size_t i1, size_t i2, size_t i3, size_t i4, const char *error_msg, size_t idx)
 Return a reference to the value of the specified vector at the specified base-one indexes. More...
 
template<typename T >
const T & get_base1 (const std::vector< std::vector< std::vector< std::vector< std::vector< T > > > > > &x, size_t i1, size_t i2, size_t i3, size_t i4, size_t i5, const char *error_msg, size_t idx)
 Return a reference to the value of the specified vector at the specified base-one indexes. More...
 
template<typename T >
const T & get_base1 (const std::vector< std::vector< std::vector< std::vector< std::vector< std::vector< T > > > > > > &x, size_t i1, size_t i2, size_t i3, size_t i4, size_t i5, size_t i6, const char *error_msg, size_t idx)
 Return a reference to the value of the specified vector at the specified base-one indexes. More...
 
template<typename T >
const T & get_base1 (const std::vector< std::vector< std::vector< std::vector< std::vector< std::vector< std::vector< T > > > > > > > &x, size_t i1, size_t i2, size_t i3, size_t i4, size_t i5, size_t i6, size_t i7, const char *error_msg, size_t idx)
 Return a reference to the value of the specified vector at the specified base-one indexes. More...
 
template<typename T >
const T & get_base1 (const std::vector< std::vector< std::vector< std::vector< std::vector< std::vector< std::vector< std::vector< T > > > > > > > > &x, size_t i1, size_t i2, size_t i3, size_t i4, size_t i5, size_t i6, size_t i7, size_t i8, const char *error_msg, size_t idx)
 Return a reference to the value of the specified vector at the specified base-one indexes. More...
 
template<typename T >
Eigen::Matrix< T, 1, Eigen::Dynamic > get_base1 (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &x, size_t m, const char *error_msg, size_t idx)
 Return a copy of the row of the specified vector at the specified base-one row index. More...
 
template<typename T >
const T & get_base1 (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &x, size_t m, size_t n, const char *error_msg, size_t idx)
 Return a reference to the value of the specified matrix at the specified base-one row and column indexes. More...
 
template<typename T >
const T & get_base1 (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &x, size_t m, const char *error_msg, size_t idx)
 Return a reference to the value of the specified column vector at the specified base-one index. More...
 
template<typename T >
const T & get_base1 (const Eigen::Matrix< T, 1, Eigen::Dynamic > &x, size_t n, const char *error_msg, size_t idx)
 Return a reference to the value of the specified row vector at the specified base-one index. More...
 
template<typename T >
T & get_base1_lhs (std::vector< T > &x, size_t i, const char *error_msg, size_t idx)
 Return a reference to the value of the specified vector at the specified base-one index. More...
 
template<typename T >
T & get_base1_lhs (std::vector< std::vector< T > > &x, size_t i1, size_t i2, const char *error_msg, size_t idx)
 Return a reference to the value of the specified vector at the specified base-one indexes. More...
 
template<typename T >
T & get_base1_lhs (std::vector< std::vector< std::vector< T > > > &x, size_t i1, size_t i2, size_t i3, const char *error_msg, size_t idx)
 Return a reference to the value of the specified vector at the specified base-one indexes. More...
 
template<typename T >
T & get_base1_lhs (std::vector< std::vector< std::vector< std::vector< T > > > > &x, size_t i1, size_t i2, size_t i3, size_t i4, const char *error_msg, size_t idx)
 Return a reference to the value of the specified vector at the specified base-one indexes. More...
 
template<typename T >
T & get_base1_lhs (std::vector< std::vector< std::vector< std::vector< std::vector< T > > > > > &x, size_t i1, size_t i2, size_t i3, size_t i4, size_t i5, const char *error_msg, size_t idx)
 Return a reference to the value of the specified vector at the specified base-one indexes. More...
 
template<typename T >
T & get_base1_lhs (std::vector< std::vector< std::vector< std::vector< std::vector< std::vector< T > > > > > > &x, size_t i1, size_t i2, size_t i3, size_t i4, size_t i5, size_t i6, const char *error_msg, size_t idx)
 Return a reference to the value of the specified vector at the specified base-one indexes. More...
 
template<typename T >
T & get_base1_lhs (std::vector< std::vector< std::vector< std::vector< std::vector< std::vector< std::vector< T > > > > > > > &x, size_t i1, size_t i2, size_t i3, size_t i4, size_t i5, size_t i6, size_t i7, const char *error_msg, size_t idx)
 Return a reference to the value of the specified vector at the specified base-one indexes. More...
 
template<typename T >
T & get_base1_lhs (std::vector< std::vector< std::vector< std::vector< std::vector< std::vector< std::vector< std::vector< T > > > > > > > > &x, size_t i1, size_t i2, size_t i3, size_t i4, size_t i5, size_t i6, size_t i7, size_t i8, const char *error_msg, size_t idx)
 Return a reference to the value of the specified vector at the specified base-one indexes. More...
 
template<typename T >
Eigen::Block< Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > > get_base1_lhs (Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &x, size_t m, const char *error_msg, size_t idx)
 Return a copy of the row of the specified vector at the specified base-one row index. More...
 
template<typename T >
T & get_base1_lhs (Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &x, size_t m, size_t n, const char *error_msg, size_t idx)
 Return a reference to the value of the specified matrix at the specified base-one row and column indexes. More...
 
template<typename T >
T & get_base1_lhs (Eigen::Matrix< T, Eigen::Dynamic, 1 > &x, size_t m, const char *error_msg, size_t idx)
 Return a reference to the value of the specified column vector at the specified base-one index. More...
 
template<typename T >
T & get_base1_lhs (Eigen::Matrix< T, 1, Eigen::Dynamic > &x, size_t n, const char *error_msg, size_t idx)
 Return a reference to the value of the specified row vector at the specified base-one index. More...
 
template<typename T_lp , typename T_lp_accum >
boost::math::tools::promote_args< T_lp, T_lp_accum >::type get_lp (const T_lp &lp, const accumulator< T_lp_accum > &lp_accum)
 
template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, 1 > head (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &v, size_t n)
 Return the specified number of elements as a vector from the front of the specified vector. More...
 
template<typename T >
Eigen::Matrix< T, 1, Eigen::Dynamic > head (const Eigen::Matrix< T, 1, Eigen::Dynamic > &rv, size_t n)
 Return the specified number of elements as a row vector from the front of the specified row vector. More...
 
template<typename T >
std::vector< T > head (const std::vector< T > &sv, size_t n)
 Return the specified number of elements as a standard vector from the front of the specified standard vector. More...
 
template<typename T >
void initialize (T &x, const T &v)
 
template<typename T , typename V >
boost::enable_if_c< boost::is_arithmetic< V >::value, void >::type initialize (T &x, V v)
 
template<typename T , int R, int C, typename V >
void initialize (Eigen::Matrix< T, R, C > &x, const V &v)
 
template<typename T , typename V >
void initialize (std::vector< T > &x, const V &v)
 
template<typename T >
apply_scalar_unary< inv_fun, T >::return_t inv (const T &x)
 Vectorized version of inv(). More...
 
template<typename T >
apply_scalar_unary< inv_cloglog_fun, T >::return_t inv_cloglog (const T &x)
 Vectorized version of inv_cloglog(). More...
 
template<typename T >
apply_scalar_unary< inv_logit_fun, T >::return_t inv_logit (const T &x)
 Vectorized version of inv_logit(). More...
 
template<typename T >
apply_scalar_unary< inv_Phi_fun, T >::return_t inv_Phi (const T &x)
 Vectorized version of inv_Phi(). More...
 
template<typename T >
apply_scalar_unary< inv_sqrt_fun, T >::return_t inv_sqrt (const T &x)
 Vectorized version of inv_sqrt(). More...
 
template<typename T >
apply_scalar_unary< inv_square_fun, T >::return_t inv_square (const T &x)
 Vectorized version of inv_square(). More...
 
template<typename T , int R, int C>
Eigen::Matrix< T, R, C > inverse (const Eigen::Matrix< T, R, C > &m)
 Returns the inverse of the specified matrix. More...
 
template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > inverse_spd (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &m)
 Returns the inverse of the specified symmetric, pos/neg-definite matrix. More...
 
template<typename T >
apply_scalar_unary< lgamma_fun, T >::return_t lgamma (const T &x)
 Vectorized version of lgamma(). More...
 
template<typename T >
apply_scalar_unary< log_fun, T >::return_t log (const T &x)
 Return the elementwise natural log of the specified argument, which may be a scalar or any Stan container of numeric scalars. More...
 
template<typename T >
apply_scalar_unary< log10_fun, T >::return_t log10 (const T &x)
 Vectorized version of log10(). More...
 
template<typename T >
apply_scalar_unary< log1m_fun, T >::return_t log1m (const T &x)
 Vectorized version of log1m(). More...
 
template<typename T >
apply_scalar_unary< log1m_exp_fun, T >::return_t log1m_exp (const T &x)
 Vectorized version of log1m_exp(). More...
 
template<typename T >
apply_scalar_unary< log1m_inv_logit_fun, T >::return_t log1m_inv_logit (const T &x)
 Return the elementwise application of log1m_inv_logit() to specified argument container. More...
 
template<typename T >
apply_scalar_unary< log1p_fun, T >::return_t log1p (const T &x)
 Return the elementwise application of log1p() to specified argument container. More...
 
template<typename T >
apply_scalar_unary< log1p_exp_fun, T >::return_t log1p_exp (const T &x)
 Vectorized version of log1m_exp(). More...
 
template<typename T >
apply_scalar_unary< log2_fun, T >::return_t log2 (const T &x)
 Return the elementwise application of log2() to specified argument container. More...
 
template<typename T , int R, int C>
log_determinant (const Eigen::Matrix< T, R, C > &m)
 Returns the log absolute determinant of the specified square matrix. More...
 
template<int R, int C, typename T >
log_determinant_ldlt (LDLT_factor< T, R, C > &A)
 
template<typename T , int R, int C>
log_determinant_spd (const Eigen::Matrix< T, R, C > &m)
 Returns the log absolute determinant of the specified square matrix. More...
 
template<typename T >
apply_scalar_unary< log_inv_logit_fun, T >::return_t log_inv_logit (const T &x)
 Return the elementwise application of log_inv_logit() to specified argument container. More...
 
template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, 1 > log_softmax (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &v)
 Return the natural logarithm of the softmax of the specified vector. More...
 
template<int R, int C>
double log_sum_exp (const Eigen::Matrix< double, R, C > &x)
 Return the log of the sum of the exponentiated values of the specified matrix of values. More...
 
template<typename T >
apply_scalar_unary< logit_fun, T >::return_t logit (const T &x)
 Return the elementwise application of logit() to specified argument container. More...
 
template<typename T >
const Eigen::Array< T, Eigen::Dynamic, 1 > make_nu (const T eta, size_t K)
 This function calculates the degrees of freedom for the t distribution that corresponds to the shape parameter in the Lewandowski et. More...
 
template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > matrix_exp (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > A)
 Return the matrix exponential of the input matrix. More...
 
template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > matrix_exp_2x2 (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &A)
 Return the matrix exponential of a 2x2 matrix. More...
 
template<typename MatrixType >
MatrixType matrix_exp_pade (const MatrixType &arg)
 Computes the matrix exponential, using a Pade approximation, coupled with scaling and squaring. More...
 
int max (const std::vector< int > &x)
 Returns the maximum coefficient in the specified column vector. More...
 
template<typename T >
max (const std::vector< T > &x)
 Returns the maximum coefficient in the specified column vector. More...
 
template<typename T , int R, int C>
max (const Eigen::Matrix< T, R, C > &m)
 Returns the maximum coefficient in the specified vector, row vector, or matrix. More...
 
template<typename T1 , typename T2 , int R1, int C1, int R2, int C2>
Eigen::Matrix< typename boost::math::tools::promote_args< T1, T2 >::type, R1, C2 > mdivide_left (const Eigen::Matrix< T1, R1, C1 > &A, const Eigen::Matrix< T2, R2, C2 > &b)
 Returns the solution of the system Ax=b. More...
 
template<int R1, int C1, int R2, int C2, typename T1 , typename T2 >
Eigen::Matrix< typename boost::math::tools::promote_args< T1, T2 >::type, R1, C2 > mdivide_left_ldlt (const LDLT_factor< T1, R1, C1 > &A, const Eigen::Matrix< T2, R2, C2 > &b)
 Returns the solution of the system Ax=b given an LDLT_factor of A. More...
 
template<typename T1 , typename T2 , int R1, int C1, int R2, int C2>
Eigen::Matrix< typename boost::math::tools::promote_args< T1, T2 >::type, R1, C2 > mdivide_left_spd (const Eigen::Matrix< T1, R1, C1 > &A, const Eigen::Matrix< T2, R2, C2 > &b)
 Returns the solution of the system Ax=b where A is symmetric positive definite. More...
 
template<int TriView, typename T1 , typename T2 , int R1, int C1, int R2, int C2>
Eigen::Matrix< typename boost::math::tools::promote_args< T1, T2 >::type, R1, C2 > mdivide_left_tri (const Eigen::Matrix< T1, R1, C1 > &A, const Eigen::Matrix< T2, R2, C2 > &b)
 Returns the solution of the system Ax=b when A is triangular. More...
 
template<int TriView, typename T , int R1, int C1>
Eigen::Matrix< T, R1, C1 > mdivide_left_tri (const Eigen::Matrix< T, R1, C1 > &A)
 Returns the solution of the system Ax=b when A is triangular and b=I. More...
 
template<typename T1 , typename T2 , int R1, int C1, int R2, int C2>
Eigen::Matrix< typename boost::math::tools::promote_args< T1, T2 >::type, R1, C2 > mdivide_left_tri_low (const Eigen::Matrix< T1, R1, C1 > &A, const Eigen::Matrix< T2, R2, C2 > &b)
 
template<typename T , int R1, int C1>
Eigen::Matrix< T, R1, C1 > mdivide_left_tri_low (const Eigen::Matrix< T, R1, C1 > &A)
 
template<typename T1 , typename T2 , int R1, int C1, int R2, int C2>
Eigen::Matrix< typename boost::math::tools::promote_args< T1, T2 >::type, R1, C2 > mdivide_right (const Eigen::Matrix< T1, R1, C1 > &b, const Eigen::Matrix< T2, R2, C2 > &A)
 Returns the solution of the system Ax=b. More...
 
template<typename T1 , typename T2 , int R1, int C1, int R2, int C2>
Eigen::Matrix< typename boost::math::tools::promote_args< T1, T2 >::type, R1, C2 > mdivide_right_ldlt (const Eigen::Matrix< T1, R1, C1 > &b, const LDLT_factor< T2, R2, C2 > &A)
 Returns the solution of the system xA=b given an LDLT_factor of A. More...
 
template<int R1, int C1, int R2, int C2>
Eigen::Matrix< double, R1, C2 > mdivide_right_ldlt (const Eigen::Matrix< double, R1, C1 > &b, const LDLT_factor< double, R2, C2 > &A)
 
template<typename T1 , typename T2 , int R1, int C1, int R2, int C2>
Eigen::Matrix< typename boost::math::tools::promote_args< T1, T2 >::type, R1, C2 > mdivide_right_spd (const Eigen::Matrix< T1, R1, C1 > &b, const Eigen::Matrix< T2, R2, C2 > &A)
 Returns the solution of the system Ax=b where A is symmetric positive definite. More...
 
template<int TriView, typename T1 , typename T2 , int R1, int C1, int R2, int C2>
Eigen::Matrix< typename boost::math::tools::promote_args< T1, T2 >::type, R1, C2 > mdivide_right_tri (const Eigen::Matrix< T1, R1, C1 > &b, const Eigen::Matrix< T2, R2, C2 > &A)
 Returns the solution of the system Ax=b when A is triangular. More...
 
template<typename T1 , typename T2 , int R1, int C1, int R2, int C2>
Eigen::Matrix< typename boost::math::tools::promote_args< T1, T2 >::type, R1, C2 > mdivide_right_tri_low (const Eigen::Matrix< T1, R1, C1 > &b, const Eigen::Matrix< T2, R2, C2 > &A)
 Returns the solution of the system tri(A)x=b when tri(A) is a lower triangular view of the matrix A. More...
 
template<typename T >
boost::math::tools::promote_args< T >::type mean (const std::vector< T > &v)
 Returns the sample mean (i.e., average) of the coefficients in the specified standard vector. More...
 
template<typename T , int R, int C>
boost::math::tools::promote_args< T >::type mean (const Eigen::Matrix< T, R, C > &m)
 Returns the sample mean (i.e., average) of the coefficients in the specified vector, row vector, or matrix. More...
 
int min (const std::vector< int > &x)
 Returns the minimum coefficient in the specified column vector. More...
 
template<typename T >
min (const std::vector< T > &x)
 Returns the minimum coefficient in the specified column vector. More...
 
template<typename T , int R, int C>
min (const Eigen::Matrix< T, R, C > &m)
 Returns the minimum coefficient in the specified matrix, vector, or row vector. More...
 
template<typename T >
minus (const T &x)
 Returns the negation of the specified scalar or matrix. More...
 
template<int R, int C, typename T >
boost::enable_if_c< boost::is_arithmetic< T >::value, Eigen::Matrix< double, R, C > >::type multiply (const Eigen::Matrix< double, R, C > &m, T c)
 Return specified matrix multiplied by specified scalar. More...
 
template<int R, int C, typename T >
boost::enable_if_c< boost::is_arithmetic< T >::value, Eigen::Matrix< double, R, C > >::type multiply (T c, const Eigen::Matrix< double, R, C > &m)
 Return specified scalar multiplied by specified matrix. More...
 
template<int R1, int C1, int R2, int C2>
Eigen::Matrix< double, R1, C2 > multiply (const Eigen::Matrix< double, R1, C1 > &m1, const Eigen::Matrix< double, R2, C2 > &m2)
 Return the product of the specified matrices. More...
 
template<int C1, int R2>
double multiply (const Eigen::Matrix< double, 1, C1 > &rv, const Eigen::Matrix< double, R2, 1 > &v)
 Return the scalar product of the specified row vector and specified column vector. More...
 
matrix_d multiply_lower_tri_self_transpose (const matrix_d &L)
 Returns the result of multiplying the lower triangular portion of the input matrix by its own transpose. More...
 
template<typename T >
int num_elements (const T &x)
 Returns 1, the number of elements in a primitive type. More...
 
template<typename T , int R, int C>
int num_elements (const Eigen::Matrix< T, R, C > &m)
 Returns the size of the specified matrix. More...
 
template<typename T >
int num_elements (const std::vector< T > &v)
 Returns the number of elements in the specified vector. More...
 
template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, 1 > ordered_constrain (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &x)
 Return an increasing ordered vector derived from the specified free vector. More...
 
template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, 1 > ordered_constrain (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &x, T &lp)
 Return a positive valued, increasing ordered vector derived from the specified free vector and increment the specified log probability reference with the log absolute Jacobian determinant of the transform. More...
 
template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, 1 > ordered_free (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &y)
 Return the vector of unconstrained scalars that transform to the specified positive ordered vector. More...
 
template<typename T >
apply_scalar_unary< Phi_fun, T >::return_t Phi (const T &x)
 Vectorized version of Phi(). More...
 
template<typename T >
apply_scalar_unary< Phi_approx_fun, T >::return_t Phi_approx (const T &x)
 Return the elementwise application of Phi_approx() to specified argument container. More...
 
template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, 1 > positive_ordered_constrain (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &x)
 Return an increasing positive ordered vector derived from the specified free vector. More...
 
template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, 1 > positive_ordered_constrain (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &x, T &lp)
 Return a positive valued, increasing positive ordered vector derived from the specified free vector and increment the specified log probability reference with the log absolute Jacobian determinant of the transform. More...
 
template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, 1 > positive_ordered_free (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &y)
 Return the vector of unconstrained scalars that transform to the specified positive ordered vector. More...
 
template<typename T >
prod (const std::vector< T > &v)
 Returns the product of the coefficients of the specified standard vector. More...
 
template<typename T , int R, int C>
prod (const Eigen::Matrix< T, R, C > &v)
 Returns the product of the coefficients of the specified column vector. More...
 
template<typename T1 , typename T2 , typename F >
common_type< T1, T2 >::type promote_common (const F &u)
 
template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > qr_Q (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &m)
 
template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > qr_R (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &m)
 
template<int RA, int CA, int RB, int CB, typename T >
Eigen::Matrix< T, CB, CB > quad_form (const Eigen::Matrix< T, RA, CA > &A, const Eigen::Matrix< T, RB, CB > &B)
 Compute B^T A B. More...
 
template<int RA, int CA, int RB, typename T >
quad_form (const Eigen::Matrix< T, RA, CA > &A, const Eigen::Matrix< T, RB, 1 > &B)
 
template<typename T1 , typename T2 , int R, int C>
Eigen::Matrix< typename boost::math::tools::promote_args< T1, T2 >::type, Eigen::Dynamic, Eigen::Dynamic > quad_form_diag (const Eigen::Matrix< T1, Eigen::Dynamic, Eigen::Dynamic > &mat, const Eigen::Matrix< T2, R, C > &vec)
 
template<int RA, int CA, int RB, int CB, typename T >
Eigen::Matrix< T, CB, CB > quad_form_sym (const Eigen::Matrix< T, RA, CA > &A, const Eigen::Matrix< T, RB, CB > &B)
 
template<int RA, int CA, int RB, typename T >
quad_form_sym (const Eigen::Matrix< T, RA, CA > &A, const Eigen::Matrix< T, RB, 1 > &B)
 
template<typename T >
int rank (const std::vector< T > &v, int s)
 Return the number of components of v less than v[s]. More...
 
template<typename T , int R, int C>
int rank (const Eigen::Matrix< T, R, C > &v, int s)
 Return the number of components of v less than v[s]. More...
 
template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > read_corr_L (const Eigen::Array< T, Eigen::Dynamic, 1 > &CPCs, size_t K)
 Return the Cholesky factor of the correlation matrix of the specified dimensionality corresponding to the specified canonical partial correlations. More...
 
template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > read_corr_L (const Eigen::Array< T, Eigen::Dynamic, 1 > &CPCs, size_t K, T &log_prob)
 Return the Cholesky factor of the correlation matrix of the specified dimensionality corresponding to the specified canonical partial correlations, incrementing the specified scalar reference with the log absolute determinant of the Jacobian of the transformation. More...
 
template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > read_corr_matrix (const Eigen::Array< T, Eigen::Dynamic, 1 > &CPCs, size_t K)
 Return the correlation matrix of the specified dimensionality corresponding to the specified canonical partial correlations. More...
 
template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > read_corr_matrix (const Eigen::Array< T, Eigen::Dynamic, 1 > &CPCs, size_t K, T &log_prob)
 Return the correlation matrix of the specified dimensionality corresponding to the specified canonical partial correlations, incrementing the specified scalar reference with the log absolute determinant of the Jacobian of the transformation. More...
 
template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > read_cov_L (const Eigen::Array< T, Eigen::Dynamic, 1 > &CPCs, const Eigen::Array< T, Eigen::Dynamic, 1 > &sds, T &log_prob)
 This is the function that should be called prior to evaluating the density of any elliptical distribution. More...
 
template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > read_cov_matrix (const Eigen::Array< T, Eigen::Dynamic, 1 > &CPCs, const Eigen::Array< T, Eigen::Dynamic, 1 > &sds, T &log_prob)
 A generally worse alternative to call prior to evaluating the density of an elliptical distribution. More...
 
template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > read_cov_matrix (const Eigen::Array< T, Eigen::Dynamic, 1 > &CPCs, const Eigen::Array< T, Eigen::Dynamic, 1 > &sds)
 Builds a covariance matrix from CPCs and standard deviations. More...
 
template<typename T >
Eigen::Matrix< typename boost::math::tools::promote_args< T >::type, Eigen::Dynamic, Eigen::Dynamic > rep_matrix (const T &x, int m, int n)
 
template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > rep_matrix (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &v, int n)
 
template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > rep_matrix (const Eigen::Matrix< T, 1, Eigen::Dynamic > &rv, int m)
 
template<typename T >
Eigen::Matrix< typename boost::math::tools::promote_args< T >::type, 1, Eigen::Dynamic > rep_row_vector (const T &x, int m)
 
template<typename T >
Eigen::Matrix< typename boost::math::tools::promote_args< T >::type, Eigen::Dynamic, 1 > rep_vector (const T &x, int n)
 
template<typename T >
void resize (T &x, std::vector< size_t > dims)
 Recursively resize the specified vector of vectors, which must bottom out at scalar values, Eigen vectors or Eigen matrices. More...
 
template<typename T >
apply_scalar_unary< round_fun, T >::return_t round (const T &x)
 Vectorized version of round. More...
 
template<typename T >
Eigen::Matrix< T, 1, Eigen::Dynamic > row (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &m, size_t i)
 Return the specified row of the specified matrix, using start-at-1 indexing. More...
 
template<typename T , int R, int C>
int rows (const Eigen::Matrix< T, R, C > &m)
 Return the number of rows in the specified matrix, vector, or row vector. More...
 
template<int R1, int C1, int R2, int C2>
Eigen::Matrix< double, R1, 1 > rows_dot_product (const Eigen::Matrix< double, R1, C1 > &v1, const Eigen::Matrix< double, R2, C2 > &v2)
 Returns the dot product of the specified vectors. More...
 
template<typename T , int R, int C>
Eigen::Matrix< T, R, 1 > rows_dot_self (const Eigen::Matrix< T, R, C > &x)
 Returns the dot product of each row of a matrix with itself. More...
 
template<typename T >
boost::math::tools::promote_args< T >::type sd (const std::vector< T > &v)
 Returns the unbiased sample standard deviation of the coefficients in the specified column vector. More...
 
template<typename T , int R, int C>
boost::math::tools::promote_args< T >::type sd (const Eigen::Matrix< T, R, C > &m)
 Returns the unbiased sample standard deviation of the coefficients in the specified vector, row vector, or matrix. More...
 
template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, 1 > segment (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &v, size_t i, size_t n)
 Return the specified number of elements as a vector starting from the specified element - 1 of the specified vector. More...
 
template<typename T >
Eigen::Matrix< T, 1, Eigen::Dynamic > segment (const Eigen::Matrix< T, 1, Eigen::Dynamic > &v, size_t i, size_t n)
 
template<typename T >
std::vector< T > segment (const std::vector< T > &sv, size_t i, size_t n)
 
template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, 1 > simplex_constrain (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &y)
 Return the simplex corresponding to the specified free vector. More...
 
template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, 1 > simplex_constrain (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &y, T &lp)
 Return the simplex corresponding to the specified free vector and increment the specified log probability reference with the log absolute Jacobian determinant of the transform. More...
 
template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, 1 > simplex_free (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &x)
 Return an unconstrained vector that when transformed produces the specified simplex. More...
 
template<typename T >
apply_scalar_unary< sin_fun, T >::return_t sin (const T &x)
 Vectorized version of sin(). More...
 
template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, 1 > singular_values (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &m)
 Return the vector of the singular values of the specified matrix in decreasing order of magnitude. More...
 
template<typename T >
apply_scalar_unary< sinh_fun, T >::return_t sinh (const T &x)
 Vectorized version of sinh(). More...
 
template<typename T >
int size (const std::vector< T > &x)
 Return the size of the specified standard vector. More...
 
template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, 1 > softmax (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &v)
 Return the softmax of the specified vector. More...
 
template<typename T , int R, int C>
Eigen::Matrix< T, R, C > sort_asc (Eigen::Matrix< T, R, C > xs)
 Return the specified vector in ascending order. More...
 
template<typename T , int R, int C>
Eigen::Matrix< T, R, C > sort_desc (Eigen::Matrix< T, R, C > xs)
 Return the specified vector in descending order. More...
 
template<typename C >
std::vector< int > sort_indices_asc (const C &xs)
 Return a sorted copy of the argument container in ascending order. More...
 
template<typename C >
std::vector< int > sort_indices_desc (const C &xs)
 Return a sorted copy of the argument container in ascending order. More...
 
template<typename T >
apply_scalar_unary< sqrt_fun, T >::return_t sqrt (const T &x)
 Vectorized version of sqrt(). More...
 
template<typename T >
apply_scalar_unary< square_fun, T >::return_t square (const T &x)
 Vectorized version of square(). More...
 
template<int R, int C>
double squared_distance (const Eigen::Matrix< double, R, C > &v1, const Eigen::Matrix< double, R, C > &v2)
 Returns the squared distance between the specified vectors of the same dimensions. More...
 
template<int R1, int C1, int R2, int C2>
double squared_distance (const Eigen::Matrix< double, R1, C1 > &v1, const Eigen::Matrix< double, R2, C2 > &v2)
 Returns the squared distance between the specified vectors of the same dimensions. More...
 
template<typename T >
void stan_print (std::ostream *o, const T &x)
 
template<typename T >
void stan_print (std::ostream *o, const std::vector< T > &x)
 
template<typename T >
void stan_print (std::ostream *o, const Eigen::Matrix< T, Eigen::Dynamic, 1 > &x)
 
template<typename T >
void stan_print (std::ostream *o, const Eigen::Matrix< T, 1, Eigen::Dynamic > &x)
 
template<typename T >
void stan_print (std::ostream *o, const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &x)
 
template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, 1 > sub_col (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &m, size_t i, size_t j, size_t nrows)
 Return a nrows x 1 subcolumn starting at (i-1, j-1). More...
 
template<typename T >
Eigen::Matrix< T, 1, Eigen::Dynamic > sub_row (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &m, size_t i, size_t j, size_t ncols)
 Return a 1 x nrows subrow starting at (i-1, j-1). More...
 
template<typename T1 , typename T2 , int R, int C>
Eigen::Matrix< typename boost::math::tools::promote_args< T1, T2 >::type, R, C > subtract (const Eigen::Matrix< T1, R, C > &m1, const Eigen::Matrix< T2, R, C > &m2)
 Return the result of subtracting the second specified matrix from the first specified matrix. More...
 
template<typename T1 , typename T2 , int R, int C>
Eigen::Matrix< typename boost::math::tools::promote_args< T1, T2 >::type, R, C > subtract (const T1 &c, const Eigen::Matrix< T2, R, C > &m)
 
template<typename T1 , typename T2 , int R, int C>
Eigen::Matrix< typename boost::math::tools::promote_args< T1, T2 >::type, R, C > subtract (const Eigen::Matrix< T1, R, C > &m, const T2 &c)
 
template<typename T , int R, int C>
double sum (const Eigen::Matrix< T, R, C > &v)
 Returns the sum of the coefficients of the specified column vector. More...
 
template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, 1 > tail (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &v, size_t n)
 Return the specified number of elements as a vector from the back of the specified vector. More...
 
template<typename T >
Eigen::Matrix< T, 1, Eigen::Dynamic > tail (const Eigen::Matrix< T, 1, Eigen::Dynamic > &rv, size_t n)
 Return the specified number of elements as a row vector from the back of the specified row vector. More...
 
template<typename T >
std::vector< T > tail (const std::vector< T > &sv, size_t n)
 Return the specified number of elements as a standard vector from the back of the specified standard vector. More...
 
template<typename T >
apply_scalar_unary< tan_fun, T >::return_t tan (const T &x)
 Vectorized version of tan(). More...
 
template<typename T >
apply_scalar_unary< tanh_fun, T >::return_t tanh (const T &x)
 Vectorized version of tanh(). More...
 
matrix_d tcrossprod (const matrix_d &M)
 Returns the result of post-multiplying a matrix by its own transpose. More...
 
template<typename T >
apply_scalar_unary< tgamma_fun, T >::return_t tgamma (const T &x)
 Vectorized version of tgamma(). More...
 
template<typename T , int R, int C>
std::vector< T > to_array_1d (const Eigen::Matrix< T, R, C > &matrix)
 
template<typename T >
std::vector< T > to_array_1d (const std::vector< T > &x)
 
template<typename T >
std::vector< typename scalar_type< T >::type > to_array_1d (const std::vector< std::vector< T > > &x)
 
template<typename T >
std::vector< std::vector< T > > to_array_2d (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &matrix)
 
template<typename T , int R, int C>
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > to_matrix (Eigen::Matrix< T, R, C > matrix)
 
template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > to_matrix (const std::vector< std::vector< T > > &vec)
 
Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > to_matrix (const std::vector< std::vector< int > > &vec)
 
template<typename T , int R, int C>
Eigen::Matrix< T, 1, Eigen::Dynamic > to_row_vector (const Eigen::Matrix< T, R, C > &matrix)
 
template<typename T >
Eigen::Matrix< T, 1, Eigen::Dynamic > to_row_vector (const std::vector< T > &vec)
 
Eigen::Matrix< double, 1, Eigen::Dynamic > to_row_vector (const std::vector< int > &vec)
 
template<typename T , int R, int C>
Eigen::Matrix< T, Eigen::Dynamic, 1 > to_vector (const Eigen::Matrix< T, R, C > &matrix)
 
template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, 1 > to_vector (const std::vector< T > &vec)
 
Eigen::Matrix< double, Eigen::Dynamic, 1 > to_vector (const std::vector< int > &vec)
 
template<typename T >
trace (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &m)
 Returns the trace of the specified matrix. More...
 
template<typename T >
trace (const T &m)
 
template<typename T1 , typename T2 , typename T3 , int R1, int C1, int R2, int C2, int R3, int C3>
boost::enable_if_c<!stan::is_var< T1 >::value &&!stan::is_var< T2 >::value &&!stan::is_var< T3 >::value, typename boost::math::tools::promote_args< T1, T2, T3 >::type >::type trace_gen_inv_quad_form_ldlt (const Eigen::Matrix< T1, R1, C1 > &D, const LDLT_factor< T2, R2, C2 > &A, const Eigen::Matrix< T3, R3, C3 > &B)
 
template<int RD, int CD, int RA, int CA, int RB, int CB>
double trace_gen_quad_form (const Eigen::Matrix< double, RD, CD > &D, const Eigen::Matrix< double, RA, CA > &A, const Eigen::Matrix< double, RB, CB > &B)
 Compute trace(D B^T A B). More...
 
template<typename T1 , typename T2 , int R2, int C2, int R3, int C3>
boost::enable_if_c<!stan::is_var< T1 >::value &&!stan::is_var< T2 >::value, typename boost::math::tools::promote_args< T1, T2 >::type >::type trace_inv_quad_form_ldlt (const LDLT_factor< T1, R2, C2 > &A, const Eigen::Matrix< T2, R3, C3 > &B)
 
template<int RA, int CA, int RB, int CB>
double trace_quad_form (const Eigen::Matrix< double, RA, CA > &A, const Eigen::Matrix< double, RB, CB > &B)
 Compute trace(B^T A B). More...
 
template<typename T , int R, int C>
Eigen::Matrix< T, C, R > transpose (const Eigen::Matrix< T, R, C > &m)
 
template<typename T >
apply_scalar_unary< trigamma_fun, T >::return_t trigamma (const T &x)
 Return the elementwise application of trigamma() to specified argument container. More...
 
template<typename T >
apply_scalar_unary< trunc_fun, T >::return_t trunc (const T &x)
 Return the elementwise application of trunc() to specified argument container. More...
 
template<typename T , int R, int C>
Eigen::Matrix< T, R, C > unit_vector_constrain (const Eigen::Matrix< T, R, C > &y)
 Return the unit length vector corresponding to the free vector y. More...
 
template<typename T , int R, int C>
Eigen::Matrix< T, R, C > unit_vector_constrain (const Eigen::Matrix< T, R, C > &y, T &lp)
 Return the unit length vector corresponding to the free vector y. More...
 
template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, 1 > unit_vector_free (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &x)
 Transformation of a unit length vector to a "free" vector However, we are just fixing the unidentified radius to 1. More...
 
template<typename T , int R, int C>
Eigen::Matrix< typename child_type< T >::type, R, C > value_of (const Eigen::Matrix< T, R, C > &M)
 Convert a matrix of type T to a matrix of doubles. More...
 
template<int R, int C>
Eigen::Matrix< double, R, C > value_of (const Eigen::Matrix< double, R, C > &x)
 Return the specified argument. More...
 
template<typename T , int R, int C>
Eigen::Matrix< double, R, C > value_of_rec (const Eigen::Matrix< T, R, C > &M)
 Convert a matrix of type T to a matrix of doubles. More...
 
template<int R, int C>
Eigen::Matrix< double, R, C > value_of_rec (const Eigen::Matrix< double, R, C > &x)
 Return the specified argument. More...
 
template<typename T >
boost::math::tools::promote_args< T >::type variance (const std::vector< T > &v)
 Returns the sample variance (divide by length - 1) of the coefficients in the specified standard vector. More...
 
template<typename T , int R, int C>
boost::math::tools::promote_args< T >::type variance (const Eigen::Matrix< T, R, C > &m)
 Returns the sample variance (divide by length - 1) of the coefficients in the specified column vector. More...
 
template<typename F >
void finite_diff_gradient (const F &f, const Eigen::Matrix< double, -1, 1 > &x, double &fx, Eigen::Matrix< double, -1, 1 > &grad_fx, double epsilon=1e-03)
 Calculate the value and the gradient of the specified function at the specified argument using finite difference. More...
 
template<typename F >
double finite_diff_hess_helper (const F &f, const Eigen::Matrix< double, Eigen::Dynamic, 1 > &x, int lambda, double epsilon=1e-03)
 
template<typename F >
void finite_diff_hessian (const F &f, const Eigen::Matrix< double, -1, 1 > &x, double &fx, Eigen::Matrix< double, -1, 1 > &grad_fx, Eigen::Matrix< double, -1, -1 > &hess_fx, double epsilon=1e-03)
 Calculate the value and the Hessian of the specified function at the specified argument using second-order finite difference. More...
 
template<bool propto, typename T_prob >
boost::math::tools::promote_args< T_prob >::type categorical_log (int n, const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &theta)
 
template<typename T_prob >
boost::math::tools::promote_args< T_prob >::type categorical_log (const typename math::index_type< Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > >::type n, const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &theta)
 
template<bool propto, typename T_prob >
boost::math::tools::promote_args< T_prob >::type categorical_log (const std::vector< int > &ns, const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &theta)
 
template<typename T_prob >
boost::math::tools::promote_args< T_prob >::type categorical_log (const std::vector< int > &ns, const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &theta)
 
template<bool propto, typename T_prob >
boost::math::tools::promote_args< T_prob >::type categorical_logit_log (int n, const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &beta)
 
template<typename T_prob >
boost::math::tools::promote_args< T_prob >::type categorical_logit_log (int n, const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &beta)
 
template<bool propto, typename T_prob >
boost::math::tools::promote_args< T_prob >::type categorical_logit_log (const std::vector< int > &ns, const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &beta)
 
template<typename T_prob >
boost::math::tools::promote_args< T_prob >::type categorical_logit_log (const std::vector< int > &ns, const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &beta)
 
template<bool propto, typename T_prob >
boost::math::tools::promote_args< T_prob >::type categorical_logit_lpmf (int n, const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &beta)
 
template<typename T_prob >
boost::math::tools::promote_args< T_prob >::type categorical_logit_lpmf (int n, const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &beta)
 
template<bool propto, typename T_prob >
boost::math::tools::promote_args< T_prob >::type categorical_logit_lpmf (const std::vector< int > &ns, const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &beta)
 
template<typename T_prob >
boost::math::tools::promote_args< T_prob >::type categorical_logit_lpmf (const std::vector< int > &ns, const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &beta)
 
template<bool propto, typename T_prob >
boost::math::tools::promote_args< T_prob >::type categorical_lpmf (int n, const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &theta)
 
template<typename T_prob >
boost::math::tools::promote_args< T_prob >::type categorical_lpmf (const typename math::index_type< Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > >::type n, const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &theta)
 
template<bool propto, typename T_prob >
boost::math::tools::promote_args< T_prob >::type categorical_lpmf (const std::vector< int > &ns, const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &theta)
 
template<typename T_prob >
boost::math::tools::promote_args< T_prob >::type categorical_lpmf (const std::vector< int > &ns, const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &theta)
 
template<class RNG >
int categorical_rng (const Eigen::Matrix< double, Eigen::Dynamic, 1 > &theta, RNG &rng)
 
template<bool propto, typename T_prob , typename T_prior_sample_size >
boost::math::tools::promote_args< T_prob, T_prior_sample_size >::type dirichlet_log (const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &theta, const Eigen::Matrix< T_prior_sample_size, Eigen::Dynamic, 1 > &alpha)
 The log of the Dirichlet density for the given theta and a vector of prior sample sizes, alpha. More...
 
template<typename T_prob , typename T_prior_sample_size >
boost::math::tools::promote_args< T_prob, T_prior_sample_size >::type dirichlet_log (const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &theta, const Eigen::Matrix< T_prior_sample_size, Eigen::Dynamic, 1 > &alpha)
 
template<bool propto, typename T_prob , typename T_prior_sample_size >
boost::math::tools::promote_args< T_prob, T_prior_sample_size >::type dirichlet_lpmf (const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &theta, const Eigen::Matrix< T_prior_sample_size, Eigen::Dynamic, 1 > &alpha)
 The log of the Dirichlet density for the given theta and a vector of prior sample sizes, alpha. More...
 
template<typename T_prob , typename T_prior_sample_size >
boost::math::tools::promote_args< T_prob, T_prior_sample_size >::type dirichlet_lpmf (const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &theta, const Eigen::Matrix< T_prior_sample_size, Eigen::Dynamic, 1 > &alpha)
 
template<class RNG >
Eigen::VectorXd dirichlet_rng (const Eigen::Matrix< double, Eigen::Dynamic, 1 > &alpha, RNG &rng)
 Return a draw from a Dirichlet distribution with specified parameters and pseudo-random number generator. More...
 
template<bool propto, typename T_y , typename T_F , typename T_G , typename T_V , typename T_W , typename T_m0 , typename T_C0 >
return_type< T_y, typename return_type< T_F, T_G, T_V, T_W, T_m0, T_C0 >::type >::type gaussian_dlm_obs_log (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const Eigen::Matrix< T_F, Eigen::Dynamic, Eigen::Dynamic > &F, const Eigen::Matrix< T_G, Eigen::Dynamic, Eigen::Dynamic > &G, const Eigen::Matrix< T_V, Eigen::Dynamic, Eigen::Dynamic > &V, const Eigen::Matrix< T_W, Eigen::Dynamic, Eigen::Dynamic > &W, const Eigen::Matrix< T_m0, Eigen::Dynamic, 1 > &m0, const Eigen::Matrix< T_C0, Eigen::Dynamic, Eigen::Dynamic > &C0)
 The log of a Gaussian dynamic linear model (GDLM). More...
 
template<typename T_y , typename T_F , typename T_G , typename T_V , typename T_W , typename T_m0 , typename T_C0 >
return_type< T_y, typename return_type< T_F, T_G, T_V, T_W, T_m0, T_C0 >::type >::type gaussian_dlm_obs_log (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const Eigen::Matrix< T_F, Eigen::Dynamic, Eigen::Dynamic > &F, const Eigen::Matrix< T_G, Eigen::Dynamic, Eigen::Dynamic > &G, const Eigen::Matrix< T_V, Eigen::Dynamic, Eigen::Dynamic > &V, const Eigen::Matrix< T_W, Eigen::Dynamic, Eigen::Dynamic > &W, const Eigen::Matrix< T_m0, Eigen::Dynamic, 1 > &m0, const Eigen::Matrix< T_C0, Eigen::Dynamic, Eigen::Dynamic > &C0)
 
template<bool propto, typename T_y , typename T_F , typename T_G , typename T_V , typename T_W , typename T_m0 , typename T_C0 >
return_type< T_y, typename return_type< T_F, T_G, T_V, T_W, T_m0, T_C0 >::type >::type gaussian_dlm_obs_log (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const Eigen::Matrix< T_F, Eigen::Dynamic, Eigen::Dynamic > &F, const Eigen::Matrix< T_G, Eigen::Dynamic, Eigen::Dynamic > &G, const Eigen::Matrix< T_V, Eigen::Dynamic, 1 > &V, const Eigen::Matrix< T_W, Eigen::Dynamic, Eigen::Dynamic > &W, const Eigen::Matrix< T_m0, Eigen::Dynamic, 1 > &m0, const Eigen::Matrix< T_C0, Eigen::Dynamic, Eigen::Dynamic > &C0)
 The log of a Gaussian dynamic linear model (GDLM) with uncorrelated observation disturbances. More...
 
template<typename T_y , typename T_F , typename T_G , typename T_V , typename T_W , typename T_m0 , typename T_C0 >
return_type< T_y, typename return_type< T_F, T_G, T_V, T_W, T_m0, T_C0 >::type >::type gaussian_dlm_obs_log (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const Eigen::Matrix< T_F, Eigen::Dynamic, Eigen::Dynamic > &F, const Eigen::Matrix< T_G, Eigen::Dynamic, Eigen::Dynamic > &G, const Eigen::Matrix< T_V, Eigen::Dynamic, 1 > &V, const Eigen::Matrix< T_W, Eigen::Dynamic, Eigen::Dynamic > &W, const Eigen::Matrix< T_m0, Eigen::Dynamic, 1 > &m0, const Eigen::Matrix< T_C0, Eigen::Dynamic, Eigen::Dynamic > &C0)
 
template<bool propto, typename T_y , typename T_F , typename T_G , typename T_V , typename T_W , typename T_m0 , typename T_C0 >
return_type< T_y, typename return_type< T_F, T_G, T_V, T_W, T_m0, T_C0 >::type >::type gaussian_dlm_obs_lpdf (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const Eigen::Matrix< T_F, Eigen::Dynamic, Eigen::Dynamic > &F, const Eigen::Matrix< T_G, Eigen::Dynamic, Eigen::Dynamic > &G, const Eigen::Matrix< T_V, Eigen::Dynamic, Eigen::Dynamic > &V, const Eigen::Matrix< T_W, Eigen::Dynamic, Eigen::Dynamic > &W, const Eigen::Matrix< T_m0, Eigen::Dynamic, 1 > &m0, const Eigen::Matrix< T_C0, Eigen::Dynamic, Eigen::Dynamic > &C0)
 The log of a Gaussian dynamic linear model (GDLM). More...
 
template<typename T_y , typename T_F , typename T_G , typename T_V , typename T_W , typename T_m0 , typename T_C0 >
return_type< T_y, typename return_type< T_F, T_G, T_V, T_W, T_m0, T_C0 >::type >::type gaussian_dlm_obs_lpdf (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const Eigen::Matrix< T_F, Eigen::Dynamic, Eigen::Dynamic > &F, const Eigen::Matrix< T_G, Eigen::Dynamic, Eigen::Dynamic > &G, const Eigen::Matrix< T_V, Eigen::Dynamic, Eigen::Dynamic > &V, const Eigen::Matrix< T_W, Eigen::Dynamic, Eigen::Dynamic > &W, const Eigen::Matrix< T_m0, Eigen::Dynamic, 1 > &m0, const Eigen::Matrix< T_C0, Eigen::Dynamic, Eigen::Dynamic > &C0)
 
template<bool propto, typename T_y , typename T_F , typename T_G , typename T_V , typename T_W , typename T_m0 , typename T_C0 >
return_type< T_y, typename return_type< T_F, T_G, T_V, T_W, T_m0, T_C0 >::type >::type gaussian_dlm_obs_lpdf (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const Eigen::Matrix< T_F, Eigen::Dynamic, Eigen::Dynamic > &F, const Eigen::Matrix< T_G, Eigen::Dynamic, Eigen::Dynamic > &G, const Eigen::Matrix< T_V, Eigen::Dynamic, 1 > &V, const Eigen::Matrix< T_W, Eigen::Dynamic, Eigen::Dynamic > &W, const Eigen::Matrix< T_m0, Eigen::Dynamic, 1 > &m0, const Eigen::Matrix< T_C0, Eigen::Dynamic, Eigen::Dynamic > &C0)
 The log of a Gaussian dynamic linear model (GDLM) with uncorrelated observation disturbances. More...
 
template<typename T_y , typename T_F , typename T_G , typename T_V , typename T_W , typename T_m0 , typename T_C0 >
return_type< T_y, typename return_type< T_F, T_G, T_V, T_W, T_m0, T_C0 >::type >::type gaussian_dlm_obs_lpdf (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const Eigen::Matrix< T_F, Eigen::Dynamic, Eigen::Dynamic > &F, const Eigen::Matrix< T_G, Eigen::Dynamic, Eigen::Dynamic > &G, const Eigen::Matrix< T_V, Eigen::Dynamic, 1 > &V, const Eigen::Matrix< T_W, Eigen::Dynamic, Eigen::Dynamic > &W, const Eigen::Matrix< T_m0, Eigen::Dynamic, 1 > &m0, const Eigen::Matrix< T_C0, Eigen::Dynamic, Eigen::Dynamic > &C0)
 
template<bool propto, typename T_y , typename T_dof , typename T_scale >
boost::math::tools::promote_args< T_y, T_dof, T_scale >::type inv_wishart_log (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &W, const T_dof &nu, const Eigen::Matrix< T_scale, Eigen::Dynamic, Eigen::Dynamic > &S)
 The log of the Inverse-Wishart density for the given W, degrees of freedom, and scale matrix. More...
 
template<typename T_y , typename T_dof , typename T_scale >
boost::math::tools::promote_args< T_y, T_dof, T_scale >::type inv_wishart_log (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &W, const T_dof &nu, const Eigen::Matrix< T_scale, Eigen::Dynamic, Eigen::Dynamic > &S)
 
template<bool propto, typename T_y , typename T_dof , typename T_scale >
boost::math::tools::promote_args< T_y, T_dof, T_scale >::type inv_wishart_lpdf (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &W, const T_dof &nu, const Eigen::Matrix< T_scale, Eigen::Dynamic, Eigen::Dynamic > &S)
 The log of the Inverse-Wishart density for the given W, degrees of freedom, and scale matrix. More...
 
template<typename T_y , typename T_dof , typename T_scale >
boost::math::tools::promote_args< T_y, T_dof, T_scale >::type inv_wishart_lpdf (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &W, const T_dof &nu, const Eigen::Matrix< T_scale, Eigen::Dynamic, Eigen::Dynamic > &S)
 
template<class RNG >
Eigen::MatrixXd inv_wishart_rng (double nu, const Eigen::MatrixXd &S, RNG &rng)
 
template<bool propto, typename T_covar , typename T_shape >
boost::math::tools::promote_args< T_covar, T_shape >::type lkj_corr_cholesky_log (const Eigen::Matrix< T_covar, Eigen::Dynamic, Eigen::Dynamic > &L, const T_shape &eta)
 
template<typename T_covar , typename T_shape >
boost::math::tools::promote_args< T_covar, T_shape >::type lkj_corr_cholesky_log (const Eigen::Matrix< T_covar, Eigen::Dynamic, Eigen::Dynamic > &L, const T_shape &eta)
 
template<bool propto, typename T_covar , typename T_shape >
boost::math::tools::promote_args< T_covar, T_shape >::type lkj_corr_cholesky_lpdf (const Eigen::Matrix< T_covar, Eigen::Dynamic, Eigen::Dynamic > &L, const T_shape &eta)
 
template<typename T_covar , typename T_shape >
boost::math::tools::promote_args< T_covar, T_shape >::type lkj_corr_cholesky_lpdf (const Eigen::Matrix< T_covar, Eigen::Dynamic, Eigen::Dynamic > &L, const T_shape &eta)
 
template<class RNG >
Eigen::MatrixXd lkj_corr_cholesky_rng (size_t K, double eta, RNG &rng)
 
template<bool propto, typename T_y , typename T_shape >
boost::math::tools::promote_args< T_y, T_shape >::type lkj_corr_log (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const T_shape &eta)
 
template<typename T_y , typename T_shape >
boost::math::tools::promote_args< T_y, T_shape >::type lkj_corr_log (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const T_shape &eta)
 
template<typename T_shape >
T_shape do_lkj_constant (const T_shape &eta, const unsigned int &K)
 
template<bool propto, typename T_y , typename T_shape >
boost::math::tools::promote_args< T_y, T_shape >::type lkj_corr_lpdf (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const T_shape &eta)
 
template<typename T_y , typename T_shape >
boost::math::tools::promote_args< T_y, T_shape >::type lkj_corr_lpdf (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const T_shape &eta)
 
template<class RNG >
Eigen::MatrixXd lkj_corr_rng (size_t K, double eta, RNG &rng)
 Return a random correlation matrix (symmetric, positive definite, unit diagonal) of the specified dimensionality drawn from the LKJ distribution with the specified degrees of freedom using the specified random number generator. More...
 
template<bool propto, typename T_y , typename T_loc , typename T_scale , typename T_shape >
boost::math::tools::promote_args< T_y, T_loc, T_scale, T_shape >::type lkj_cov_log (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const Eigen::Matrix< T_loc, Eigen::Dynamic, 1 > &mu, const Eigen::Matrix< T_scale, Eigen::Dynamic, 1 > &sigma, const T_shape &eta)
 
template<typename T_y , typename T_loc , typename T_scale , typename T_shape >
boost::math::tools::promote_args< T_y, T_loc, T_scale, T_shape >::type lkj_cov_log (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const Eigen::Matrix< T_loc, Eigen::Dynamic, 1 > &mu, const Eigen::Matrix< T_scale, Eigen::Dynamic, 1 > &sigma, const T_shape &eta)
 
template<bool propto, typename T_y , typename T_loc , typename T_scale , typename T_shape >
boost::math::tools::promote_args< T_y, T_loc, T_scale, T_shape >::type lkj_cov_log (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const T_loc &mu, const T_scale &sigma, const T_shape &eta)
 
template<typename T_y , typename T_loc , typename T_scale , typename T_shape >
boost::math::tools::promote_args< T_y, T_loc, T_scale, T_shape >::type lkj_cov_log (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const T_loc &mu, const T_scale &sigma, const T_shape &eta)
 
template<bool propto, typename T_y , typename T_loc , typename T_scale , typename T_shape >
boost::math::tools::promote_args< T_y, T_loc, T_scale, T_shape >::type lkj_cov_lpdf (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const Eigen::Matrix< T_loc, Eigen::Dynamic, 1 > &mu, const Eigen::Matrix< T_scale, Eigen::Dynamic, 1 > &sigma, const T_shape &eta)
 
template<typename T_y , typename T_loc , typename T_scale , typename T_shape >
boost::math::tools::promote_args< T_y, T_loc, T_scale, T_shape >::type lkj_cov_lpdf (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const Eigen::Matrix< T_loc, Eigen::Dynamic, 1 > &mu, const Eigen::Matrix< T_scale, Eigen::Dynamic, 1 > &sigma, const T_shape &eta)
 
template<bool propto, typename T_y , typename T_loc , typename T_scale , typename T_shape >
boost::math::tools::promote_args< T_y, T_loc, T_scale, T_shape >::type lkj_cov_lpdf (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const T_loc &mu, const T_scale &sigma, const T_shape &eta)
 
template<typename T_y , typename T_loc , typename T_scale , typename T_shape >
boost::math::tools::promote_args< T_y, T_loc, T_scale, T_shape >::type lkj_cov_lpdf (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const T_loc &mu, const T_scale &sigma, const T_shape &eta)
 
template<bool propto, typename T_y , typename T_Mu , typename T_Sigma , typename T_D >
boost::math::tools::promote_args< T_y, T_Mu, T_Sigma, T_D >::type matrix_normal_prec_log (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const Eigen::Matrix< T_Mu, Eigen::Dynamic, Eigen::Dynamic > &Mu, const Eigen::Matrix< T_Sigma, Eigen::Dynamic, Eigen::Dynamic > &Sigma, const Eigen::Matrix< T_D, Eigen::Dynamic, Eigen::Dynamic > &D)
 The log of the matrix normal density for the given y, mu, Sigma and D where Sigma and D are given as precision matrices, not covariance matrices. More...
 
template<typename T_y , typename T_Mu , typename T_Sigma , typename T_D >
boost::math::tools::promote_args< T_y, T_Mu, T_Sigma, T_D >::type matrix_normal_prec_log (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const Eigen::Matrix< T_Mu, Eigen::Dynamic, Eigen::Dynamic > &Mu, const Eigen::Matrix< T_Sigma, Eigen::Dynamic, Eigen::Dynamic > &Sigma, const Eigen::Matrix< T_D, Eigen::Dynamic, Eigen::Dynamic > &D)
 
template<bool propto, typename T_y , typename T_Mu , typename T_Sigma , typename T_D >
boost::math::tools::promote_args< T_y, T_Mu, T_Sigma, T_D >::type matrix_normal_prec_lpdf (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const Eigen::Matrix< T_Mu, Eigen::Dynamic, Eigen::Dynamic > &Mu, const Eigen::Matrix< T_Sigma, Eigen::Dynamic, Eigen::Dynamic > &Sigma, const Eigen::Matrix< T_D, Eigen::Dynamic, Eigen::Dynamic > &D)
 The log of the matrix normal density for the given y, mu, Sigma and D where Sigma and D are given as precision matrices, not covariance matrices. More...
 
template<typename T_y , typename T_Mu , typename T_Sigma , typename T_D >
boost::math::tools::promote_args< T_y, T_Mu, T_Sigma, T_D >::type matrix_normal_prec_lpdf (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const Eigen::Matrix< T_Mu, Eigen::Dynamic, Eigen::Dynamic > &Mu, const Eigen::Matrix< T_Sigma, Eigen::Dynamic, Eigen::Dynamic > &Sigma, const Eigen::Matrix< T_D, Eigen::Dynamic, Eigen::Dynamic > &D)
 
template<bool propto, typename T_y , typename T_covar , typename T_w >
boost::math::tools::promote_args< T_y, T_covar, T_w >::type multi_gp_cholesky_log (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const Eigen::Matrix< T_covar, Eigen::Dynamic, Eigen::Dynamic > &L, const Eigen::Matrix< T_w, Eigen::Dynamic, 1 > &w)
 The log of a multivariate Gaussian Process for the given y, w, and a Cholesky factor L of the kernel matrix Sigma. More...
 
template<typename T_y , typename T_covar , typename T_w >
boost::math::tools::promote_args< T_y, T_covar, T_w >::type multi_gp_cholesky_log (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const Eigen::Matrix< T_covar, Eigen::Dynamic, Eigen::Dynamic > &L, const Eigen::Matrix< T_w, Eigen::Dynamic, 1 > &w)
 
template<bool propto, typename T_y , typename T_covar , typename T_w >
boost::math::tools::promote_args< T_y, T_covar, T_w >::type multi_gp_cholesky_lpdf (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const Eigen::Matrix< T_covar, Eigen::Dynamic, Eigen::Dynamic > &L, const Eigen::Matrix< T_w, Eigen::Dynamic, 1 > &w)
 The log of a multivariate Gaussian Process for the given y, w, and a Cholesky factor L of the kernel matrix Sigma. More...
 
template<typename T_y , typename T_covar , typename T_w >
boost::math::tools::promote_args< T_y, T_covar, T_w >::type multi_gp_cholesky_lpdf (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const Eigen::Matrix< T_covar, Eigen::Dynamic, Eigen::Dynamic > &L, const Eigen::Matrix< T_w, Eigen::Dynamic, 1 > &w)
 
template<bool propto, typename T_y , typename T_covar , typename T_w >
boost::math::tools::promote_args< T_y, T_covar, T_w >::type multi_gp_log (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const Eigen::Matrix< T_covar, Eigen::Dynamic, Eigen::Dynamic > &Sigma, const Eigen::Matrix< T_w, Eigen::Dynamic, 1 > &w)
 The log of a multivariate Gaussian Process for the given y, Sigma, and w. More...
 
template<typename T_y , typename T_covar , typename T_w >
boost::math::tools::promote_args< T_y, T_covar, T_w >::type multi_gp_log (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const Eigen::Matrix< T_covar, Eigen::Dynamic, Eigen::Dynamic > &Sigma, const Eigen::Matrix< T_w, Eigen::Dynamic, 1 > &w)
 
template<bool propto, typename T_y , typename T_covar , typename T_w >
boost::math::tools::promote_args< T_y, T_covar, T_w >::type multi_gp_lpdf (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const Eigen::Matrix< T_covar, Eigen::Dynamic, Eigen::Dynamic > &Sigma, const Eigen::Matrix< T_w, Eigen::Dynamic, 1 > &w)
 The log of a multivariate Gaussian Process for the given y, Sigma, and w. More...
 
template<typename T_y , typename T_covar , typename T_w >
boost::math::tools::promote_args< T_y, T_covar, T_w >::type multi_gp_lpdf (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const Eigen::Matrix< T_covar, Eigen::Dynamic, Eigen::Dynamic > &Sigma, const Eigen::Matrix< T_w, Eigen::Dynamic, 1 > &w)
 
template<bool propto, typename T_y , typename T_loc , typename T_covar >
return_type< T_y, T_loc, T_covar >::type multi_normal_cholesky_log (const T_y &y, const T_loc &mu, const T_covar &L)
 The log of the multivariate normal density for the given y, mu, and a Cholesky factor L of the variance matrix. More...
 
template<typename T_y , typename T_loc , typename T_covar >
return_type< T_y, T_loc, T_covar >::type multi_normal_cholesky_log (const T_y &y, const T_loc &mu, const T_covar &L)
 
template<bool propto, typename T_y , typename T_loc , typename T_covar >
return_type< T_y, T_loc, T_covar >::type multi_normal_cholesky_lpdf (const T_y &y, const T_loc &mu, const T_covar &L)
 The log of the multivariate normal density for the given y, mu, and a Cholesky factor L of the variance matrix. More...
 
template<typename T_y , typename T_loc , typename T_covar >
return_type< T_y, T_loc, T_covar >::type multi_normal_cholesky_lpdf (const T_y &y, const T_loc &mu, const T_covar &L)
 
template<class RNG >
Eigen::VectorXd multi_normal_cholesky_rng (const Eigen::Matrix< double, Eigen::Dynamic, 1 > &mu, const Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > &S, RNG &rng)
 
template<bool propto, typename T_y , typename T_loc , typename T_covar >
return_type< T_y, T_loc, T_covar >::type multi_normal_log (const T_y &y, const T_loc &mu, const T_covar &Sigma)
 
template<typename T_y , typename T_loc , typename T_covar >
return_type< T_y, T_loc, T_covar >::type multi_normal_log (const T_y &y, const T_loc &mu, const T_covar &Sigma)
 
template<bool propto, typename T_y , typename T_loc , typename T_covar >
return_type< T_y, T_loc, T_covar >::type multi_normal_lpdf (const T_y &y, const T_loc &mu, const T_covar &Sigma)
 
template<typename T_y , typename T_loc , typename T_covar >
return_type< T_y, T_loc, T_covar >::type multi_normal_lpdf (const T_y &y, const T_loc &mu, const T_covar &Sigma)
 
template<bool propto, typename T_y , typename T_loc , typename T_covar >
return_type< T_y, T_loc, T_covar >::type multi_normal_prec_log (const T_y &y, const T_loc &mu, const T_covar &Sigma)
 
template<typename T_y , typename T_loc , typename T_covar >
return_type< T_y, T_loc, T_covar >::type multi_normal_prec_log (const T_y &y, const T_loc &mu, const T_covar &Sigma)
 
template<bool propto, typename T_y , typename T_loc , typename T_covar >
return_type< T_y, T_loc, T_covar >::type multi_normal_prec_lpdf (const T_y &y, const T_loc &mu, const T_covar &Sigma)
 
template<typename T_y , typename T_loc , typename T_covar >
return_type< T_y, T_loc, T_covar >::type multi_normal_prec_lpdf (const T_y &y, const T_loc &mu, const T_covar &Sigma)
 
template<class RNG >
Eigen::VectorXd multi_normal_rng (const Eigen::VectorXd &mu, const Eigen::MatrixXd &S, RNG &rng)
 Return a pseudo-random vector with a multi-variate normal distribution given the specified location parameter and covariance matrix and pseudo-random number generator. More...
 
template<bool propto, typename T_y , typename T_dof , typename T_loc , typename T_scale >
return_type< T_y, T_dof, T_loc, T_scale >::type multi_student_t_log (const T_y &y, const T_dof &nu, const T_loc &mu, const T_scale &Sigma)
 Return the log of the multivariate Student t distribution at the specified arguments. More...
 
template<typename T_y , typename T_dof , typename T_loc , typename T_scale >
return_type< T_y, T_dof, T_loc, T_scale >::type multi_student_t_log (const T_y &y, const T_dof &nu, const T_loc &mu, const T_scale &Sigma)
 
template<bool propto, typename T_y , typename T_dof , typename T_loc , typename T_scale >
return_type< T_y, T_dof, T_loc, T_scale >::type multi_student_t_lpdf (const T_y &y, const T_dof &nu, const T_loc &mu, const T_scale &Sigma)
 Return the log of the multivariate Student t distribution at the specified arguments. More...
 
template<typename T_y , typename T_dof , typename T_loc , typename T_scale >
return_type< T_y, T_dof, T_loc, T_scale >::type multi_student_t_lpdf (const T_y &y, const T_dof &nu, const T_loc &mu, const T_scale &Sigma)
 
template<class RNG >
Eigen::VectorXd multi_student_t_rng (double nu, const Eigen::Matrix< double, Eigen::Dynamic, 1 > &mu, const Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > &s, RNG &rng)
 
template<bool propto, typename T_prob >
boost::math::tools::promote_args< T_prob >::type multinomial_log (const std::vector< int > &ns, const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &theta)
 
template<typename T_prob >
boost::math::tools::promote_args< T_prob >::type multinomial_log (const std::vector< int > &ns, const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &theta)
 
template<bool propto, typename T_prob >
boost::math::tools::promote_args< T_prob >::type multinomial_lpmf (const std::vector< int > &ns, const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &theta)
 
template<typename T_prob >
boost::math::tools::promote_args< T_prob >::type multinomial_lpmf (const std::vector< int > &ns, const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &theta)
 
template<class RNG >
std::vector< int > multinomial_rng (const Eigen::Matrix< double, Eigen::Dynamic, 1 > &theta, int N, RNG &rng)
 
template<bool propto, typename T_lambda , typename T_cut >
boost::math::tools::promote_args< T_lambda, T_cut >::type ordered_logistic_log (int y, const T_lambda &lambda, const Eigen::Matrix< T_cut, Eigen::Dynamic, 1 > &c)
 Returns the (natural) log probability of the specified integer outcome given the continuous location and specified cutpoints in an ordered logistic model. More...
 
template<typename T_lambda , typename T_cut >
boost::math::tools::promote_args< T_lambda, T_cut >::type ordered_logistic_log (int y, const T_lambda &lambda, const Eigen::Matrix< T_cut, Eigen::Dynamic, 1 > &c)
 
template<typename T >
log_inv_logit_diff (const T &alpha, const T &beta)
 
template<bool propto, typename T_lambda , typename T_cut >
boost::math::tools::promote_args< T_lambda, T_cut >::type ordered_logistic_lpmf (int y, const T_lambda &lambda, const Eigen::Matrix< T_cut, Eigen::Dynamic, 1 > &c)
 Returns the (natural) log probability of the specified integer outcome given the continuous location and specified cutpoints in an ordered logistic model. More...
 
template<typename T_lambda , typename T_cut >
boost::math::tools::promote_args< T_lambda, T_cut >::type ordered_logistic_lpmf (int y, const T_lambda &lambda, const Eigen::Matrix< T_cut, Eigen::Dynamic, 1 > &c)
 
template<class RNG >
int ordered_logistic_rng (double eta, const Eigen::Matrix< double, Eigen::Dynamic, 1 > &c, RNG &rng)
 
template<bool propto, typename T_y , typename T_dof , typename T_scale >
boost::math::tools::promote_args< T_y, T_dof, T_scale >::type wishart_log (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &W, const T_dof &nu, const Eigen::Matrix< T_scale, Eigen::Dynamic, Eigen::Dynamic > &S)
 The log of the Wishart density for the given W, degrees of freedom, and scale matrix. More...
 
template<typename T_y , typename T_dof , typename T_scale >
boost::math::tools::promote_args< T_y, T_dof, T_scale >::type wishart_log (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &W, const T_dof &nu, const Eigen::Matrix< T_scale, Eigen::Dynamic, Eigen::Dynamic > &S)
 
template<bool propto, typename T_y , typename T_dof , typename T_scale >
boost::math::tools::promote_args< T_y, T_dof, T_scale >::type wishart_lpdf (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &W, const T_dof &nu, const Eigen::Matrix< T_scale, Eigen::Dynamic, Eigen::Dynamic > &S)
 The log of the Wishart density for the given W, degrees of freedom, and scale matrix. More...
 
template<typename T_y , typename T_dof , typename T_scale >
boost::math::tools::promote_args< T_y, T_dof, T_scale >::type wishart_lpdf (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &W, const T_dof &nu, const Eigen::Matrix< T_scale, Eigen::Dynamic, Eigen::Dynamic > &S)
 
template<class RNG >
Eigen::MatrixXd wishart_rng (double nu, const Eigen::MatrixXd &S, RNG &rng)
 
template<typename T_y , typename T_low , typename T_high >
void check_bounded (const char *function, const char *name, const T_y &y, const T_low &low, const T_high &high)
 Check if the value is between the low and high values, inclusively. More...
 
template<typename T >
void check_consistent_size (const char *function, const char *name, const T &x, size_t expected_size)
 Check if the dimension of x is consistent, which is defined to be expected_size if x is a vector or 1 if x is not a vector. More...
 
template<typename T1 , typename T2 >
void check_consistent_sizes (const char *function, const char *name1, const T1 &x1, const char *name2, const T2 &x2)
 Check if the dimension of x1 is consistent with x2. More...
 
template<typename T1 , typename T2 , typename T3 >
void check_consistent_sizes (const char *function, const char *name1, const T1 &x1, const char *name2, const T2 &x2, const char *name3, const T3 &x3)
 Check if the dimension of x1, x2, and x3 are consistent. More...
 
template<typename T1 , typename T2 , typename T3 , typename T4 >
void check_consistent_sizes (const char *function, const char *name1, const T1 &x1, const char *name2, const T2 &x2, const char *name3, const T3 &x3, const char *name4, const T4 &x4)
 Check if the dimension of x1, x2, x3, and x4 are consistent. More...
 
template<typename T1 , typename T2 , typename T3 , typename T4 , typename T5 >
void check_consistent_sizes (const char *function, const char *name1, const T1 &x1, const char *name2, const T2 &x2, const char *name3, const T3 &x3, const char *name4, const T4 &x4, const char *name5, const T5 &x5)
 
template<typename T_y >
void check_finite (const char *function, const char *name, const T_y &y)
 Check if y is finite. More...
 
template<typename T_y , typename T_low >
void check_greater (const char *function, const char *name, const T_y &y, const T_low &low)
 Check if y is strictly greater than low. More...
 
template<typename T_y , typename T_low >
void check_greater_or_equal (const char *function, const char *name, const T_y &y, const T_low &low)
 Check if y is greater or equal than low. More...
 
template<typename T_y , typename T_high >
void check_less (const char *function, const char *name, const T_y &y, const T_high &high)
 Check if y is strictly less than high. More...
 
template<typename T_y , typename T_high >
void check_less_or_equal (const char *function, const char *name, const T_y &y, const T_high &high)
 Check if y is less or equal to high. More...
 
template<typename T_y >
void check_nonnegative (const char *function, const char *name, const T_y &y)
 Check if y is non-negative. More...
 
template<typename T_y >
void check_not_nan (const char *function, const char *name, const T_y &y)
 Check if y is not NaN. More...
 
template<typename T_y >
void check_positive (const char *function, const char *name, const T_y &y)
 Check if y is positive. More...
 
template<typename T_y >
void check_positive_finite (const char *function, const char *name, const T_y &y)
 Check if y is positive and finite. More...
 
void check_positive_size (const char *function, const char *name, const char *expr, int size)
 Check if size is positive. More...
 
template<typename T_size1 , typename T_size2 >
void check_size_match (const char *function, const char *name_i, T_size1 i, const char *name_j, T_size2 j)
 Check if the provided sizes match. More...
 
template<typename T_size1 , typename T_size2 >
void check_size_match (const char *function, const char *expr_i, const char *name_i, T_size1 i, const char *expr_j, const char *name_j, T_size2 j)
 Check if the provided sizes match. More...
 
template<typename T >
void domain_error (const char *function, const char *name, const T &y, const char *msg1, const char *msg2)
 Throw a domain error with a consistently formatted message. More...
 
template<typename T >
void domain_error (const char *function, const char *name, const T &y, const char *msg1)
 Throw a domain error with a consistently formatted message. More...
 
template<typename T >
void domain_error_vec (const char *function, const char *name, const T &y, size_t i, const char *msg1, const char *msg2)
 Throw a domain error with a consistently formatted message. More...
 
template<typename T >
void domain_error_vec (const char *function, const char *name, const T &y, size_t i, const char *msg)
 Throw a domain error with a consistently formatted message. More...
 
template<typename T >
void invalid_argument (const char *function, const char *name, const T &y, const char *msg1, const char *msg2)
 Throw an invalid_argument exception with a consistently formatted message. More...
 
template<typename T >
void invalid_argument (const char *function, const char *name, const T &y, const char *msg1)
 Throw an invalid_argument exception with a consistently formatted message. More...
 
template<typename T >
void invalid_argument_vec (const char *function, const char *name, const T &y, size_t i, const char *msg1, const char *msg2)
 Throw an invalid argument exception with a consistently formatted message. More...
 
template<typename T >
void invalid_argument_vec (const char *function, const char *name, const T &y, size_t i, const char *msg)
 Throw an invalid argument exception with a consistently formatted message. More...
 
void out_of_range (const char *function, int max, int index, const char *msg1="", const char *msg2="")
 Throw an out_of_range exception with a consistently formatted message. More...
 
double abs (double x)
 Return floating-point absolute value. More...
 
double acosh (double x)
 Return the inverse hyperbolic cosine of the specified value. More...
 
double acosh (int x)
 Integer version of acosh. More...
 
template<typename T >
bool as_bool (const T x)
 Return 1 if the argument is unequal to zero and 0 otherwise. More...
 
double asinh (double x)
 Return the inverse hyperbolic sine of the specified value. More...
 
double asinh (int x)
 Integer version of asinh. More...
 
double atanh (double x)
 Return the inverse hyperbolic tangent of the specified value. More...
 
double atanh (int x)
 Integer version of atanh. More...
 
template<typename T2 >
T2 bessel_first_kind (int v, const T2 z)
 

\[ \mbox{bessel\_first\_kind}(v, x) = \begin{cases} J_v(x) & \mbox{if } -\infty\leq x \leq \infty \\[6pt] \textrm{error} & \mbox{if } x = \textrm{NaN} \end{cases} \]

More...
 
template<typename T2 >
T2 bessel_second_kind (int v, const T2 z)
 

\[ \mbox{bessel\_second\_kind}(v, x) = \begin{cases} \textrm{error} & \mbox{if } x \leq 0 \\ Y_v(x) & \mbox{if } x > 0 \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

More...
 
template<typename T >
boost::math::tools::promote_args< T >::type binary_log_loss (int y, const T y_hat)
 Returns the log loss function for binary classification with specified reference and response values. More...
 
template<typename T_N , typename T_n >
boost::math::tools::promote_args< T_N, T_n >::type binomial_coefficient_log (const T_N N, const T_n n)
 Return the log of the binomial coefficient for the specified arguments. More...
 
double cbrt (double x)
 Return the cube root of the specified value. More...
 
double cbrt (int x)
 Integer version of cbrt. More...
 
int choose (int n, int k)
 Return the binomial coefficient for the specified integer arguments. More...
 
double pi ()
 Return the value of pi. More...
 
double e ()
 Return the base of the natural logarithm. More...
 
double sqrt2 ()
 Return the square root of two. More...
 
double log10 ()
 Return natural logarithm of ten. More...
 
double positive_infinity ()
 Return positive infinity. More...
 
double negative_infinity ()
 Return negative infinity. More...
 
double not_a_number ()
 Return (quiet) not-a-number. More...
 
double machine_precision ()
 Returns the difference between 1.0 and the next value representable. More...
 
template<typename T >
corr_constrain (const T x)
 Return the result of transforming the specified scalar to have a valid correlation value between -1 and 1 (inclusive). More...
 
template<typename T >
corr_constrain (const T x, T &lp)
 Return the result of transforming the specified scalar to have a valid correlation value between -1 and 1 (inclusive). More...
 
template<typename T >
corr_free (const T y)
 Return the unconstrained scalar that when transformed to a valid correlation produces the specified value. More...
 
double digamma (double x)
 Return the derivative of the log gamma function at the specified value. More...
 
template<typename T1 , typename T2 >
stan::return_type< T1, T2 >::type divide (const T1 &x, const T2 &y)
 Return the division of the first scalar by the second scalar. More...
 
int divide (int x, int y)
 
double erf (double x)
 Return the error function of the specified value. More...
 
double erf (int x)
 Return the error function of the specified argument. More...
 
double erfc (double x)
 Return the complementary error function of the specified value. More...
 
double erfc (int x)
 Return the error function of the specified argument. More...
 
double exp (int x)
 Return the natural exponential of the specified argument. More...
 
double exp2 (double y)
 Return the exponent base 2 of the specified argument (C99, C++11). More...
 
double exp2 (int y)
 Return the exponent base 2 of the specified argument (C99, C++11). More...
 
double expm1 (double x)
 Return the natural exponentiation of x minus one. More...
 
double expm1 (int x)
 Integer version of expm1. More...
 
template<typename T >
F32 (T a, T b, T c, T d, T e, T z, T precision=1e-6)
 
template<typename T1 , typename T2 >
boost::math::tools::promote_args< T1, T2 >::type falling_factorial (const T1 x, const T2 n)
 

\[ \mbox{falling\_factorial}(x, n) = \begin{cases} \textrm{error} & \mbox{if } x \leq 0\\ (x)_n & \mbox{if } x > 0 \textrm{ and } -\infty \leq n \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN or } n = \textrm{NaN} \end{cases} \]

More...
 
template<typename T1 , typename T2 >
boost::math::tools::promote_args< T1, T2 >::type fdim (T1 x, T2 y)
 Return the positive difference of the specified values (C++11). More...
 
template<typename T , typename S >
void fill (T &x, const S &y)
 Fill the specified container with the specified value. More...
 
template<typename T1 , typename T2 , typename T3 >
boost::math::tools::promote_args< T1, T2, T3 >::type fma (const T1 &x, const T2 &y, const T3 &z)
 Return the product of the first two arguments plus the third argument. More...
 
template<typename T1 , typename T2 >
boost::math::tools::promote_args< T1, T2 >::type fmax (const T1 &x, const T2 &y)
 Return the greater of the two specified arguments. More...
 
template<typename T1 , typename T2 >
boost::math::tools::promote_args< T1, T2 >::type fmin (const T1 &x, const T2 &y)
 Return the lesser of the two specified arguments. More...
 
double gamma_p (double x, double a)
 

\[ \mbox{gamma\_p}(a, z) = \begin{cases} \textrm{error} & \mbox{if } a\leq 0 \textrm{ or } z < 0\\ P(a, z) & \mbox{if } a > 0, z \geq 0 \\[6pt] \textrm{NaN} & \mbox{if } a = \textrm{NaN or } z = \textrm{NaN} \end{cases} \]

More...
 
double gamma_q (double x, double a)
 

\[ \mbox{gamma\_q}(a, z) = \begin{cases} \textrm{error} & \mbox{if } a\leq 0 \textrm{ or } z < 0\\ Q(a, z) & \mbox{if } a > 0, z \geq 0 \\[6pt] \textrm{NaN} & \mbox{if } a = \textrm{NaN or } z = \textrm{NaN} \end{cases} \]

More...
 
template<typename T >
void grad_2F1 (T &gradA, T &gradC, T a, T b, T c, T z, T precision=1e-6)
 
template<typename T >
void grad_F32 (T *g, T a, T b, T c, T d, T e, T z, T precision=1e-6)
 
void grad_inc_beta (double &g1, double &g2, double a, double b, double z)
 
template<typename T >
void grad_reg_inc_beta (T &g1, T &g2, const T &a, const T &b, const T &z, const T &digammaA, const T &digammaB, const T &digammaSum, const T &betaAB)
 Computes the gradients of the regularized incomplete beta function. More...
 
template<typename T >
grad_reg_inc_gamma (T a, T z, T g, T dig, double precision=1e-6)
 Gradient of the regularized incomplete gamma functions igamma(a, z) More...
 
template<typename T1 , typename T2 >
boost::math::tools::promote_args< T1, T2 >::type hypot (const T1 &x, const T2 &y)
 Return the length of the hypoteneuse of a right triangle with opposite and adjacent side lengths given by the specified arguments (C++11). More...
 
double ibeta (double a, double b, double x)
 The normalized incomplete beta function of a, b, and x. More...
 
template<typename T >
identity_constrain (T x)
 Returns the result of applying the identity constraint transform to the input. More...
 
template<typename T >
identity_constrain (const T x, T &)
 Returns the result of applying the identity constraint transform to the input and increments the log probability reference with the log absolute Jacobian determinant. More...
 
template<typename T >
identity_free (const T y)
 Returns the result of applying the inverse of the identity constraint transform to the input. More...
 
template<typename T_true , typename T_false >
boost::math::tools::promote_args< T_true, T_false >::type if_else (const bool c, const T_true y_true, const T_false y_false)
 Return the second argument if the first argument is true and otherwise return the second argument. More...
 
double inc_beta (double a, double b, double x)
 
template<typename T >
inc_beta_ddb (T a, T b, T z, T digamma_b, T digamma_ab)
 Returns the partial derivative of the regularized incomplete beta function, I_{z}(a, b) with respect to b. More...
 
template<typename T >
inc_beta_dda (T a, T b, T z, T digamma_a, T digamma_ab)
 Returns the partial derivative of the regularized incomplete beta function, I_{z}(a, b) with respect to a. More...
 
template<typename T >
inc_beta_ddz (T a, T b, T z)
 Returns the partial derivative of the regularized incomplete beta function, I_{z}(a, b) with respect to z. More...
 
template<>
double inc_beta_ddz (double a, double b, double z)
 
template<typename T >
unsigned int int_step (const T y)
 The integer step, or Heaviside, function. More...
 
double inv (double x)
 
double inv_cloglog (double x)
 The inverse complementary log-log function. More...
 
double inv_logit (double a)
 Returns the inverse logit function applied to the argument. More...
 
double inv_Phi (double p)
 The inverse of the unit normal cumulative distribution function. More...
 
double inv_sqrt (double x)
 
double inv_square (double x)
 
int is_inf (double x)
 Returns 1 if the input is infinite and 0 otherwise. More...
 
bool is_nan (double x)
 Returns 1 if the input is NaN and 0 otherwise. More...
 
template<typename T >
bool is_uninitialized (T x)
 Returns true if the specified variable is uninitialized. More...
 
template<typename T , typename TL >
lb_constrain (const T x, const TL lb)
 Return the lower-bounded value for the specified unconstrained input and specified lower bound. More...
 
template<typename T , typename TL >
boost::math::tools::promote_args< T, TL >::type lb_constrain (const T x, const TL lb, T &lp)
 Return the lower-bounded value for the speicifed unconstrained input and specified lower bound, incrementing the specified reference with the log absolute Jacobian determinant of the transform. More...
 
template<typename T , typename TL >
boost::math::tools::promote_args< T, TL >::type lb_free (const T y, const TL lb)
 Return the unconstrained value that produces the specified lower-bound constrained value. More...
 
template<typename T1 , typename T2 >
boost::math::tools::promote_args< T1, T2 >::type lbeta (const T1 a, const T2 b)
 Return the log of the beta function applied to the specified arguments. More...
 
template<typename T >
ldexp (const T &a, int b)
 Returns the product of a (the significand) and 2 to power b (the exponent). More...
 
double lgamma (double x)
 Return the natural logarithm of the gamma function applied to the specified argument. More...
 
double lgamma (int x)
 Return the natural logarithm of the gamma function applied to the specified argument. More...
 
template<typename T >
boost::math::tools::promote_args< T >::type lmgamma (int k, T x)
 Return the natural logarithm of the multivariate gamma function with the speciifed dimensions and argument. More...
 
double log (int x)
 Return the natural log of the specified argument. More...
 
double log1m (double x)
 Return the natural logarithm of one minus the specified value. More...
 
double log1m_exp (double a)
 Calculates the natural logarithm of one minus the exponential of the specified value without overflow,. More...
 
double log1m_inv_logit (double u)
 Returns the natural logarithm of 1 minus the inverse logit of the specified argument. More...
 
double log1m_inv_logit (int u)
 Return the natural logarithm of one minus the inverse logit of the specified argument. More...
 
double log1p (double x)
 Return the natural logarithm of one plus the specified value. More...
 
double log1p (int x)
 Return the natural logarithm of one plus the specified argument. More...
 
double log1p_exp (double a)
 Calculates the log of 1 plus the exponential of the specified value without overflow. More...
 
double log2 (double u)
 Returns the base two logarithm of the argument (C99, C++11). More...
 
double log2 (int u)
 Return the base two logarithm of the specified argument. More...
 
double log2 ()
 Return natural logarithm of two. More...
 
template<typename T1 , typename T2 >
boost::math::tools::promote_args< T1, T2 >::type log_diff_exp (const T1 x, const T2 y)
 The natural logarithm of the difference of the natural exponentiation of x1 and the natural exponentiation of x2. More...
 
template<typename T1 , typename T2 >
boost::math::tools::promote_args< T1, T2 >::type log_falling_factorial (const T1 x, const T2 n)
 Return the natural log of the falling factorial of the specified arguments. More...
 
double log_inv_logit (double u)
 Returns the natural logarithm of the inverse logit of the specified argument. More...
 
double log_inv_logit (int u)
 Returns the natural logarithm of the inverse logit of the specified argument. More...
 
double log_mix (double theta, double lambda1, double lambda2)
 Return the log mixture density with specified mixing proportion and log densities. More...
 
template<typename T1 , typename T2 >
boost::math::tools::promote_args< T1, T2 >::type log_rising_factorial (const T1 &x, const T2 &n)
 Return the natural logarithm of the rising factorial from the first specified argument to the second. More...
 
template<typename T1 , typename T2 >
boost::math::tools::promote_args< T1, T2 >::type log_sum_exp (const T2 &a, const T1 &b)
 Calculates the log sum of exponetials without overflow. More...
 
template<typename T1 , typename T2 >
int logical_and (const T1 x1, const T2 x2)
 The logical and function which returns 1 if both arguments are unequal to zero and 0 otherwise. More...
 
template<typename T1 , typename T2 >
int logical_eq (const T1 x1, const T2 x2)
 Return 1 if the first argument is equal to the second. More...
 
template<typename T1 , typename T2 >
int logical_gt (const T1 x1, const T2 x2)
 Return 1 if the first argument is strictly greater than the second. More...
 
template<typename T1 , typename T2 >
int logical_gte (const T1 x1, const T2 x2)
 Return 1 if the first argument is greater than or equal to the second. More...
 
template<typename T1 , typename T2 >
int logical_lt (T1 x1, T2 x2)
 Return 1 if the first argument is strictly less than the second. More...
 
template<typename T1 , typename T2 >
int logical_lte (const T1 x1, const T2 x2)
 Return 1 if the first argument is less than or equal to the second. More...
 
template<typename T >
int logical_negation (const T x)
 The logical negation function which returns 1 if the input is equal to zero and 0 otherwise. More...
 
template<typename T1 , typename T2 >
int logical_neq (const T1 x1, const T2 x2)
 Return 1 if the first argument is unequal to the second. More...
 
template<typename T1 , typename T2 >
int logical_or (T1 x1, T2 x2)
 The logical or function which returns 1 if either argument is unequal to zero and 0 otherwise. More...
 
double logit (double u)
 Return the log odds of the argument. More...
 
double logit (int u)
 Return the log odds of the argument. More...
 
template<typename T , typename TL , typename TU >
boost::math::tools::promote_args< T, TL, TU >::type lub_constrain (const T x, TL lb, TU ub)
 Return the lower- and upper-bounded scalar derived by transforming the specified free scalar given the specified lower and upper bounds. More...
 
template<typename T , typename TL , typename TU >
boost::math::tools::promote_args< T, TL, TU >::type lub_constrain (const T x, const TL lb, const TU ub, T &lp)
 Return the lower- and upper-bounded scalar derived by transforming the specified free scalar given the specified lower and upper bounds and increment the specified log probability with the log absolute Jacobian determinant. More...
 
template<typename T , typename TL , typename TU >
boost::math::tools::promote_args< T, TL, TU >::type lub_free (const T y, TL lb, TU ub)
 Return the unconstrained scalar that transforms to the specified lower- and upper-bounded scalar given the specified bounds. More...
 
template<typename T2 >
T2 modified_bessel_first_kind (int v, const T2 z)
 

\[ \mbox{modified\_bessel\_first\_kind}(v, z) = \begin{cases} I_v(z) & \mbox{if } -\infty\leq z \leq \infty \\[6pt] \textrm{error} & \mbox{if } z = \textrm{NaN} \end{cases} \]

More...
 
template<typename T2 >
T2 modified_bessel_second_kind (int v, const T2 z)
 

\[ \mbox{modified\_bessel\_second\_kind}(v, z) = \begin{cases} \textrm{error} & \mbox{if } z \leq 0 \\ K_v(z) & \mbox{if } z > 0 \\[6pt] \textrm{NaN} & \mbox{if } z = \textrm{NaN} \end{cases} \]

More...
 
int modulus (int x, int y)
 
template<typename T_a , typename T_b >
boost::math::tools::promote_args< T_a, T_b >::type multiply_log (const T_a a, const T_b b)
 Calculated the value of the first argument times log of the second argument while behaving properly with 0 inputs. More...
 
double owens_t (double h, double a)
 Return the result of applying Owen's T function to the specified arguments. More...
 
double Phi (double x)
 The unit normal cumulative distribution function. More...
 
double Phi_approx (double x)
 Return an approximation of the unit normal CDF. More...
 
double Phi_approx (int x)
 Return an approximation of the unit normal CDF. More...
 
template<typename T >
positive_constrain (const T x)
 Return the positive value for the specified unconstrained input. More...
 
template<typename T >
positive_constrain (const T x, T &lp)
 Return the positive value for the specified unconstrained input, incrementing the scalar reference with the log absolute Jacobian determinant. More...
 
template<typename T >
positive_free (const T y)
 Return the unconstrained value corresponding to the specified positive-constrained value. More...
 
template<typename T >
boost::enable_if< boost::is_arithmetic< T >, T >::type primitive_value (T x)
 Return the value of the specified arithmetic argument unmodified with its own declared type. More...
 
template<typename T >
boost::disable_if< boost::is_arithmetic< T >, double >::type primitive_value (const T &x)
 Return the primitive value of the specified argument. More...
 
template<typename T >
prob_constrain (const T x)
 Return a probability value constrained to fall between 0 and 1 (inclusive) for the specified free scalar. More...
 
template<typename T >
prob_constrain (const T x, T &lp)
 Return a probability value constrained to fall between 0 and 1 (inclusive) for the specified free scalar and increment the specified log probability reference with the log absolute Jacobian determinant of the transform. More...
 
template<typename T >
prob_free (const T y)
 Return the free scalar that when transformed to a probability produces the specified scalar. More...
 
template<typename T , typename S >
promote_scalar_type< T, S >::type promote_scalar (const S &x)
 This is the top-level function to call to promote the scalar types of an input of type S to type T. More...
 
template<typename T1 , typename T2 >
boost::math::tools::promote_args< T1, T2 >::type rising_factorial (const T1 x, const T2 n)
 

\[ \mbox{rising\_factorial}(x, n) = \begin{cases} \textrm{error} & \mbox{if } x \leq 0\\ x^{(n)} & \mbox{if } x > 0 \textrm{ and } -\infty \leq n \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN or } n = \textrm{NaN} \end{cases} \]

More...
 
double round (double x)
 Return the closest integer to the specified argument, with halfway cases rounded away from zero. More...
 
double round (int x)
 Return the closest integer to the specified argument, with halfway cases rounded away from zero. More...
 
template<typename T >
int sign (const T &z)
 
double square (double x)
 Return the square of the specified argument. More...
 
template<typename T1 , typename T2 >
boost::math::tools::promote_args< T1, T2 >::type squared_distance (const T1 &x1, const T2 &x2)
 Returns the squared distance. More...
 
template<typename T >
int step (const T y)
 The step, or Heaviside, function. More...
 
double tgamma (double x)
 Return the gamma function applied to the specified argument. More...
 
template<typename T >
trigamma_impl (const T &x)
 Return the trigamma function applied to the argument. More...
 
double trigamma (double u)
 Return the second derivative of the log Gamma function evaluated at the specified argument. More...
 
double trigamma (int u)
 Return the second derivative of the log Gamma function evaluated at the specified argument. More...
 
double trunc (double x)
 Return the nearest integral value that is not larger in magnitude than the specified argument. More...
 
double trunc (int x)
 Return the nearest integral value that is not larger in magnitude than the specified argument. More...
 
template<typename T , typename TU >
boost::math::tools::promote_args< T, TU >::type ub_constrain (const T x, const TU ub)
 Return the upper-bounded value for the specified unconstrained scalar and upper bound. More...
 
template<typename T , typename TU >
boost::math::tools::promote_args< T, TU >::type ub_constrain (const T x, const TU ub, T &lp)
 Return the upper-bounded value for the specified unconstrained scalar and upper bound and increment the specified log probability reference with the log absolute Jacobian determinant of the transform. More...
 
template<typename T , typename TU >
boost::math::tools::promote_args< T, TU >::type ub_free (const T y, const TU ub)
 Return the free scalar that corresponds to the specified upper-bounded value with respect to the specified upper bound. More...
 
template<typename T >
double value_of (const T x)
 Return the value of the specified scalar argument converted to a double value. More...
 
template<>
double value_of< double > (double x)
 Return the specified argument. More...
 
template<typename T >
double value_of_rec (const T x)
 Return the value of the specified scalar argument converted to a double value. More...
 
template<>
double value_of_rec< double > (double x)
 Return the specified argument. More...
 
template<typename T_n , typename T_prob >
return_type< T_prob >::type bernoulli_ccdf_log (const T_n &n, const T_prob &theta)
 
template<typename T_n , typename T_prob >
return_type< T_prob >::type bernoulli_cdf (const T_n &n, const T_prob &theta)
 
template<typename T_n , typename T_prob >
return_type< T_prob >::type bernoulli_cdf_log (const T_n &n, const T_prob &theta)
 
template<typename T_n , typename T_prob >
return_type< T_prob >::type bernoulli_lccdf (const T_n &n, const T_prob &theta)
 
template<typename T_n , typename T_prob >
return_type< T_prob >::type bernoulli_lcdf (const T_n &n, const T_prob &theta)
 
template<bool propto, typename T_n , typename T_prob >
return_type< T_prob >::type bernoulli_log (const T_n &n, const T_prob &theta)
 
template<typename T_y , typename T_prob >
return_type< T_prob >::type bernoulli_log (const T_y &n, const T_prob &theta)
 
template<bool propto, typename T_n , typename T_prob >
return_type< T_prob >::type bernoulli_logit_log (const T_n &n, const T_prob &theta)
 
template<typename T_n , typename T_prob >
return_type< T_prob >::type bernoulli_logit_log (const T_n &n, const T_prob &theta)
 
template<bool propto, typename T_n , typename T_prob >
return_type< T_prob >::type bernoulli_logit_lpmf (const T_n &n, const T_prob &theta)
 
template<typename T_n , typename T_prob >
return_type< T_prob >::type bernoulli_logit_lpmf (const T_n &n, const T_prob &theta)
 
template<class RNG >
int bernoulli_logit_rng (double t, RNG &rng)
 A Bernoulli random number generator which takes as its argument the often more convenient logit-parametrization. More...
 
template<bool propto, typename T_n , typename T_prob >
return_type< T_prob >::type bernoulli_lpmf (const T_n &n, const T_prob &theta)
 
template<typename T_y , typename T_prob >
return_type< T_prob >::type bernoulli_lpmf (const T_y &n, const T_prob &theta)
 
template<class RNG >
int bernoulli_rng (double theta, RNG &rng)
 
template<typename T_n , typename T_N , typename T_size1 , typename T_size2 >
return_type< T_size1, T_size2 >::type beta_binomial_ccdf_log (const T_n &n, const T_N &N, const T_size1 &alpha, const T_size2 &beta)
 
template<typename T_n , typename T_N , typename T_size1 , typename T_size2 >
return_type< T_size1, T_size2 >::type beta_binomial_cdf (const T_n &n, const T_N &N, const T_size1 &alpha, const T_size2 &beta)
 
template<typename T_n , typename T_N , typename T_size1 , typename T_size2 >
return_type< T_size1, T_size2 >::type beta_binomial_cdf_log (const T_n &n, const T_N &N, const T_size1 &alpha, const T_size2 &beta)
 
template<typename T_n , typename T_N , typename T_size1 , typename T_size2 >
return_type< T_size1, T_size2 >::type beta_binomial_lccdf (const T_n &n, const T_N &N, const T_size1 &alpha, const T_size2 &beta)
 
template<typename T_n , typename T_N , typename T_size1 , typename T_size2 >
return_type< T_size1, T_size2 >::type beta_binomial_lcdf (const T_n &n, const T_N &N, const T_size1 &alpha, const T_size2 &beta)
 
template<bool propto, typename T_n , typename T_N , typename T_size1 , typename T_size2 >
return_type< T_size1, T_size2 >::type beta_binomial_log (const T_n &n, const T_N &N, const T_size1 &alpha, const T_size2 &beta)
 
template<typename T_n , typename T_N , typename T_size1 , typename T_size2 >
return_type< T_size1, T_size2 >::type beta_binomial_log (const T_n &n, const T_N &N, const T_size1 &alpha, const T_size2 &beta)
 
template<bool propto, typename T_n , typename T_N , typename T_size1 , typename T_size2 >
return_type< T_size1, T_size2 >::type beta_binomial_lpmf (const T_n &n, const T_N &N, const T_size1 &alpha, const T_size2 &beta)
 
template<typename T_n , typename T_N , typename T_size1 , typename T_size2 >
return_type< T_size1, T_size2 >::type beta_binomial_lpmf (const T_n &n, const T_N &N, const T_size1 &alpha, const T_size2 &beta)
 
template<class RNG >
int beta_binomial_rng (int N, double alpha, double beta, RNG &rng)
 
template<typename T_y , typename T_scale_succ , typename T_scale_fail >
return_type< T_y, T_scale_succ, T_scale_fail >::type beta_ccdf_log (const T_y &y, const T_scale_succ &alpha, const T_scale_fail &beta)
 
template<typename T_y , typename T_scale_succ , typename T_scale_fail >
return_type< T_y, T_scale_succ, T_scale_fail >::type beta_cdf (const T_y &y, const T_scale_succ &alpha, const T_scale_fail &beta)
 Calculates the beta cumulative distribution function for the given variate and scale variables. More...
 
template<typename T_y , typename T_scale_succ , typename T_scale_fail >
return_type< T_y, T_scale_succ, T_scale_fail >::type beta_cdf_log (const T_y &y, const T_scale_succ &alpha, const T_scale_fail &beta)
 
template<typename T_y , typename T_scale_succ , typename T_scale_fail >
return_type< T_y, T_scale_succ, T_scale_fail >::type beta_lccdf (const T_y &y, const T_scale_succ &alpha, const T_scale_fail &beta)
 
template<typename T_y , typename T_scale_succ , typename T_scale_fail >
return_type< T_y, T_scale_succ, T_scale_fail >::type beta_lcdf (const T_y &y, const T_scale_succ &alpha, const T_scale_fail &beta)
 
template<bool propto, typename T_y , typename T_scale_succ , typename T_scale_fail >
return_type< T_y, T_scale_succ, T_scale_fail >::type beta_log (const T_y &y, const T_scale_succ &alpha, const T_scale_fail &beta)
 The log of the beta density for the specified scalar(s) given the specified sample size(s). More...
 
template<typename T_y , typename T_scale_succ , typename T_scale_fail >
return_type< T_y, T_scale_succ, T_scale_fail >::type beta_log (const T_y &y, const T_scale_succ &alpha, const T_scale_fail &beta)
 
template<bool propto, typename T_y , typename T_scale_succ , typename T_scale_fail >
return_type< T_y, T_scale_succ, T_scale_fail >::type beta_lpdf (const T_y &y, const T_scale_succ &alpha, const T_scale_fail &beta)
 The log of the beta density for the specified scalar(s) given the specified sample size(s). More...
 
template<typename T_y , typename T_scale_succ , typename T_scale_fail >
return_type< T_y, T_scale_succ, T_scale_fail >::type beta_lpdf (const T_y &y, const T_scale_succ &alpha, const T_scale_fail &beta)
 
template<class RNG >
double beta_rng (double alpha, double beta, RNG &rng)
 
template<typename T_n , typename T_N , typename T_prob >
return_type< T_prob >::type binomial_ccdf_log (const T_n &n, const T_N &N, const T_prob &theta)
 
template<typename T_n , typename T_N , typename T_prob >
return_type< T_prob >::type binomial_cdf (const T_n &n, const T_N &N, const T_prob &theta)
 
template<typename T_n , typename T_N , typename T_prob >
return_type< T_prob >::type binomial_cdf_log (const T_n &n, const T_N &N, const T_prob &theta)
 
template<typename T_n , typename T_N , typename T_prob >
return_type< T_prob >::type binomial_lccdf (const T_n &n, const T_N &N, const T_prob &theta)
 
template<typename T_n , typename T_N , typename T_prob >
return_type< T_prob >::type binomial_lcdf (const T_n &n, const T_N &N, const T_prob &theta)
 
template<bool propto, typename T_n , typename T_N , typename T_prob >
return_type< T_prob >::type binomial_log (const T_n &n, const T_N &N, const T_prob &theta)
 
template<typename T_n , typename T_N , typename T_prob >
return_type< T_prob >::type binomial_log (const T_n &n, const T_N &N, const T_prob &theta)
 
template<bool propto, typename T_n , typename T_N , typename T_prob >
return_type< T_prob >::type binomial_logit_log (const T_n &n, const T_N &N, const T_prob &alpha)
 
template<typename T_n , typename T_N , typename T_prob >
return_type< T_prob >::type binomial_logit_log (const T_n &n, const T_N &N, const T_prob &alpha)
 
template<bool propto, typename T_n , typename T_N , typename T_prob >
return_type< T_prob >::type binomial_logit_lpmf (const T_n &n, const T_N &N, const T_prob &alpha)
 
template<typename T_n , typename T_N , typename T_prob >
return_type< T_prob >::type binomial_logit_lpmf (const T_n &n, const T_N &N, const T_prob &alpha)
 
template<bool propto, typename T_n , typename T_N , typename T_prob >
return_type< T_prob >::type binomial_lpmf (const T_n &n, const T_N &N, const T_prob &theta)
 
template<typename T_n , typename T_N , typename T_prob >
return_type< T_prob >::type binomial_lpmf (const T_n &n, const T_N &N, const T_prob &theta)
 
template<class RNG >
int binomial_rng (int N, double theta, RNG &rng)
 
template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type cauchy_ccdf_log (const T_y &y, const T_loc &mu, const T_scale &sigma)
 
template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type cauchy_cdf (const T_y &y, const T_loc &mu, const T_scale &sigma)
 Calculates the cauchy cumulative distribution function for the given variate, location, and scale. More...
 
template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type cauchy_cdf_log (const T_y &y, const T_loc &mu, const T_scale &sigma)
 
template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type cauchy_lccdf (const T_y &y, const T_loc &mu, const T_scale &sigma)
 
template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type cauchy_lcdf (const T_y &y, const T_loc &mu, const T_scale &sigma)
 
template<bool propto, typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type cauchy_log (const T_y &y, const T_loc &mu, const T_scale &sigma)
 The log of the Cauchy density for the specified scalar(s) given the specified location parameter(s) and scale parameter(s). More...
 
template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type cauchy_log (const T_y &y, const T_loc &mu, const T_scale &sigma)
 
template<bool propto, typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type cauchy_lpdf (const T_y &y, const T_loc &mu, const T_scale &sigma)
 The log of the Cauchy density for the specified scalar(s) given the specified location parameter(s) and scale parameter(s). More...
 
template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type cauchy_lpdf (const T_y &y, const T_loc &mu, const T_scale &sigma)
 
template<class RNG >
double cauchy_rng (double mu, double sigma, RNG &rng)
 
template<typename T_y , typename T_dof >
return_type< T_y, T_dof >::type chi_square_ccdf_log (const T_y &y, const T_dof &nu)
 
template<typename T_y , typename T_dof >
return_type< T_y, T_dof >::type chi_square_cdf (const T_y &y, const T_dof &nu)
 Calculates the chi square cumulative distribution function for the given variate and degrees of freedom. More...
 
template<typename T_y , typename T_dof >
return_type< T_y, T_dof >::type chi_square_cdf_log (const T_y &y, const T_dof &nu)
 
template<typename T_y , typename T_dof >
return_type< T_y, T_dof >::type chi_square_lccdf (const T_y &y, const T_dof &nu)
 
template<typename T_y , typename T_dof >
return_type< T_y, T_dof >::type chi_square_lcdf (const T_y &y, const T_dof &nu)
 
template<bool propto, typename T_y , typename T_dof >
return_type< T_y, T_dof >::type chi_square_log (const T_y &y, const T_dof &nu)
 The log of a chi-squared density for y with the specified degrees of freedom parameter. More...
 
template<typename T_y , typename T_dof >
return_type< T_y, T_dof >::type chi_square_log (const T_y &y, const T_dof &nu)
 
template<bool propto, typename T_y , typename T_dof >
return_type< T_y, T_dof >::type chi_square_lpdf (const T_y &y, const T_dof &nu)
 The log of a chi-squared density for y with the specified degrees of freedom parameter. More...
 
template<typename T_y , typename T_dof >
return_type< T_y, T_dof >::type chi_square_lpdf (const T_y &y, const T_dof &nu)
 
template<class RNG >
double chi_square_rng (double nu, RNG &rng)
 
template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type double_exponential_ccdf_log (const T_y &y, const T_loc &mu, const T_scale &sigma)
 
template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type double_exponential_cdf (const T_y &y, const T_loc &mu, const T_scale &sigma)
 Calculates the double exponential cumulative density function. More...
 
template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type double_exponential_cdf_log (const T_y &y, const T_loc &mu, const T_scale &sigma)
 
template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type double_exponential_lccdf (const T_y &y, const T_loc &mu, const T_scale &sigma)
 
template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type double_exponential_lcdf (const T_y &y, const T_loc &mu, const T_scale &sigma)
 
template<bool propto, typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type double_exponential_log (const T_y &y, const T_loc &mu, const T_scale &sigma)
 
template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type double_exponential_log (const T_y &y, const T_loc &mu, const T_scale &sigma)
 
template<bool propto, typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type double_exponential_lpdf (const T_y &y, const T_loc &mu, const T_scale &sigma)
 
template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type double_exponential_lpdf (const T_y &y, const T_loc &mu, const T_scale &sigma)
 
template<class RNG >
double double_exponential_rng (double mu, double sigma, RNG &rng)
 
template<typename T_y , typename T_loc , typename T_scale , typename T_inv_scale >
return_type< T_y, T_loc, T_scale, T_inv_scale >::type exp_mod_normal_ccdf_log (const T_y &y, const T_loc &mu, const T_scale &sigma, const T_inv_scale &lambda)
 
template<typename T_y , typename T_loc , typename T_scale , typename T_inv_scale >
return_type< T_y, T_loc, T_scale, T_inv_scale >::type exp_mod_normal_cdf (const T_y &y, const T_loc &mu, const T_scale &sigma, const T_inv_scale &lambda)
 
template<typename T_y , typename T_loc , typename T_scale , typename T_inv_scale >
return_type< T_y, T_loc, T_scale, T_inv_scale >::type exp_mod_normal_cdf_log (const T_y &y, const T_loc &mu, const T_scale &sigma, const T_inv_scale &lambda)
 
template<typename T_y , typename T_loc , typename T_scale , typename T_inv_scale >
return_type< T_y, T_loc, T_scale, T_inv_scale >::type exp_mod_normal_lccdf (const T_y &y, const T_loc &mu, const T_scale &sigma, const T_inv_scale &lambda)
 
template<typename T_y , typename T_loc , typename T_scale , typename T_inv_scale >
return_type< T_y, T_loc, T_scale, T_inv_scale >::type exp_mod_normal_lcdf (const T_y &y, const T_loc &mu, const T_scale &sigma, const T_inv_scale &lambda)
 
template<bool propto, typename T_y , typename T_loc , typename T_scale , typename T_inv_scale >
return_type< T_y, T_loc, T_scale, T_inv_scale >::type exp_mod_normal_log (const T_y &y, const T_loc &mu, const T_scale &sigma, const T_inv_scale &lambda)
 
template<typename T_y , typename T_loc , typename T_scale , typename T_inv_scale >
return_type< T_y, T_loc, T_scale, T_inv_scale >::type exp_mod_normal_log (const T_y &y, const T_loc &mu, const T_scale &sigma, const T_inv_scale &lambda)
 
template<bool propto, typename T_y , typename T_loc , typename T_scale , typename T_inv_scale >
return_type< T_y, T_loc, T_scale, T_inv_scale >::type exp_mod_normal_lpdf (const T_y &y, const T_loc &mu, const T_scale &sigma, const T_inv_scale &lambda)
 
template<typename T_y , typename T_loc , typename T_scale , typename T_inv_scale >
return_type< T_y, T_loc, T_scale, T_inv_scale >::type exp_mod_normal_lpdf (const T_y &y, const T_loc &mu, const T_scale &sigma, const T_inv_scale &lambda)
 
template<class RNG >
double exp_mod_normal_rng (double mu, double sigma, double lambda, RNG &rng)
 
template<typename T_y , typename T_inv_scale >
return_type< T_y, T_inv_scale >::type exponential_ccdf_log (const T_y &y, const T_inv_scale &beta)
 
template<typename T_y , typename T_inv_scale >
return_type< T_y, T_inv_scale >::type exponential_cdf (const T_y &y, const T_inv_scale &beta)
 Calculates the exponential cumulative distribution function for the given y and beta. More...
 
template<typename T_y , typename T_inv_scale >
return_type< T_y, T_inv_scale >::type exponential_cdf_log (const T_y &y, const T_inv_scale &beta)
 
template<typename T_y , typename T_inv_scale >
return_type< T_y, T_inv_scale >::type exponential_lccdf (const T_y &y, const T_inv_scale &beta)
 
template<typename T_y , typename T_inv_scale >
return_type< T_y, T_inv_scale >::type exponential_lcdf (const T_y &y, const T_inv_scale &beta)
 
template<bool propto, typename T_y , typename T_inv_scale >
return_type< T_y, T_inv_scale >::type exponential_log (const T_y &y, const T_inv_scale &beta)
 The log of an exponential density for y with the specified inverse scale parameter. More...
 
template<typename T_y , typename T_inv_scale >
return_type< T_y, T_inv_scale >::type exponential_log (const T_y &y, const T_inv_scale &beta)
 
template<bool propto, typename T_y , typename T_inv_scale >
return_type< T_y, T_inv_scale >::type exponential_lpdf (const T_y &y, const T_inv_scale &beta)
 The log of an exponential density for y with the specified inverse scale parameter. More...
 
template<typename T_y , typename T_inv_scale >
return_type< T_y, T_inv_scale >::type exponential_lpdf (const T_y &y, const T_inv_scale &beta)
 
template<class RNG >
double exponential_rng (double beta, RNG &rng)
 
template<typename T_y , typename T_shape , typename T_scale >
return_type< T_y, T_shape, T_scale >::type frechet_ccdf_log (const T_y &y, const T_shape &alpha, const T_scale &sigma)
 
template<typename T_y , typename T_shape , typename T_scale >
return_type< T_y, T_shape, T_scale >::type frechet_cdf (const T_y &y, const T_shape &alpha, const T_scale &sigma)
 
template<typename T_y , typename T_shape , typename T_scale >
return_type< T_y, T_shape, T_scale >::type frechet_cdf_log (const T_y &y, const T_shape &alpha, const T_scale &sigma)
 
template<typename T_y , typename T_shape , typename T_scale >
return_type< T_y, T_shape, T_scale >::type frechet_lccdf (const T_y &y, const T_shape &alpha, const T_scale &sigma)
 
template<typename T_y , typename T_shape , typename T_scale >
return_type< T_y, T_shape, T_scale >::type frechet_lcdf (const T_y &y, const T_shape &alpha, const T_scale &sigma)
 
template<bool propto, typename T_y , typename T_shape , typename T_scale >
return_type< T_y, T_shape, T_scale >::type frechet_log (const T_y &y, const T_shape &alpha, const T_scale &sigma)
 
template<typename T_y , typename T_shape , typename T_scale >
return_type< T_y, T_shape, T_scale >::type frechet_log (const T_y &y, const T_shape &alpha, const T_scale &sigma)
 
template<bool propto, typename T_y , typename T_shape , typename T_scale >
return_type< T_y, T_shape, T_scale >::type frechet_lpdf (const T_y &y, const T_shape &alpha, const T_scale &sigma)
 
template<typename T_y , typename T_shape , typename T_scale >
return_type< T_y, T_shape, T_scale >::type frechet_lpdf (const T_y &y, const T_shape &alpha, const T_scale &sigma)
 
template<class RNG >
double frechet_rng (double alpha, double sigma, RNG &rng)
 
template<typename T_y , typename T_shape , typename T_inv_scale >
return_type< T_y, T_shape, T_inv_scale >::type gamma_ccdf_log (const T_y &y, const T_shape &alpha, const T_inv_scale &beta)
 
template<typename T_y , typename T_shape , typename T_inv_scale >
return_type< T_y, T_shape, T_inv_scale >::type gamma_cdf (const T_y &y, const T_shape &alpha, const T_inv_scale &beta)
 The cumulative density function for a gamma distribution for y with the specified shape and inverse scale parameters. More...
 
template<typename T_y , typename T_shape , typename T_inv_scale >
return_type< T_y, T_shape, T_inv_scale >::type gamma_cdf_log (const T_y &y, const T_shape &alpha, const T_inv_scale &beta)
 
template<typename T_y , typename T_shape , typename T_inv_scale >
return_type< T_y, T_shape, T_inv_scale >::type gamma_lccdf (const T_y &y, const T_shape &alpha, const T_inv_scale &beta)
 
template<typename T_y , typename T_shape , typename T_inv_scale >
return_type< T_y, T_shape, T_inv_scale >::type gamma_lcdf (const T_y &y, const T_shape &alpha, const T_inv_scale &beta)
 
template<bool propto, typename T_y , typename T_shape , typename T_inv_scale >
return_type< T_y, T_shape, T_inv_scale >::type gamma_log (const T_y &y, const T_shape &alpha, const T_inv_scale &beta)
 The log of a gamma density for y with the specified shape and inverse scale parameters. More...
 
template<typename T_y , typename T_shape , typename T_inv_scale >
return_type< T_y, T_shape, T_inv_scale >::type gamma_log (const T_y &y, const T_shape &alpha, const T_inv_scale &beta)
 
template<bool propto, typename T_y , typename T_shape , typename T_inv_scale >
return_type< T_y, T_shape, T_inv_scale >::type gamma_lpdf (const T_y &y, const T_shape &alpha, const T_inv_scale &beta)
 The log of a gamma density for y with the specified shape and inverse scale parameters. More...
 
template<typename T_y , typename T_shape , typename T_inv_scale >
return_type< T_y, T_shape, T_inv_scale >::type gamma_lpdf (const T_y &y, const T_shape &alpha, const T_inv_scale &beta)
 
template<class RNG >
double gamma_rng (double alpha, double beta, RNG &rng)
 
template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type gumbel_ccdf_log (const T_y &y, const T_loc &mu, const T_scale &beta)
 
template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type gumbel_cdf (const T_y &y, const T_loc &mu, const T_scale &beta)
 
template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type gumbel_cdf_log (const T_y &y, const T_loc &mu, const T_scale &beta)
 
template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type gumbel_lccdf (const T_y &y, const T_loc &mu, const T_scale &beta)
 
template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type gumbel_lcdf (const T_y &y, const T_loc &mu, const T_scale &beta)
 
template<bool propto, typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type gumbel_log (const T_y &y, const T_loc &mu, const T_scale &beta)
 
template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type gumbel_log (const T_y &y, const T_loc &mu, const T_scale &beta)
 
template<bool propto, typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type gumbel_lpdf (const T_y &y, const T_loc &mu, const T_scale &beta)
 
template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type gumbel_lpdf (const T_y &y, const T_loc &mu, const T_scale &beta)
 
template<class RNG >
double gumbel_rng (double mu, double beta, RNG &rng)
 
template<bool propto, typename T_n , typename T_N , typename T_a , typename T_b >
double hypergeometric_log (const T_n &n, const T_N &N, const T_a &a, const T_b &b)
 
template<typename T_n , typename T_N , typename T_a , typename T_b >
double hypergeometric_log (const T_n &n, const T_N &N, const T_a &a, const T_b &b)
 
template<bool propto, typename T_n , typename T_N , typename T_a , typename T_b >
double hypergeometric_lpmf (const T_n &n, const T_N &N, const T_a &a, const T_b &b)
 
template<typename T_n , typename T_N , typename T_a , typename T_b >
double hypergeometric_lpmf (const T_n &n, const T_N &N, const T_a &a, const T_b &b)
 
template<class RNG >
int hypergeometric_rng (int N, int a, int b, RNG &rng)
 
template<typename T_y , typename T_dof >
return_type< T_y, T_dof >::type inv_chi_square_ccdf_log (const T_y &y, const T_dof &nu)
 
template<typename T_y , typename T_dof >
return_type< T_y, T_dof >::type inv_chi_square_cdf (const T_y &y, const T_dof &nu)
 
template<typename T_y , typename T_dof >
return_type< T_y, T_dof >::type inv_chi_square_cdf_log (const T_y &y, const T_dof &nu)
 
template<typename T_y , typename T_dof >
return_type< T_y, T_dof >::type inv_chi_square_lccdf (const T_y &y, const T_dof &nu)
 
template<typename T_y , typename T_dof >
return_type< T_y, T_dof >::type inv_chi_square_lcdf (const T_y &y, const T_dof &nu)
 
template<bool propto, typename T_y , typename T_dof >
return_type< T_y, T_dof >::type inv_chi_square_log (const T_y &y, const T_dof &nu)
 The log of an inverse chi-squared density for y with the specified degrees of freedom parameter. More...
 
template<typename T_y , typename T_dof >
return_type< T_y, T_dof >::type inv_chi_square_log (const T_y &y, const T_dof &nu)
 
template<bool propto, typename T_y , typename T_dof >
return_type< T_y, T_dof >::type inv_chi_square_lpdf (const T_y &y, const T_dof &nu)
 The log of an inverse chi-squared density for y with the specified degrees of freedom parameter. More...
 
template<typename T_y , typename T_dof >
return_type< T_y, T_dof >::type inv_chi_square_lpdf (const T_y &y, const T_dof &nu)
 
template<class RNG >
double inv_chi_square_rng (double nu, RNG &rng)
 
template<typename T_y , typename T_shape , typename T_scale >
return_type< T_y, T_shape, T_scale >::type inv_gamma_ccdf_log (const T_y &y, const T_shape &alpha, const T_scale &beta)
 
template<typename T_y , typename T_shape , typename T_scale >
return_type< T_y, T_shape, T_scale >::type inv_gamma_cdf (const T_y &y, const T_shape &alpha, const T_scale &beta)
 The CDF of an inverse gamma density for y with the specified shape and scale parameters. More...
 
template<typename T_y , typename T_shape , typename T_scale >
return_type< T_y, T_shape, T_scale >::type inv_gamma_cdf_log (const T_y &y, const T_shape &alpha, const T_scale &beta)
 
template<typename T_y , typename T_shape , typename T_scale >
return_type< T_y, T_shape, T_scale >::type inv_gamma_lccdf (const T_y &y, const T_shape &alpha, const T_scale &beta)
 
template<typename T_y , typename T_shape , typename T_scale >
return_type< T_y, T_shape, T_scale >::type inv_gamma_lcdf (const T_y &y, const T_shape &alpha, const T_scale &beta)
 
template<bool propto, typename T_y , typename T_shape , typename T_scale >
return_type< T_y, T_shape, T_scale >::type inv_gamma_log (const T_y &y, const T_shape &alpha, const T_scale &beta)
 The log of an inverse gamma density for y with the specified shape and scale parameters. More...
 
template<typename T_y , typename T_shape , typename T_scale >
return_type< T_y, T_shape, T_scale >::type inv_gamma_log (const T_y &y, const T_shape &alpha, const T_scale &beta)
 
template<bool propto, typename T_y , typename T_shape , typename T_scale >
return_type< T_y, T_shape, T_scale >::type inv_gamma_lpdf (const T_y &y, const T_shape &alpha, const T_scale &beta)
 The log of an inverse gamma density for y with the specified shape and scale parameters. More...
 
template<typename T_y , typename T_shape , typename T_scale >
return_type< T_y, T_shape, T_scale >::type inv_gamma_lpdf (const T_y &y, const T_shape &alpha, const T_scale &beta)
 
template<class RNG >
double inv_gamma_rng (double alpha, double beta, RNG &rng)
 
template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type logistic_ccdf_log (const T_y &y, const T_loc &mu, const T_scale &sigma)
 
template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type logistic_cdf (const T_y &y, const T_loc &mu, const T_scale &sigma)
 
template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type logistic_cdf_log (const T_y &y, const T_loc &mu, const T_scale &sigma)
 
template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type logistic_lccdf (const T_y &y, const T_loc &mu, const T_scale &sigma)
 
template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type logistic_lcdf (const T_y &y, const T_loc &mu, const T_scale &sigma)
 
template<bool propto, typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type logistic_log (const T_y &y, const T_loc &mu, const T_scale &sigma)
 
template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type logistic_log (const T_y &y, const T_loc &mu, const T_scale &sigma)
 
template<bool propto, typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type logistic_lpdf (const T_y &y, const T_loc &mu, const T_scale &sigma)
 
template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type logistic_lpdf (const T_y &y, const T_loc &mu, const T_scale &sigma)
 
template<class RNG >
double logistic_rng (double mu, double sigma, RNG &rng)
 
template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type lognormal_ccdf_log (const T_y &y, const T_loc &mu, const T_scale &sigma)
 
template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type lognormal_cdf (const T_y &y, const T_loc &mu, const T_scale &sigma)
 
template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type lognormal_cdf_log (const T_y &y, const T_loc &mu, const T_scale &sigma)
 
template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type lognormal_lccdf (const T_y &y, const T_loc &mu, const T_scale &sigma)
 
template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type lognormal_lcdf (const T_y &y, const T_loc &mu, const T_scale &sigma)
 
template<bool propto, typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type lognormal_log (const T_y &y, const T_loc &mu, const T_scale &sigma)
 
template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type lognormal_log (const T_y &y, const T_loc &mu, const T_scale &sigma)
 
template<bool propto, typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type lognormal_lpdf (const T_y &y, const T_loc &mu, const T_scale &sigma)
 
template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type lognormal_lpdf (const T_y &y, const T_loc &mu, const T_scale &sigma)
 
template<class RNG >
double lognormal_rng (double mu, double sigma, RNG &rng)
 
template<typename T_n , typename T_location , typename T_precision >
return_type< T_location, T_precision >::type neg_binomial_2_ccdf_log (const T_n &n, const T_location &mu, const T_precision &phi)
 
template<typename T_n , typename T_location , typename T_precision >
return_type< T_location, T_precision >::type neg_binomial_2_cdf (const T_n &n, const T_location &mu, const T_precision &phi)
 
template<typename T_n , typename T_location , typename T_precision >
return_type< T_location, T_precision >::type neg_binomial_2_cdf_log (const T_n &n, const T_location &mu, const T_precision &phi)
 
template<typename T_n , typename T_location , typename T_precision >
return_type< T_location, T_precision >::type neg_binomial_2_lccdf (const T_n &n, const T_location &mu, const T_precision &phi)
 
template<typename T_n , typename T_location , typename T_precision >
return_type< T_location, T_precision >::type neg_binomial_2_lcdf (const T_n &n, const T_location &mu, const T_precision &phi)
 
template<bool propto, typename T_n , typename T_location , typename T_precision >
return_type< T_location, T_precision >::type neg_binomial_2_log (const T_n &n, const T_location &mu, const T_precision &phi)
 
template<typename T_n , typename T_location , typename T_precision >
return_type< T_location, T_precision >::type neg_binomial_2_log (const T_n &n, const T_location &mu, const T_precision &phi)
 
template<bool propto, typename T_n , typename T_log_location , typename T_precision >
return_type< T_log_location, T_precision >::type neg_binomial_2_log_log (const T_n &n, const T_log_location &eta, const T_precision &phi)
 
template<typename T_n , typename T_log_location , typename T_precision >
return_type< T_log_location, T_precision >::type neg_binomial_2_log_log (const T_n &n, const T_log_location &eta, const T_precision &phi)
 
template<bool propto, typename T_n , typename T_log_location , typename T_precision >
return_type< T_log_location, T_precision >::type neg_binomial_2_log_lpmf (const T_n &n, const T_log_location &eta, const T_precision &phi)
 
template<typename T_n , typename T_log_location , typename T_precision >
return_type< T_log_location, T_precision >::type neg_binomial_2_log_lpmf (const T_n &n, const T_log_location &eta, const T_precision &phi)
 
template<class RNG >
int neg_binomial_2_log_rng (double eta, double phi, RNG &rng)
 
template<bool propto, typename T_n , typename T_location , typename T_precision >
return_type< T_location, T_precision >::type neg_binomial_2_lpmf (const T_n &n, const T_location &mu, const T_precision &phi)
 
template<typename T_n , typename T_location , typename T_precision >
return_type< T_location, T_precision >::type neg_binomial_2_lpmf (const T_n &n, const T_location &mu, const T_precision &phi)
 
template<class RNG >
int neg_binomial_2_rng (double mu, double phi, RNG &rng)
 
template<typename T_n , typename T_shape , typename T_inv_scale >
return_type< T_shape, T_inv_scale >::type neg_binomial_ccdf_log (const T_n &n, const T_shape &alpha, const T_inv_scale &beta)
 
template<typename T_n , typename T_shape , typename T_inv_scale >
return_type< T_shape, T_inv_scale >::type neg_binomial_cdf (const T_n &n, const T_shape &alpha, const T_inv_scale &beta)
 
template<typename T_n , typename T_shape , typename T_inv_scale >
return_type< T_shape, T_inv_scale >::type neg_binomial_cdf_log (const T_n &n, const T_shape &alpha, const T_inv_scale &beta)
 
template<typename T_n , typename T_shape , typename T_inv_scale >
return_type< T_shape, T_inv_scale >::type neg_binomial_lccdf (const T_n &n, const T_shape &alpha, const T_inv_scale &beta)
 
template<typename T_n , typename T_shape , typename T_inv_scale >
return_type< T_shape, T_inv_scale >::type neg_binomial_lcdf (const T_n &n, const T_shape &alpha, const T_inv_scale &beta)
 
template<bool propto, typename T_n , typename T_shape , typename T_inv_scale >
return_type< T_shape, T_inv_scale >::type neg_binomial_log (const T_n &n, const T_shape &alpha, const T_inv_scale &beta)
 
template<typename T_n , typename T_shape , typename T_inv_scale >
return_type< T_shape, T_inv_scale >::type neg_binomial_log (const T_n &n, const T_shape &alpha, const T_inv_scale &beta)
 
template<bool propto, typename T_n , typename T_shape , typename T_inv_scale >
return_type< T_shape, T_inv_scale >::type neg_binomial_lpmf (const T_n &n, const T_shape &alpha, const T_inv_scale &beta)
 
template<typename T_n , typename T_shape , typename T_inv_scale >
return_type< T_shape, T_inv_scale >::type neg_binomial_lpmf (const T_n &n, const T_shape &alpha, const T_inv_scale &beta)
 
template<class RNG >
int neg_binomial_rng (double alpha, double beta, RNG &rng)
 
template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type normal_ccdf_log (const T_y &y, const T_loc &mu, const T_scale &sigma)
 
template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type normal_cdf (const T_y &y, const T_loc &mu, const T_scale &sigma)
 Calculates the normal cumulative distribution function for the given variate, location, and scale. More...
 
template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type normal_cdf_log (const T_y &y, const T_loc &mu, const T_scale &sigma)
 
template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type normal_lccdf (const T_y &y, const T_loc &mu, const T_scale &sigma)
 
template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type normal_lcdf (const T_y &y, const T_loc &mu, const T_scale &sigma)
 
template<bool propto, typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type normal_log (const T_y &y, const T_loc &mu, const T_scale &sigma)
 The log of the normal density for the specified scalar(s) given the specified mean(s) and deviation(s). More...
 
template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type normal_log (const T_y &y, const T_loc &mu, const T_scale &sigma)
 
template<bool propto, typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type normal_lpdf (const T_y &y, const T_loc &mu, const T_scale &sigma)
 The log of the normal density for the specified scalar(s) given the specified mean(s) and deviation(s). More...
 
template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type normal_lpdf (const T_y &y, const T_loc &mu, const T_scale &sigma)
 
template<class RNG >
double normal_rng (double mu, double sigma, RNG &rng)
 
template<typename T_y , typename T_scale , typename T_shape >
return_type< T_y, T_scale, T_shape >::type pareto_ccdf_log (const T_y &y, const T_scale &y_min, const T_shape &alpha)
 
template<typename T_y , typename T_scale , typename T_shape >
return_type< T_y, T_scale, T_shape >::type pareto_cdf (const T_y &y, const T_scale &y_min, const T_shape &alpha)
 
template<typename T_y , typename T_scale , typename T_shape >
return_type< T_y, T_scale, T_shape >::type pareto_cdf_log (const T_y &y, const T_scale &y_min, const T_shape &alpha)
 
template<typename T_y , typename T_scale , typename T_shape >
return_type< T_y, T_scale, T_shape >::type pareto_lccdf (const T_y &y, const T_scale &y_min, const T_shape &alpha)
 
template<typename T_y , typename T_scale , typename T_shape >
return_type< T_y, T_scale, T_shape >::type pareto_lcdf (const T_y &y, const T_scale &y_min, const T_shape &alpha)
 
template<bool propto, typename T_y , typename T_scale , typename T_shape >
return_type< T_y, T_scale, T_shape >::type pareto_log (const T_y &y, const T_scale &y_min, const T_shape &alpha)
 
template<typename T_y , typename T_scale , typename T_shape >
return_type< T_y, T_scale, T_shape >::type pareto_log (const T_y &y, const T_scale &y_min, const T_shape &alpha)
 
template<bool propto, typename T_y , typename T_scale , typename T_shape >
return_type< T_y, T_scale, T_shape >::type pareto_lpdf (const T_y &y, const T_scale &y_min, const T_shape &alpha)
 
template<typename T_y , typename T_scale , typename T_shape >
return_type< T_y, T_scale, T_shape >::type pareto_lpdf (const T_y &y, const T_scale &y_min, const T_shape &alpha)
 
template<class RNG >
double pareto_rng (double y_min, double alpha, RNG &rng)
 
template<typename T_y , typename T_loc , typename T_scale , typename T_shape >
return_type< T_y, T_loc, T_scale, T_shape >::type pareto_type_2_ccdf_log (const T_y &y, const T_loc &mu, const T_scale &lambda, const T_shape &alpha)
 
template<typename T_y , typename T_loc , typename T_scale , typename T_shape >
return_type< T_y, T_loc, T_scale, T_shape >::type pareto_type_2_cdf (const T_y &y, const T_loc &mu, const T_scale &lambda, const T_shape &alpha)
 
template<typename T_y , typename T_loc , typename T_scale , typename T_shape >
return_type< T_y, T_loc, T_scale, T_shape >::type pareto_type_2_cdf_log (const T_y &y, const T_loc &mu, const T_scale &lambda, const T_shape &alpha)
 
template<typename T_y , typename T_loc , typename T_scale , typename T_shape >
return_type< T_y, T_loc, T_scale, T_shape >::type pareto_type_2_lccdf (const T_y &y, const T_loc &mu, const T_scale &lambda, const T_shape &alpha)
 
template<typename T_y , typename T_loc , typename T_scale , typename T_shape >
return_type< T_y, T_loc, T_scale, T_shape >::type pareto_type_2_lcdf (const T_y &y, const T_loc &mu, const T_scale &lambda, const T_shape &alpha)
 
template<bool propto, typename T_y , typename T_loc , typename T_scale , typename T_shape >
return_type< T_y, T_loc, T_scale, T_shape >::type pareto_type_2_log (const T_y &y, const T_loc &mu, const T_scale &lambda, const T_shape &alpha)
 
template<typename T_y , typename T_loc , typename T_scale , typename T_shape >
return_type< T_y, T_loc, T_scale, T_shape >::type pareto_type_2_log (const T_y &y, const T_loc &mu, const T_scale &lambda, const T_shape &alpha)
 
template<bool propto, typename T_y , typename T_loc , typename T_scale , typename T_shape >
return_type< T_y, T_loc, T_scale, T_shape >::type pareto_type_2_lpdf (const T_y &y, const T_loc &mu, const T_scale &lambda, const T_shape &alpha)
 
template<typename T_y , typename T_loc , typename T_scale , typename T_shape >
return_type< T_y, T_loc, T_scale, T_shape >::type pareto_type_2_lpdf (const T_y &y, const T_loc &mu, const T_scale &lambda, const T_shape &alpha)
 
template<class RNG >
double pareto_type_2_rng (double mu, double lambda, double alpha, RNG &rng)
 
template<typename T_n , typename T_rate >
return_type< T_rate >::type poisson_ccdf_log (const T_n &n, const T_rate &lambda)
 
template<typename T_n , typename T_rate >
return_type< T_rate >::type poisson_cdf (const T_n &n, const T_rate &lambda)
 
template<typename T_n , typename T_rate >
return_type< T_rate >::type poisson_cdf_log (const T_n &n, const T_rate &lambda)
 
template<typename T_n , typename T_rate >
return_type< T_rate >::type poisson_lccdf (const T_n &n, const T_rate &lambda)
 
template<typename T_n , typename T_rate >
return_type< T_rate >::type poisson_lcdf (const T_n &n, const T_rate &lambda)
 
template<bool propto, typename T_n , typename T_rate >
return_type< T_rate >::type poisson_log (const T_n &n, const T_rate &lambda)
 
template<typename T_n , typename T_rate >
return_type< T_rate >::type poisson_log (const T_n &n, const T_rate &lambda)
 
template<bool propto, typename T_n , typename T_log_rate >
return_type< T_log_rate >::type poisson_log_log (const T_n &n, const T_log_rate &alpha)
 
template<typename T_n , typename T_log_rate >
return_type< T_log_rate >::type poisson_log_log (const T_n &n, const T_log_rate &alpha)
 
template<bool propto, typename T_n , typename T_log_rate >
return_type< T_log_rate >::type poisson_log_lpmf (const T_n &n, const T_log_rate &alpha)
 
template<typename T_n , typename T_log_rate >
return_type< T_log_rate >::type poisson_log_lpmf (const T_n &n, const T_log_rate &alpha)
 
template<class RNG >
int poisson_log_rng (double alpha, RNG &rng)
 
template<bool propto, typename T_n , typename T_rate >
return_type< T_rate >::type poisson_lpmf (const T_n &n, const T_rate &lambda)
 
template<typename T_n , typename T_rate >
return_type< T_rate >::type poisson_lpmf (const T_n &n, const T_rate &lambda)
 
template<class RNG >
int poisson_rng (double lambda, RNG &rng)
 
template<typename T_y , typename T_scale >
return_type< T_y, T_scale >::type rayleigh_ccdf_log (const T_y &y, const T_scale &sigma)
 
template<typename T_y , typename T_scale >
return_type< T_y, T_scale >::type rayleigh_cdf (const T_y &y, const T_scale &sigma)
 
template<typename T_y , typename T_scale >
return_type< T_y, T_scale >::type rayleigh_cdf_log (const T_y &y, const T_scale &sigma)
 
template<typename T_y , typename T_scale >
return_type< T_y, T_scale >::type rayleigh_lccdf (const T_y &y, const T_scale &sigma)
 
template<typename T_y , typename T_scale >
return_type< T_y, T_scale >::type rayleigh_lcdf (const T_y &y, const T_scale &sigma)
 
template<bool propto, typename T_y , typename T_scale >
return_type< T_y, T_scale >::type rayleigh_log (const T_y &y, const T_scale &sigma)
 
template<typename T_y , typename T_scale >
return_type< T_y, T_scale >::type rayleigh_log (const T_y &y, const T_scale &sigma)
 
template<bool propto, typename T_y , typename T_scale >
return_type< T_y, T_scale >::type rayleigh_lpdf (const T_y &y, const T_scale &sigma)
 
template<typename T_y , typename T_scale >
return_type< T_y, T_scale >::type rayleigh_lpdf (const T_y &y, const T_scale &sigma)
 
template<class RNG >
double rayleigh_rng (double sigma, RNG &rng)
 
template<typename T_y , typename T_dof , typename T_scale >
return_type< T_y, T_dof, T_scale >::type scaled_inv_chi_square_ccdf_log (const T_y &y, const T_dof &nu, const T_scale &s)
 
template<typename T_y , typename T_dof , typename T_scale >
return_type< T_y, T_dof, T_scale >::type scaled_inv_chi_square_cdf (const T_y &y, const T_dof &nu, const T_scale &s)
 The CDF of a scaled inverse chi-squared density for y with the specified degrees of freedom parameter and scale parameter. More...
 
template<typename T_y , typename T_dof , typename T_scale >
return_type< T_y, T_dof, T_scale >::type scaled_inv_chi_square_cdf_log (const T_y &y, const T_dof &nu, const T_scale &s)
 
template<typename T_y , typename T_dof , typename T_scale >
return_type< T_y, T_dof, T_scale >::type scaled_inv_chi_square_lccdf (const T_y &y, const T_dof &nu, const T_scale &s)
 
template<typename T_y , typename T_dof , typename T_scale >
return_type< T_y, T_dof, T_scale >::type scaled_inv_chi_square_lcdf (const T_y &y, const T_dof &nu, const T_scale &s)
 
template<bool propto, typename T_y , typename T_dof , typename T_scale >
return_type< T_y, T_dof, T_scale >::type scaled_inv_chi_square_log (const T_y &y, const T_dof &nu, const T_scale &s)
 The log of a scaled inverse chi-squared density for y with the specified degrees of freedom parameter and scale parameter. More...
 
template<typename T_y , typename T_dof , typename T_scale >
return_type< T_y, T_dof, T_scale >::type scaled_inv_chi_square_log (const T_y &y, const T_dof &nu, const T_scale &s)
 
template<bool propto, typename T_y , typename T_dof , typename T_scale >
return_type< T_y, T_dof, T_scale >::type scaled_inv_chi_square_lpdf (const T_y &y, const T_dof &nu, const T_scale &s)
 The log of a scaled inverse chi-squared density for y with the specified degrees of freedom parameter and scale parameter. More...
 
template<typename T_y , typename T_dof , typename T_scale >
return_type< T_y, T_dof, T_scale >::type scaled_inv_chi_square_lpdf (const T_y &y, const T_dof &nu, const T_scale &s)
 
template<class RNG >
double scaled_inv_chi_square_rng (double nu, double s, RNG &rng)
 
template<typename T_y , typename T_loc , typename T_scale , typename T_shape >
return_type< T_y, T_loc, T_scale, T_shape >::type skew_normal_ccdf_log (const T_y &y, const T_loc &mu, const T_scale &sigma, const T_shape &alpha)
 
template<typename T_y , typename T_loc , typename T_scale , typename T_shape >
return_type< T_y, T_loc, T_scale, T_shape >::type skew_normal_cdf (const T_y &y, const T_loc &mu, const T_scale &sigma, const T_shape &alpha)
 
template<typename T_y , typename T_loc , typename T_scale , typename T_shape >
return_type< T_y, T_loc, T_scale, T_shape >::type skew_normal_cdf_log (const T_y &y, const T_loc &mu, const T_scale &sigma, const T_shape &alpha)
 
template<typename T_y , typename T_loc , typename T_scale , typename T_shape >
return_type< T_y, T_loc, T_scale, T_shape >::type skew_normal_lccdf (const T_y &y, const T_loc &mu, const T_scale &sigma, const T_shape &alpha)
 
template<typename T_y , typename T_loc , typename T_scale , typename T_shape >
return_type< T_y, T_loc, T_scale, T_shape >::type skew_normal_lcdf (const T_y &y, const T_loc &mu, const T_scale &sigma, const T_shape &alpha)
 
template<bool propto, typename T_y , typename T_loc , typename T_scale , typename T_shape >
return_type< T_y, T_loc, T_scale, T_shape >::type skew_normal_log (const T_y &y, const T_loc &mu, const T_scale &sigma, const T_shape &alpha)
 
template<typename T_y , typename T_loc , typename T_scale , typename T_shape >
return_type< T_y, T_loc, T_scale, T_shape >::type skew_normal_log (const T_y &y, const T_loc &mu, const T_scale &sigma, const T_shape &alpha)
 
template<bool propto, typename T_y , typename T_loc , typename T_scale , typename T_shape >
return_type< T_y, T_loc, T_scale, T_shape >::type skew_normal_lpdf (const T_y &y, const T_loc &mu, const T_scale &sigma, const T_shape &alpha)
 
template<typename T_y , typename T_loc , typename T_scale , typename T_shape >
return_type< T_y, T_loc, T_scale, T_shape >::type skew_normal_lpdf (const T_y &y, const T_loc &mu, const T_scale &sigma, const T_shape &alpha)
 
template<class RNG >
double skew_normal_rng (double mu, double sigma, double alpha, RNG &rng)
 
template<typename T_y , typename T_dof , typename T_loc , typename T_scale >
return_type< T_y, T_dof, T_loc, T_scale >::type student_t_ccdf_log (const T_y &y, const T_dof &nu, const T_loc &mu, const T_scale &sigma)
 
template<typename T_y , typename T_dof , typename T_loc , typename T_scale >
return_type< T_y, T_dof, T_loc, T_scale >::type student_t_cdf (const T_y &y, const T_dof &nu, const T_loc &mu, const T_scale &sigma)
 
template<typename T_y , typename T_dof , typename T_loc , typename T_scale >
return_type< T_y, T_dof, T_loc, T_scale >::type student_t_cdf_log (const T_y &y, const T_dof &nu, const T_loc &mu, const T_scale &sigma)
 
template<typename T_y , typename T_dof , typename T_loc , typename T_scale >
return_type< T_y, T_dof, T_loc, T_scale >::type student_t_lccdf (const T_y &y, const T_dof &nu, const T_loc &mu, const T_scale &sigma)
 
template<typename T_y , typename T_dof , typename T_loc , typename T_scale >
return_type< T_y, T_dof, T_loc, T_scale >::type student_t_lcdf (const T_y &y, const T_dof &nu, const T_loc &mu, const T_scale &sigma)
 
template<bool propto, typename T_y , typename T_dof , typename T_loc , typename T_scale >
return_type< T_y, T_dof, T_loc, T_scale >::type student_t_log (const T_y &y, const T_dof &nu, const T_loc &mu, const T_scale &sigma)
 The log of the Student-t density for the given y, nu, mean, and scale parameter. More...
 
template<typename T_y , typename T_dof , typename T_loc , typename T_scale >
return_type< T_y, T_dof, T_loc, T_scale >::type student_t_log (const T_y &y, const T_dof &nu, const T_loc &mu, const T_scale &sigma)
 
template<bool propto, typename T_y , typename T_dof , typename T_loc , typename T_scale >
return_type< T_y, T_dof, T_loc, T_scale >::type student_t_lpdf (const T_y &y, const T_dof &nu, const T_loc &mu, const T_scale &sigma)
 The log of the Student-t density for the given y, nu, mean, and scale parameter. More...
 
template<typename T_y , typename T_dof , typename T_loc , typename T_scale >
return_type< T_y, T_dof, T_loc, T_scale >::type student_t_lpdf (const T_y &y, const T_dof &nu, const T_loc &mu, const T_scale &sigma)
 
template<class RNG >
double student_t_rng (double nu, double mu, double sigma, RNG &rng)
 
template<typename T_y , typename T_low , typename T_high >
return_type< T_y, T_low, T_high >::type uniform_ccdf_log (const T_y &y, const T_low &alpha, const T_high &beta)
 
template<typename T_y , typename T_low , typename T_high >
return_type< T_y, T_low, T_high >::type uniform_cdf (const T_y &y, const T_low &alpha, const T_high &beta)
 
template<typename T_y , typename T_low , typename T_high >
return_type< T_y, T_low, T_high >::type uniform_cdf_log (const T_y &y, const T_low &alpha, const T_high &beta)
 
template<typename T_y , typename T_low , typename T_high >
return_type< T_y, T_low, T_high >::type uniform_lccdf (const T_y &y, const T_low &alpha, const T_high &beta)
 
template<typename T_y , typename T_low , typename T_high >
return_type< T_y, T_low, T_high >::type uniform_lcdf (const T_y &y, const T_low &alpha, const T_high &beta)
 
template<bool propto, typename T_y , typename T_low , typename T_high >
return_type< T_y, T_low, T_high >::type uniform_log (const T_y &y, const T_low &alpha, const T_high &beta)
 The log of a uniform density for the given y, lower, and upper bound. More...
 
template<typename T_y , typename T_low , typename T_high >
return_type< T_y, T_low, T_high >::type uniform_log (const T_y &y, const T_low &alpha, const T_high &beta)
 
template<bool propto, typename T_y , typename T_low , typename T_high >
return_type< T_y, T_low, T_high >::type uniform_lpdf (const T_y &y, const T_low &alpha, const T_high &beta)
 The log of a uniform density for the given y, lower, and upper bound. More...
 
template<typename T_y , typename T_low , typename T_high >
return_type< T_y, T_low, T_high >::type uniform_lpdf (const T_y &y, const T_low &alpha, const T_high &beta)
 
template<class RNG >
double uniform_rng (double alpha, double beta, RNG &rng)
 
template<bool propto, typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type von_mises_log (T_y const &y, T_loc const &mu, T_scale const &kappa)
 
template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type von_mises_log (T_y const &y, T_loc const &mu, T_scale const &kappa)
 
template<bool propto, typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type von_mises_lpdf (T_y const &y, T_loc const &mu, T_scale const &kappa)
 
template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type von_mises_lpdf (T_y const &y, T_loc const &mu, T_scale const &kappa)
 
template<class RNG >
double von_mises_rng (double mu, double kappa, RNG &rng)
 
template<typename T_y , typename T_shape , typename T_scale >
return_type< T_y, T_shape, T_scale >::type weibull_ccdf_log (const T_y &y, const T_shape &alpha, const T_scale &sigma)
 
template<typename T_y , typename T_shape , typename T_scale >
return_type< T_y, T_shape, T_scale >::type weibull_cdf (const T_y &y, const T_shape &alpha, const T_scale &sigma)
 
template<typename T_y , typename T_shape , typename T_scale >
return_type< T_y, T_shape, T_scale >::type weibull_cdf_log (const T_y &y, const T_shape &alpha, const T_scale &sigma)
 
template<typename T_y , typename T_shape , typename T_scale >
return_type< T_y, T_shape, T_scale >::type weibull_lccdf (const T_y &y, const T_shape &alpha, const T_scale &sigma)
 
template<typename T_y , typename T_shape , typename T_scale >
return_type< T_y, T_shape, T_scale >::type weibull_lcdf (const T_y &y, const T_shape &alpha, const T_scale &sigma)
 
template<bool propto, typename T_y , typename T_shape , typename T_scale >
return_type< T_y, T_shape, T_scale >::type weibull_log (const T_y &y, const T_shape &alpha, const T_scale &sigma)
 
template<typename T_y , typename T_shape , typename T_scale >
return_type< T_y, T_shape, T_scale >::type weibull_log (const T_y &y, const T_shape &alpha, const T_scale &sigma)
 
template<bool propto, typename T_y , typename T_shape , typename T_scale >
return_type< T_y, T_shape, T_scale >::type weibull_lpdf (const T_y &y, const T_shape &alpha, const T_scale &sigma)
 
template<typename T_y , typename T_shape , typename T_scale >
return_type< T_y, T_shape, T_scale >::type weibull_lpdf (const T_y &y, const T_shape &alpha, const T_scale &sigma)
 
template<class RNG >
double weibull_rng (double alpha, double sigma, RNG &rng)
 
template<bool propto, typename T_y , typename T_alpha , typename T_tau , typename T_beta , typename T_delta >
return_type< T_y, T_alpha, T_tau, T_beta, T_delta >::type wiener_log (const T_y &y, const T_alpha &alpha, const T_tau &tau, const T_beta &beta, const T_delta &delta)
 The log of the first passage time density function for a (Wiener) drift diffusion model for the given $y$, boundary separation $\alpha$, nondecision time $\tau$, relative bias $\beta$, and drift rate $\delta$. More...
 
template<typename T_y , typename T_alpha , typename T_tau , typename T_beta , typename T_delta >
return_type< T_y, T_alpha, T_tau, T_beta, T_delta >::type wiener_log (const T_y &y, const T_alpha &alpha, const T_tau &tau, const T_beta &beta, const T_delta &delta)
 
template<bool propto, typename T_y , typename T_alpha , typename T_tau , typename T_beta , typename T_delta >
return_type< T_y, T_alpha, T_tau, T_beta, T_delta >::type wiener_lpdf (const T_y &y, const T_alpha &alpha, const T_tau &tau, const T_beta &beta, const T_delta &delta)
 The log of the first passage time density function for a (Wiener) drift diffusion model for the given $y$, boundary separation $\alpha$, nondecision time $\tau$, relative bias $\beta$, and drift rate $\delta$. More...
 
template<typename T_y , typename T_alpha , typename T_tau , typename T_beta , typename T_delta >
return_type< T_y, T_alpha, T_tau, T_beta, T_delta >::type wiener_lpdf (const T_y &y, const T_alpha &alpha, const T_tau &tau, const T_beta &beta, const T_delta &delta)
 
template<typename T_initial , typename T_param >
std::vector< std::vector< typename stan::return_type< T_initial, T_param >::type > > decouple_ode_states (const std::vector< std::vector< double > > &y, const std::vector< T_initial > &y0, const std::vector< T_param > &theta)
 Takes sensitivity output from integrators and returns results in precomputed_gradients format. More...
 
template<>
std::vector< std::vector< double > > decouple_ode_states (const std::vector< std::vector< double > > &y, const std::vector< double > &y0, const std::vector< double > &theta)
 The decouple ODE states operation for the case of no sensitivities is equal to the indentity operation. More...
 
var log_sum_exp (const std::vector< var > &x)
 Returns the log sum of exponentials. More...
 
var sum (const std::vector< var > &m)
 Returns the sum of the entries of the specified vector. More...
 
std::vector< varto_var (const std::vector< double > &v)
 Converts argument to an automatic differentiation variable. More...
 
std::vector< varto_var (const std::vector< var > &v)
 Converts argument to an automatic differentiation variable. More...
 
void add_initial_values (const std::vector< var > &y0, std::vector< std::vector< var > > &y)
 Increment the state derived from the coupled system in the with the original initial state. More...
 
static bool empty_nested ()
 Return true if there is no nested autodiff being executed. More...
 
static void grad (vari *vi)
 Compute the gradient for all variables starting from the specified root variable implementation. More...
 
static size_t nested_size ()
 
var operator+ (const var &a, const var &b)
 Addition operator for variables (C++). More...
 
var operator+ (const var &a, double b)
 Addition operator for variable and scalar (C++). More...
 
var operator+ (double a, const var &b)
 Addition operator for scalar and variable (C++). More...
 
var operator/ (const var &a, const var &b)
 Division operator for two variables (C++). More...
 
var operator/ (const var &a, double b)
 Division operator for dividing a variable by a scalar (C++). More...
 
var operator/ (double a, const var &b)
 Division operator for dividing a scalar by a variable (C++). More...
 
bool operator== (const var &a, const var &b)
 Equality operator comparing two variables' values (C++). More...
 
bool operator== (const var &a, double b)
 Equality operator comparing a variable's value and a double (C++). More...
 
bool operator== (double a, const var &b)
 Equality operator comparing a scalar and a variable's value (C++). More...
 
bool operator> (const var &a, const var &b)
 Greater than operator comparing variables' values (C++). More...
 
bool operator> (const var &a, double b)
 Greater than operator comparing variable's value and double (C++). More...
 
bool operator> (double a, const var &b)
 Greater than operator comparing a double and a variable's value (C++). More...
 
bool operator>= (const var &a, const var &b)
 Greater than or equal operator comparing two variables' values (C++). More...
 
bool operator>= (const var &a, double b)
 Greater than or equal operator comparing variable's value and double (C++). More...
 
bool operator>= (double a, const var &b)
 Greater than or equal operator comparing double and variable's value (C++). More...
 
bool operator< (const var &a, const var &b)
 Less than operator comparing variables' values (C++). More...
 
bool operator< (const var &a, double b)
 Less than operator comparing variable's value and a double (C++). More...
 
bool operator< (double a, const var &b)
 Less than operator comparing a double and variable's value (C++). More...
 
bool operator<= (const var &a, const var &b)
 Less than or equal operator comparing two variables' values (C++). More...
 
bool operator<= (const var &a, double b)
 Less than or equal operator comparing a variable's value and a scalar (C++). More...
 
bool operator<= (double a, const var &b)
 Less than or equal operator comparing a double and variable's value (C++). More...
 
var operator* (const var &a, const var &b)
 Multiplication operator for two variables (C++). More...
 
var operator* (const var &a, double b)
 Multiplication operator for a variable and a scalar (C++). More...
 
var operator* (double a, const var &b)
 Multiplication operator for a scalar and a variable (C++). More...
 
bool operator!= (const var &a, const var &b)
 Inequality operator comparing two variables' values (C++). More...
 
bool operator!= (const var &a, double b)
 Inequality operator comparing a variable's value and a double (C++). More...
 
bool operator!= (double a, const var &b)
 Inequality operator comparing a double and a variable's value (C++). More...
 
var operator- (const var &a, const var &b)
 Subtraction operator for variables (C++). More...
 
var operator- (const var &a, double b)
 Subtraction operator for variable and scalar (C++). More...
 
var operator- (double a, const var &b)
 Subtraction operator for scalar and variable (C++). More...
 
varoperator-- (var &a)
 Prefix decrement operator for variables (C++). More...
 
var operator-- (var &a, int)
 Postfix decrement operator for variables (C++). More...
 
varoperator++ (var &a)
 Prefix increment operator for variables (C++). More...
 
var operator++ (var &a, int)
 Postfix increment operator for variables (C++). More...
 
var operator- (const var &a)
 Unary negation operator for variables (C++). More...
 
bool operator! (const var &a)
 Prefix logical negation for the value of variables (C++). More...
 
var operator+ (const var &a)
 Unary plus operator for variables (C++). More...
 
var precomputed_gradients (double value, const std::vector< var > &operands, const std::vector< double > &gradients)
 This function returns a var for an expression that has the specified value, vector of operands, and vector of partial derivatives of value with respect to the operands. More...
 
void print_stack (std::ostream &o)
 Prints the auto-dif variable stack. More...
 
static void recover_memory ()
 Recover memory used for all variables for reuse. More...
 
static void recover_memory_nested ()
 Recover only the memory used for the top nested call. More...
 
static void set_zero_all_adjoints ()
 Reset all adjoint values in the stack to zero. More...
 
static void set_zero_all_adjoints_nested ()
 Reset all adjoint values in the top nested portion of the stack to zero. More...
 
static void start_nested ()
 Record the current position so that recover_memory_nested() can find it. More...
 
static void grad (vari *vi)
 
Eigen::Matrix< var, -1, -1 > cholesky_decompose (const Eigen::Matrix< var, -1, -1 > &A)
 
template<typename T1 , int R1, int C1, typename T2 , int R2, int C2>
boost::enable_if_c< boost::is_same< T1, var >::value||boost::is_same< T2, var >::value, Eigen::Matrix< var, 1, C1 > >::type columns_dot_product (const Eigen::Matrix< T1, R1, C1 > &v1, const Eigen::Matrix< T2, R2, C2 > &v2)
 
template<int R, int C>
Eigen::Matrix< var, 1, C > columns_dot_self (const Eigen::Matrix< var, R, C > &x)
 Returns the dot product of each column of a matrix with itself. More...
 
template<typename T_x >
boost::enable_if_c< boost::is_same< typename scalar_type< T_x >::type, double >::value, Eigen::Matrix< var, -1, -1 > >::type cov_exp_quad (const std::vector< T_x > &x, const var &sigma, const var &l)
 Returns a squared exponential kernel. More...
 
template<typename T_x >
boost::enable_if_c< boost::is_same< typename scalar_type< T_x >::type, double >::value, Eigen::Matrix< var, -1, -1 > >::type cov_exp_quad (const std::vector< T_x > &x, double sigma, const var &l)
 Returns a squared exponential kernel. More...
 
matrix_v crossprod (const matrix_v &M)
 Returns the result of pre-multiplying a matrix by its own transpose. More...
 
template<int R, int C>
var determinant (const Eigen::Matrix< var, R, C > &m)
 
template<typename T1 , typename T2 , int R, int C>
Eigen::Matrix< var, R, C > divide (const Eigen::Matrix< T1, R, C > &v, const T2 &c)
 Return the division of the specified column vector by the specified scalar. More...
 
template<typename T1 , int R1, int C1, typename T2 , int R2, int C2>
boost::enable_if_c< boost::is_same< T1, var >::value||boost::is_same< T2, var >::value, var >::type dot_product (const Eigen::Matrix< T1, R1, C1 > &v1, const Eigen::Matrix< T2, R2, C2 > &v2)
 Returns the dot product. More...
 
template<typename T1 , typename T2 >
boost::enable_if_c< boost::is_same< T1, var >::value||boost::is_same< T2, var >::value, var >::type dot_product (const T1 *v1, const T2 *v2, size_t length)
 Returns the dot product. More...
 
template<typename T1 , typename T2 >
boost::enable_if_c< boost::is_same< T1, var >::value||boost::is_same< T2, var >::value, var >::type dot_product (const std::vector< T1 > &v1, const std::vector< T2 > &v2)
 Returns the dot product. More...
 
template<int R, int C>
var dot_self (const Eigen::Matrix< var, R, C > &v)
 Returns the dot product of a vector with itself. More...
 
void grad (var &v, Eigen::Matrix< var, Eigen::Dynamic, 1 > &x, Eigen::VectorXd &g)
 Propagate chain rule to calculate gradients starting from the specified variable. More...
 
void initialize_variable (var &variable, const var &value)
 Initialize variable to value. More...
 
template<int R, int C>
void initialize_variable (Eigen::Matrix< var, R, C > &matrix, const var &value)
 Initialize every cell in the matrix to the specified value. More...
 
template<typename T >
void initialize_variable (std::vector< T > &variables, const var &value)
 Initialize the variables in the standard vector recursively. More...
 
template<int R, int C>
var log_determinant (const Eigen::Matrix< var, R, C > &m)
 
template<int R, int C>
var log_determinant_ldlt (LDLT_factor< var, R, C > &A)
 
template<int R, int C>
var log_determinant_spd (const Eigen::Matrix< var, R, C > &m)
 
Eigen::Matrix< var, Eigen::Dynamic, 1 > log_softmax (const Eigen::Matrix< var, Eigen::Dynamic, 1 > &alpha)
 Return the softmax of the specified Eigen vector. More...
 
template<int R, int C>
var log_sum_exp (const Eigen::Matrix< var, R, C > &x)
 Returns the log sum of exponentials. More...
 
template<int R1, int C1, int R2, int C2>
Eigen::Matrix< var, R1, C2 > mdivide_left (const Eigen::Matrix< var, R1, C1 > &A, const Eigen::Matrix< var, R2, C2 > &b)
 
template<int R1, int C1, int R2, int C2>
Eigen::Matrix< var, R1, C2 > mdivide_left (const Eigen::Matrix< var, R1, C1 > &A, const Eigen::Matrix< double, R2, C2 > &b)
 
template<int R1, int C1, int R2, int C2>
Eigen::Matrix< var, R1, C2 > mdivide_left (const Eigen::Matrix< double, R1, C1 > &A, const Eigen::Matrix< var, R2, C2 > &b)
 
template<int R1, int C1, int R2, int C2>
Eigen::Matrix< var, R1, C2 > mdivide_left_ldlt (const LDLT_factor< var, R1, C1 > &A, const Eigen::Matrix< var, R2, C2 > &b)
 Returns the solution of the system Ax=b given an LDLT_factor of A. More...
 
template<int R1, int C1, int R2, int C2>
Eigen::Matrix< var, R1, C2 > mdivide_left_ldlt (const LDLT_factor< var, R1, C1 > &A, const Eigen::Matrix< double, R2, C2 > &b)
 Returns the solution of the system Ax=b given an LDLT_factor of A. More...
 
template<int R1, int C1, int R2, int C2>
Eigen::Matrix< var, R1, C2 > mdivide_left_ldlt (const LDLT_factor< double, R1, C1 > &A, const Eigen::Matrix< var, R2, C2 > &b)
 Returns the solution of the system Ax=b given an LDLT_factor of A. More...
 
template<int R1, int C1, int R2, int C2>
Eigen::Matrix< var, R1, C2 > mdivide_left_spd (const Eigen::Matrix< var, R1, C1 > &A, const Eigen::Matrix< var, R2, C2 > &b)
 
template<int R1, int C1, int R2, int C2>
Eigen::Matrix< var, R1, C2 > mdivide_left_spd (const Eigen::Matrix< var, R1, C1 > &A, const Eigen::Matrix< double, R2, C2 > &b)
 
template<int R1, int C1, int R2, int C2>
Eigen::Matrix< var, R1, C2 > mdivide_left_spd (const Eigen::Matrix< double, R1, C1 > &A, const Eigen::Matrix< var, R2, C2 > &b)
 
template<int TriView, int R1, int C1, int R2, int C2>
Eigen::Matrix< var, R1, C2 > mdivide_left_tri (const Eigen::Matrix< var, R1, C1 > &A, const Eigen::Matrix< var, R2, C2 > &b)
 
template<int TriView, int R1, int C1, int R2, int C2>
Eigen::Matrix< var, R1, C2 > mdivide_left_tri (const Eigen::Matrix< double, R1, C1 > &A, const Eigen::Matrix< var, R2, C2 > &b)
 
template<int TriView, int R1, int C1, int R2, int C2>
Eigen::Matrix< var, R1, C2 > mdivide_left_tri (const Eigen::Matrix< var, R1, C1 > &A, const Eigen::Matrix< double, R2, C2 > &b)
 
template<typename T1 , typename T2 >
boost::enable_if_c<(boost::is_scalar< T1 >::value||boost::is_same< T1, var >::value) &&(boost::is_scalar< T2 >::value||boost::is_same< T2, var >::value), typename boost::math::tools::promote_args< T1, T2 >::type >::type multiply (const T1 &v, const T2 &c)
 Return the product of two scalars. More...
 
template<typename T1 , typename T2 , int R2, int C2>
Eigen::Matrix< var, R2, C2 > multiply (const T1 &c, const Eigen::Matrix< T2, R2, C2 > &m)
 Return the product of scalar and matrix. More...
 
template<typename T1 , int R1, int C1, typename T2 >
Eigen::Matrix< var, R1, C1 > multiply (const Eigen::Matrix< T1, R1, C1 > &m, const T2 &c)
 Return the product of scalar and matrix. More...
 
template<typename TA , int RA, int CA, typename TB , int CB>
boost::enable_if_c< boost::is_same< TA, var >::value||boost::is_same< TB, var >::value, Eigen::Matrix< var, RA, CB > >::type multiply (const Eigen::Matrix< TA, RA, CA > &A, const Eigen::Matrix< TB, CA, CB > &B)
 Return the product of two matrices. More...
 
template<typename TA , int CA, typename TB >
boost::enable_if_c< boost::is_same< TA, var >::value||boost::is_same< TB, var >::value, var >::type multiply (const Eigen::Matrix< TA, 1, CA > &A, const Eigen::Matrix< TB, CA, 1 > &B)
 Return the scalar product of a row vector and a vector. More...
 
matrix_v multiply_lower_tri_self_transpose (const matrix_v &L)
 
template<typename TA , int RA, int CA, typename TB , int RB, int CB>
boost::enable_if_c< boost::is_same< TA, var >::value||boost::is_same< TB, var >::value, Eigen::Matrix< var, CB, CB > >::type quad_form (const Eigen::Matrix< TA, RA, CA > &A, const Eigen::Matrix< TB, RB, CB > &B)
 
template<typename TA , int RA, int CA, typename TB , int RB>
boost::enable_if_c< boost::is_same< TA, var >::value||boost::is_same< TB, var >::value, var >::type quad_form (const Eigen::Matrix< TA, RA, CA > &A, const Eigen::Matrix< TB, RB, 1 > &B)
 
template<typename TA , int RA, int CA, typename TB , int RB, int CB>
boost::enable_if_c< boost::is_same< TA, var >::value||boost::is_same< TB, var >::value, Eigen::Matrix< var, CB, CB > >::type quad_form_sym (const Eigen::Matrix< TA, RA, CA > &A, const Eigen::Matrix< TB, RB, CB > &B)
 
template<typename TA , int RA, int CA, typename TB , int RB>
boost::enable_if_c< boost::is_same< TA, var >::value||boost::is_same< TB, var >::value, var >::type quad_form_sym (const Eigen::Matrix< TA, RA, CA > &A, const Eigen::Matrix< TB, RB, 1 > &B)
 
template<typename T1 , int R1, int C1, typename T2 , int R2, int C2>
boost::enable_if_c< boost::is_same< T1, var >::value||boost::is_same< T2, var >::value, Eigen::Matrix< var, R1, 1 > >::type rows_dot_product (const Eigen::Matrix< T1, R1, C1 > &v1, const Eigen::Matrix< T2, R2, C2 > &v2)
 
var sd (const std::vector< var > &v)
 Return the sample standard deviation of the specified standard vector. More...
 
template<int R, int C>
var sd (const Eigen::Matrix< var, R, C > &m)
 
Eigen::Matrix< var, Eigen::Dynamic, 1 > softmax (const Eigen::Matrix< var, Eigen::Dynamic, 1 > &alpha)
 Return the softmax of the specified Eigen vector. More...
 
template<int R1, int C1, int R2, int C2>
var squared_distance (const Eigen::Matrix< var, R1, C1 > &v1, const Eigen::Matrix< var, R2, C2 > &v2)
 
template<int R1, int C1, int R2, int C2>
var squared_distance (const Eigen::Matrix< var, R1, C1 > &v1, const Eigen::Matrix< double, R2, C2 > &v2)
 
template<int R1, int C1, int R2, int C2>
var squared_distance (const Eigen::Matrix< double, R1, C1 > &v1, const Eigen::Matrix< var, R2, C2 > &v2)
 
void stan_print (std::ostream *o, const var &x)
 
template<int R, int C>
var sum (const Eigen::Matrix< var, R, C > &m)
 Returns the sum of the coefficients of the specified matrix, column vector or row vector. More...
 
matrix_v tcrossprod (const matrix_v &M)
 Returns the result of post-multiplying a matrix by its own transpose. More...
 
matrix_v to_var (const matrix_d &m)
 Converts argument to an automatic differentiation variable. More...
 
matrix_v to_var (const matrix_v &m)
 Converts argument to an automatic differentiation variable. More...
 
vector_v to_var (const vector_d &v)
 Converts argument to an automatic differentiation variable. More...
 
vector_v to_var (const vector_v &v)
 Converts argument to an automatic differentiation variable. More...
 
row_vector_v to_var (const row_vector_d &rv)
 Converts argument to an automatic differentiation variable. More...
 
row_vector_v to_var (const row_vector_v &rv)
 Converts argument to an automatic differentiation variable. More...
 
template<typename T1 , int R1, int C1, typename T2 , int R2, int C2, typename T3 , int R3, int C3>
boost::enable_if_c< stan::is_var< T1 >::value||stan::is_var< T2 >::value||stan::is_var< T3 >::value, var >::type trace_gen_inv_quad_form_ldlt (const Eigen::Matrix< T1, R1, C1 > &D, const LDLT_factor< T2, R2, C2 > &A, const Eigen::Matrix< T3, R3, C3 > &B)
 Compute the trace of an inverse quadratic form. More...
 
template<typename TD , int RD, int CD, typename TA , int RA, int CA, typename TB , int RB, int CB>
boost::enable_if_c< boost::is_same< TD, var >::value||boost::is_same< TA, var >::value||boost::is_same< TB, var >::value, var >::type trace_gen_quad_form (const Eigen::Matrix< TD, RD, CD > &D, const Eigen::Matrix< TA, RA, CA > &A, const Eigen::Matrix< TB, RB, CB > &B)
 
template<typename T2 , int R2, int C2, typename T3 , int R3, int C3>
boost::enable_if_c< stan::is_var< T2 >::value||stan::is_var< T3 >::value, var >::type trace_inv_quad_form_ldlt (const LDLT_factor< T2, R2, C2 > &A, const Eigen::Matrix< T3, R3, C3 > &B)
 Compute the trace of an inverse quadratic form. More...
 
template<typename TA , int RA, int CA, typename TB , int RB, int CB>
boost::enable_if_c< boost::is_same< TA, var >::value||boost::is_same< TB, var >::value, var >::type trace_quad_form (const Eigen::Matrix< TA, RA, CA > &A, const Eigen::Matrix< TB, RB, CB > &B)
 
template<int R, int C>
Eigen::Matrix< var, R, C > unit_vector_constrain (const Eigen::Matrix< var, R, C > &y)
 Return the unit length vector corresponding to the free vector y. More...
 
template<int R, int C>
Eigen::Matrix< var, R, C > unit_vector_constrain (const Eigen::Matrix< var, R, C > &y, var &lp)
 Return the unit length vector corresponding to the free vector y. More...
 
var variance (const std::vector< var > &v)
 Return the sample variance of the specified standard vector. More...
 
template<int R, int C>
var variance (const Eigen::Matrix< var, R, C > &m)
 
void cvodes_silent_err_handler (int error_code, const char *module, const char *function, char *msg, void *eh_data)
 
void cvodes_check_flag (int flag, const std::string &func_name)
 
void cvodes_set_options (void *cvodes_mem, double rel_tol, double abs_tol, long int max_num_steps)
 
template<typename F >
void gradient (const F &f, const Eigen::Matrix< double, Eigen::Dynamic, 1 > &x, double &fx, Eigen::Matrix< double, Eigen::Dynamic, 1 > &grad_fx)
 Calculate the value and the gradient of the specified function at the specified argument. More...
 
void free_cvodes_memory (N_Vector &cvodes_state, N_Vector *cvodes_state_sens, void *cvodes_mem, size_t S)
 Free memory allocated for CVODES state, sensitivity, and general memory. More...
 
template<typename F , typename T_initial , typename T_param >
std::vector< std::vector< typename stan::return_type< T_initial, T_param >::type > > integrate_ode_bdf (const F &f, const std::vector< T_initial > &y0, double t0, const std::vector< double > &ts, const std::vector< T_param > &theta, const std::vector< double > &x, const std::vector< int > &x_int, std::ostream *msgs=0, double relative_tolerance=1e-10, double absolute_tolerance=1e-10, long int max_num_steps=1e8)
 Return the solutions for the specified system of ordinary differential equations given the specified initial state, initial times, times of desired solution, and parameters and data, writing error and warning messages to the specified stream. More...
 
template<typename F >
void jacobian (const F &f, const Eigen::Matrix< double, Eigen::Dynamic, 1 > &x, Eigen::Matrix< double, Eigen::Dynamic, 1 > &fx, Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > &J)
 
var abs (const var &a)
 Return the absolute value of the variable (std). More...
 
var acos (const var &a)
 Return the principal value of the arc cosine of a variable, in radians (cmath). More...
 
var acosh (const var &a)
 The inverse hyperbolic cosine function for variables (C99). More...
 
int as_bool (const var &v)
 Return 1 if the argument is unequal to zero and 0 otherwise. More...
 
var asin (const var &a)
 Return the principal value of the arc sine, in radians, of the specified variable (cmath). More...
 
var asinh (const var &a)
 The inverse hyperbolic sine function for variables (C99). More...
 
var atan (const var &a)
 Return the principal value of the arc tangent, in radians, of the specified variable (cmath). More...
 
var atan2 (const var &a, const var &b)
 Return the principal value of the arc tangent, in radians, of the first variable divided by the second (cmath). More...
 
var atan2 (const var &a, double b)
 Return the principal value of the arc tangent, in radians, of the first variable divided by the second scalar (cmath). More...
 
var atan2 (double a, const var &b)
 Return the principal value of the arc tangent, in radians, of the first scalar divided by the second variable (cmath). More...
 
var atanh (const var &a)
 The inverse hyperbolic tangent function for variables (C99). More...
 
var bessel_first_kind (int v, const var &a)
 
var bessel_second_kind (int v, const var &a)
 
var binary_log_loss (int y, const var &y_hat)
 The log loss function for variables (stan). More...
 
double calculate_chain (double x, double val)
 
var cbrt (const var &a)
 Returns the cube root of the specified variable (C99). More...
 
var ceil (const var &a)
 Return the ceiling of the specified variable (cmath). More...
 
var cos (const var &a)
 Return the cosine of a radian-scaled variable (cmath). More...
 
var cosh (const var &a)
 Return the hyperbolic cosine of the specified variable (cmath). More...
 
var digamma (const var &a)
 
var erf (const var &a)
 The error function for variables (C99). More...
 
var erfc (const var &a)
 The complementary error function for variables (C99). More...
 
var exp (const var &a)
 Return the exponentiation of the specified variable (cmath). More...
 
var exp2 (const var &a)
 Exponentiation base 2 function for variables (C99). More...
 
var expm1 (const var &a)
 The exponentiation of the specified variable minus 1 (C99). More...
 
var fabs (const var &a)
 Return the absolute value of the variable (cmath). More...
 
var falling_factorial (const var &a, double b)
 
var falling_factorial (const var &a, const var &b)
 
var falling_factorial (double a, const var &b)
 
var fdim (const var &a, const var &b)
 Return the positive difference between the first variable's the value and the second's (C99, C++11). More...
 
var fdim (double a, const var &b)
 Return the positive difference between the first value and the value of the second variable (C99, C++11). More...
 
var fdim (const var &a, double b)
 Return the positive difference between the first variable's value and the second value (C99, C++11). More...
 
var floor (const var &a)
 Return the floor of the specified variable (cmath). More...
 
var fma (const var &a, const var &b, const var &c)
 The fused multiply-add function for three variables (C99). More...
 
var fma (const var &a, const var &b, double c)
 The fused multiply-add function for two variables and a value (C99). More...
 
var fma (const var &a, double b, const var &c)
 The fused multiply-add function for a variable, value, and variable (C99). More...
 
var fma (const var &a, double b, double c)
 The fused multiply-add function for a variable and two values (C99). More...
 
var fma (double a, const var &b, double c)
 The fused multiply-add function for a value, variable, and value (C99). More...
 
var fma (double a, double b, const var &c)
 The fused multiply-add function for two values and a variable, and value (C99). More...
 
var fma (double a, const var &b, const var &c)
 The fused multiply-add function for a value and two variables (C99). More...
 
var fmax (const var &a, const var &b)
 Returns the maximum of the two variable arguments (C99). More...
 
var fmax (const var &a, double b)
 Returns the maximum of the variable and scalar, promoting the scalar to a variable if it is larger (C99). More...
 
var fmax (double a, const var &b)
 Returns the maximum of a scalar and variable, promoting the scalar to a variable if it is larger (C99). More...
 
var fmin (const var &a, const var &b)
 Returns the minimum of the two variable arguments (C99). More...
 
var fmin (const var &a, double b)
 Returns the minimum of the variable and scalar, promoting the scalar to a variable if it is larger (C99). More...
 
var fmin (double a, const var &b)
 Returns the minimum of a scalar and variable, promoting the scalar to a variable if it is larger (C99). More...
 
var fmod (const var &a, const var &b)
 Return the floating point remainder after dividing the first variable by the second (cmath). More...
 
var fmod (const var &a, double b)
 Return the floating point remainder after dividing the the first variable by the second scalar (cmath). More...
 
var fmod (double a, const var &b)
 Return the floating point remainder after dividing the first scalar by the second variable (cmath). More...
 
var gamma_p (const var &a, const var &b)
 
var gamma_p (const var &a, double b)
 
var gamma_p (double a, const var &b)
 
var gamma_q (const var &a, const var &b)
 
var gamma_q (const var &a, double b)
 
var gamma_q (double a, const var &b)
 
void grad_inc_beta (var &g1, var &g2, const var &a, const var &b, const var &z)
 Gradient of the incomplete beta function beta(a, b, z) with respect to the first two arguments. More...
 
var hypot (const var &a, const var &b)
 Returns the length of the hypoteneuse of a right triangle with sides of the specified lengths (C99). More...
 
var hypot (const var &a, double b)
 Returns the length of the hypoteneuse of a right triangle with sides of the specified lengths (C99). More...
 
var hypot (double a, const var &b)
 Returns the length of the hypoteneuse of a right triangle with sides of the specified lengths (C99). More...
 
var ibeta (const var &a, const var &b, const var &x)
 The normalized incomplete beta function of a, b, and x. More...
 
var if_else (bool c, const var &y_true, const var &y_false)
 If the specified condition is true, return the first variable, otherwise return the second variable. More...
 
var if_else (bool c, double y_true, const var &y_false)
 If the specified condition is true, return a new variable constructed from the first scalar, otherwise return the second variable. More...
 
var if_else (bool c, const var &y_true, double y_false)
 If the specified condition is true, return the first variable, otherwise return a new variable constructed from the second scalar. More...
 
var inc_beta (const var &a, const var &b, const var &c)
 
var inv (const var &a)
 

\[ \mbox{inv}(x) = \begin{cases} \frac{1}{x} & \mbox{if } -\infty\leq x \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

More...
 
var inv_cloglog (const var &a)
 Return the inverse complementary log-log function applied specified variable (stan). More...
 
var inv_logit (const var &a)
 The inverse logit function for variables (stan). More...
 
var inv_Phi (const var &p)
 The inverse of unit normal cumulative density function. More...
 
var inv_sqrt (const var &a)
 

\[ \mbox{inv\_sqrt}(x) = \begin{cases} \frac{1}{\sqrt{x}} & \mbox{if } -\infty\leq x \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

More...
 
var inv_square (const var &a)
 

\[ \mbox{inv\_square}(x) = \begin{cases} \frac{1}{x^2} & \mbox{if } -\infty\leq x \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

More...
 
int is_inf (const var &v)
 Returns 1 if the input's value is infinite and 0 otherwise. More...
 
bool is_nan (const var &v)
 Returns 1 if the input's value is NaN and 0 otherwise. More...
 
bool is_uninitialized (var x)
 Returns true if the specified variable is uninitialized. More...
 
var lgamma (const var &a)
 The log gamma function for variables (C99). More...
 
var lmgamma (int a, const var &b)
 
var log (const var &a)
 Return the natural log of the specified variable (cmath). More...
 
var log10 (const var &a)
 Return the base 10 log of the specified variable (cmath). More...
 
var log1m (const var &a)
 The log (1 - x) function for variables. More...
 
var log1m_exp (const var &x)
 Return the log of 1 minus the exponential of the specified variable. More...
 
var log1m_inv_logit (const var &u)
 Return the natural logarithm of one minus the inverse logit of the specified argument. More...
 
var log1p (const var &a)
 The log (1 + x) function for variables (C99). More...
 
var log1p_exp (const var &a)
 Return the log of 1 plus the exponential of the specified variable. More...
 
var log2 (const var &a)
 Returns the base 2 logarithm of the specified variable (C99). More...
 
var log_diff_exp (const var &a, const var &b)
 Returns the log difference of the exponentiated arguments. More...
 
var log_diff_exp (const var &a, double b)
 Returns the log difference of the exponentiated arguments. More...
 
var log_diff_exp (double a, const var &b)
 Returns the log difference of the exponentiated arguments. More...
 
var log_falling_factorial (const var &a, double b)
 
var log_falling_factorial (const var &a, const var &b)
 
var log_falling_factorial (double a, const var &b)
 
var log_inv_logit (const var &u)
 Return the natural logarithm of the inverse logit of the specified argument. More...
 
void log_mix_partial_helper (double theta_val, double lambda1_val, double lambda2_val, double &one_m_exp_lam2_m_lam1, double &one_m_t_prod_exp_lam2_m_lam1, double &one_d_t_plus_one_m_t_prod_exp_lam2_m_lam1)
 
template<typename T_theta , typename T_lambda1 , typename T_lambda2 >
return_type< T_theta, T_lambda1, T_lambda2 >::type log_mix (const T_theta &theta, const T_lambda1 &lambda1, const T_lambda2 &lambda2)
 Return the log mixture density with specified mixing proportion and log densities and its derivative at each. More...
 
var log_rising_factorial (const var &a, double b)
 
var log_rising_factorial (const var &a, const var &b)
 
var log_rising_factorial (double a, const var &b)
 
var log_sum_exp (const var &a, const var &b)
 Returns the log sum of exponentials. More...
 
var log_sum_exp (const var &a, double b)
 Returns the log sum of exponentials. More...
 
var log_sum_exp (double a, const var &b)
 Returns the log sum of exponentials. More...
 
var logit (const var &u)
 Return the log odds of the specified argument. More...
 
var modified_bessel_first_kind (int v, const var &a)
 
var modified_bessel_second_kind (int v, const var &a)
 
var multiply_log (const var &a, const var &b)
 Return the value of a*log(b). More...
 
var multiply_log (const var &a, double b)
 Return the value of a*log(b). More...
 
var multiply_log (double a, const var &b)
 Return the value of a*log(b). More...
 
var owens_t (const var &h, const var &a)
 The Owen's T function of h and a. More...
 
var owens_t (const var &h, double a)
 The Owen's T function of h and a. More...
 
var owens_t (double h, const var &a)
 The Owen's T function of h and a. More...
 
var Phi (const var &a)
 The unit normal cumulative density function for variables (stan). More...
 
var Phi_approx (const var &a)
 Approximation of the unit normal CDF for variables (stan). More...
 
var pow (const var &base, const var &exponent)
 Return the base raised to the power of the exponent (cmath). More...
 
var pow (const var &base, double exponent)
 Return the base variable raised to the power of the exponent scalar (cmath). More...
 
var pow (double base, const var &exponent)
 Return the base scalar raised to the power of the exponent variable (cmath). More...
 
double primitive_value (const var &v)
 Return the primitive double value for the specified auto-diff variable. More...
 
var rising_factorial (const var &a, double b)
 
var rising_factorial (const var &a, const var &b)
 
var rising_factorial (double a, const var &b)
 
var round (const var &a)
 Returns the rounded form of the specified variable (C99). More...
 
var sin (const var &a)
 Return the sine of a radian-scaled variable (cmath). More...
 
var sinh (const var &a)
 Return the hyperbolic sine of the specified variable (cmath). More...
 
var sqrt (const var &a)
 Return the square root of the specified variable (cmath). More...
 
var square (const var &x)
 Return the square of the input variable. More...
 
var squared_distance (const var &a, const var &b)
 Returns the log sum of exponentials. More...
 
var squared_distance (const var &a, double b)
 Returns the log sum of exponentials. More...
 
var squared_distance (double a, const var &b)
 Returns the log sum of exponentials. More...
 
var step (const var &a)
 Return the step, or heaviside, function applied to the specified variable (stan). More...
 
var tan (const var &a)
 Return the tangent of a radian-scaled variable (cmath). More...
 
var tanh (const var &a)
 Return the hyperbolic tangent of the specified variable (cmath). More...
 
var tgamma (const var &a)
 Return the Gamma function applied to the specified variable (C99). More...
 
var to_var (double x)
 Converts argument to an automatic differentiation variable. More...
 
var to_var (const var &x)
 Converts argument to an automatic differentiation variable. More...
 
var trigamma (const var &u)
 Return the value of the trigamma function at the specified argument (i.e., the second derivative of the log Gamma function at the specified argument). More...
 
var trunc (const var &a)
 Returns the truncatation of the specified variable (C99). More...
 
double value_of (const var &v)
 Return the value of the specified variable. More...
 
double value_of_rec (const var &v)
 Return the value of the specified variable. More...
 

Variables

const double CONSTRAINT_TOLERANCE = 1E-8
 The tolerance for checking arithmetic bounds In rank and in simplexes. More...
 
const double E = boost::math::constants::e<double>()
 The base of the natural logarithm, $ e $. More...
 
const double SQRT_2 = std::sqrt(2.0)
 The value of the square root of 2, $ \sqrt{2} $. More...
 
const double INV_SQRT_2 = 1.0 / SQRT_2
 The value of 1 over the square root of 2, $ 1 / \sqrt{2} $. More...
 
const double LOG_2 = std::log(2.0)
 The natural logarithm of 2, $ \log 2 $. More...
 
const double LOG_10 = std::log(10.0)
 The natural logarithm of 10, $ \log 10 $. More...
 
const double INFTY = std::numeric_limits<double>::infinity()
 Positive infinity. More...
 
const double NEGATIVE_INFTY = - std::numeric_limits<double>::infinity()
 Negative infinity. More...
 
const double NOT_A_NUMBER = std::numeric_limits<double>::quiet_NaN()
 (Quiet) not-a-number value. More...
 
const double EPSILON = std::numeric_limits<double>::epsilon()
 Smallest positive value. More...
 
const double NEGATIVE_EPSILON = - std::numeric_limits<double>::epsilon()
 Largest negative value (i.e., smallest absolute value). More...
 
const double POISSON_MAX_RATE = std::pow(2.0, 30)
 Largest rate parameter allowed in Poisson RNG. More...
 
const double LOG_PI_OVER_FOUR = std::log(boost::math::constants::pi<double>()) / 4.0
 Log pi divided by 4 $ \log \pi / 4 $. More...
 
const double SQRT_PI = std::sqrt(boost::math::constants::pi<double>())
 
const double SQRT_2_TIMES_SQRT_PI = SQRT_2 * SQRT_PI
 
const double TWO_OVER_SQRT_PI = 2.0 / SQRT_PI
 
const double NEG_TWO_OVER_SQRT_PI = -TWO_OVER_SQRT_PI
 
const double INV_SQRT_TWO_PI = 1.0 / std::sqrt(2.0 * boost::math::constants::pi<double>())
 
const double LOG_PI = std::log(boost::math::constants::pi<double>())
 
const double LOG_SQRT_PI = std::log(SQRT_PI)
 
const double LOG_ZERO = std::log(0.0)
 
const double LOG_TWO = std::log(2.0)
 
const double LOG_HALF = std::log(0.5)
 
const double NEG_LOG_TWO = - LOG_TWO
 
const double NEG_LOG_SQRT_TWO_PI = - std::log(std::sqrt(2.0 * boost::math::constants::pi<double>()))
 
const double NEG_LOG_PI = - LOG_PI
 
const double NEG_LOG_SQRT_PI = -std::log(std::sqrt(boost::math::constants::pi<double>()))
 
const double NEG_LOG_TWO_OVER_TWO = - LOG_TWO / 2.0
 
const double LOG_TWO_PI = LOG_TWO + LOG_PI
 
const double NEG_LOG_TWO_PI = - LOG_TWO_PI
 
const std::string MAJOR_VERSION = STAN_STRING(STAN_MATH_MAJOR)
 Major version number for Stan math library. More...
 
const std::string MINOR_VERSION = STAN_STRING(STAN_MATH_MINOR)
 Minor version number for Stan math library. More...
 
const std::string PATCH_VERSION = STAN_STRING(STAN_MATH_PATCH)
 Patch version for Stan math library. More...
 

Detailed Description

Matrices and templated mathematical functions.

Templated probability distributions. All paramaterizations are based on Bayesian Data Analysis. Function gradients via reverse-mode automatic differentiation.

Typedef Documentation

§ boost_policy_t

typedef boost::math::policies::policy< boost::math::policies::overflow_error< boost::math::policies::errno_on_error>, boost::math::policies::pole_error< boost::math::policies::errno_on_error> > stan::math::boost_policy_t

Boost policy that overrides the defaults to match the built-in C++ standard library functions.

The non-default behavior from Boost's built-ins are (1) overflow errors return error numbers on error. (2) pole errors return error numbers on error.

Definition at line 23 of file boost_policy.hpp.

§ ChainableStack

Definition at line 10 of file chainablestack.hpp.

§ matrix_d

typedef Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic> stan::math::matrix_d

Type for matrix of double values.

Definition at line 22 of file typedefs.hpp.

§ matrix_fd

typedef Eigen::Matrix<fvar<double>, Eigen::Dynamic, Eigen::Dynamic> stan::math::matrix_fd

Definition at line 17 of file typedefs.hpp.

§ matrix_ffd

typedef Eigen::Matrix<fvar<fvar<double> >, Eigen::Dynamic, Eigen::Dynamic> stan::math::matrix_ffd

Definition at line 21 of file typedefs.hpp.

§ matrix_ffv

typedef Eigen::Matrix<fvar<fvar<var> >, Eigen::Dynamic, Eigen::Dynamic> stan::math::matrix_ffv

Definition at line 18 of file typedefs.hpp.

§ matrix_fv

typedef Eigen::Matrix<fvar<var>, Eigen::Dynamic, Eigen::Dynamic> stan::math::matrix_fv

Definition at line 14 of file typedefs.hpp.

§ matrix_v

typedef Eigen::Matrix<var, Eigen::Dynamic, Eigen::Dynamic> stan::math::matrix_v

The type of a matrix holding var values.

Definition at line 20 of file typedefs.hpp.

§ row_vector_d

typedef Eigen::Matrix<double, 1, Eigen::Dynamic> stan::math::row_vector_d

Type for (row) vector of double values.

Definition at line 36 of file typedefs.hpp.

§ row_vector_fd

typedef Eigen::Matrix<fvar<double>, 1, Eigen::Dynamic> stan::math::row_vector_fd

Definition at line 33 of file typedefs.hpp.

§ row_vector_ffd

typedef Eigen::Matrix<fvar<fvar<double> >, 1, Eigen::Dynamic> stan::math::row_vector_ffd

Definition at line 37 of file typedefs.hpp.

§ row_vector_ffv

typedef Eigen::Matrix<fvar<fvar<var> >, 1, Eigen::Dynamic> stan::math::row_vector_ffv

Definition at line 34 of file typedefs.hpp.

§ row_vector_fv

typedef Eigen::Matrix<fvar<var>, 1, Eigen::Dynamic> stan::math::row_vector_fv

Definition at line 30 of file typedefs.hpp.

§ row_vector_v

typedef Eigen::Matrix<var, 1, Eigen::Dynamic> stan::math::row_vector_v

The type of a row vector holding var values.

Definition at line 36 of file typedefs.hpp.

§ size_type

typedef Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic >::Index stan::math::size_type

Type for sizes and indexes in an Eigen matrix with double e.

Definition at line 13 of file typedefs.hpp.

§ vector_d

typedef Eigen::Matrix<double, Eigen::Dynamic, 1> stan::math::vector_d

Type for (column) vector of double values.

Definition at line 29 of file typedefs.hpp.

§ vector_fd

typedef Eigen::Matrix<fvar<double>, Eigen::Dynamic, 1> stan::math::vector_fd

Definition at line 25 of file typedefs.hpp.

§ vector_ffd

typedef Eigen::Matrix<fvar<fvar<double> >, Eigen::Dynamic, 1> stan::math::vector_ffd

Definition at line 29 of file typedefs.hpp.

§ vector_ffv

typedef Eigen::Matrix<fvar<fvar<var> >, Eigen::Dynamic, 1> stan::math::vector_ffv

Definition at line 26 of file typedefs.hpp.

§ vector_fv

typedef Eigen::Matrix<fvar<var>, Eigen::Dynamic, 1> stan::math::vector_fv

Definition at line 22 of file typedefs.hpp.

§ vector_v

typedef Eigen::Matrix<var, Eigen::Dynamic, 1> stan::math::vector_v

The type of a (column) vector holding var values.

Definition at line 28 of file typedefs.hpp.

Function Documentation

§ abs() [1/3]

template<typename T >
fvar<T> stan::math::abs ( const fvar< T > &  x)
inline

Definition at line 15 of file abs.hpp.

§ abs() [2/3]

double stan::math::abs ( double  x)
inline

Return floating-point absolute value.

Delegates to fabs(double) rather than std::abs(int).

Parameters
xscalar
Returns
absolute value of scalar

Definition at line 18 of file abs.hpp.

§ abs() [3/3]

var stan::math::abs ( const var a)
inline

Return the absolute value of the variable (std).

Delegates to fabs() (see for doc).

\[ \mbox{abs}(x) = \begin{cases} |x| & \mbox{if } -\infty\leq x\leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{abs}(x)}{\partial x} = \begin{cases} -1 & \mbox{if } x < 0 \\ 0 & \mbox{if } x = 0 \\ 1 & \mbox{if } x > 0 \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

Parameters
aVariable input.
Returns
Absolute value of variable.

Definition at line 35 of file abs.hpp.

§ acos() [1/3]

template<typename T >
fvar<T> stan::math::acos ( const fvar< T > &  x)
inline

Definition at line 14 of file acos.hpp.

§ acos() [2/3]

template<typename T >
apply_scalar_unary<acos_fun, T>::return_t stan::math::acos ( const T &  x)
inline

Vectorized version of acos().

Parameters
xContainer of variables.
Template Parameters
TContainer type.
Returns
Arc cosine of each variable in the container, in radians.

Definition at line 32 of file acos.hpp.

§ acos() [3/3]

var stan::math::acos ( const var a)
inline

Return the principal value of the arc cosine of a variable, in radians (cmath).

The derivative is defined by

$\frac{d}{dx} \arccos x = \frac{-1}{\sqrt{1 - x^2}}$.

\[ \mbox{acos}(x) = \begin{cases} \textrm{NaN} & \mbox{if } x < -1\\ \arccos(x) & \mbox{if } -1\leq x\leq 1 \\ \textrm{NaN} & \mbox{if } x > 1\\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{acos}(x)}{\partial x} = \begin{cases} \textrm{NaN} & \mbox{if } x < -1\\ \frac{\partial\, \arccos(x)}{\partial x} & \mbox{if } -1\leq x\leq 1 \\ \textrm{NaN} & \mbox{if } x < -1\\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \frac{\partial \, \arccos(x)}{\partial x} = -\frac{1}{\sqrt{1-x^2}} \]

Parameters
aVariable in range [-1, 1].
Returns
Arc cosine of variable, in radians.

Definition at line 59 of file acos.hpp.

§ acosh() [1/5]

template<typename T >
fvar<T> stan::math::acosh ( const fvar< T > &  x)
inline

Definition at line 12 of file acosh.hpp.

§ acosh() [2/5]

double stan::math::acosh ( double  x)
inline

Return the inverse hyperbolic cosine of the specified value.

Parameters
[in]xArgument.
Returns
Inverse hyperbolic cosine of the argument.
Exceptions
std::domain_errorIf argument is less than 1.

Definition at line 17 of file acosh.hpp.

§ acosh() [3/5]

double stan::math::acosh ( int  x)
inline

Integer version of acosh.

Parameters
[in]xArgument.
Returns
Inverse hyperbolic cosine of the argument.
Exceptions
std::domain_errorIf argument is less than 1.

Definition at line 28 of file acosh.hpp.

§ acosh() [4/5]

template<typename T >
apply_scalar_unary<acosh_fun, T>::return_t stan::math::acosh ( const T &  x)
inline

Return the elementwise application of acosh() to specified argument container.

The return type promotes the underlying scalar argument type to double if it is an integer, and otherwise is the argument type.

Template Parameters
TContainer type.
Parameters
xContainer.
Returns
Elementwise acosh of members of container.

Definition at line 39 of file acosh.hpp.

§ acosh() [5/5]

var stan::math::acosh ( const var a)
inline

The inverse hyperbolic cosine function for variables (C99).

For non-variable function, see acosh().

The derivative is defined by

$\frac{d}{dx} \mbox{acosh}(x) = \frac{x}{x^2 - 1}$.

\[ \mbox{acosh}(x) = \begin{cases} \textrm{NaN} & \mbox{if } x < 1 \\ \cosh^{-1}(x) & \mbox{if } x \geq 1 \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{acosh}(x)}{\partial x} = \begin{cases} \textrm{NaN} & \mbox{if } x < 1 \\ \frac{\partial\, \cosh^{-1}(x)}{\partial x} & \mbox{if } x \geq 1 \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \cosh^{-1}(x)=\ln\left(x+\sqrt{x^2-1}\right) \]

\[ \frac{\partial \, \cosh^{-1}(x)}{\partial x} = \frac{1}{\sqrt{x^2-1}} \]

Parameters
aThe variable.
Returns
Inverse hyperbolic cosine of the variable.

Definition at line 62 of file acosh.hpp.

§ add() [1/3]

template<typename T1 , typename T2 , int R, int C>
Eigen::Matrix<typename boost::math::tools::promote_args<T1, T2>::type, R, C> stan::math::add ( const Eigen::Matrix< T1, R, C > &  m1,
const Eigen::Matrix< T2, R, C > &  m2 
)
inline

Return the sum of the specified matrices.

The two matrices must have the same dimensions.

Template Parameters
T1Scalar type of first matrix.
T2Scalar type of second matrix.
RRow type of matrices.
CColumn type of matrices.
Parameters
m1First matrix.
m2Second matrix.
Returns
Sum of the matrices.
Exceptions
std::invalid_argumentif m1 and m2 do not have the same dimensions.

Definition at line 27 of file add.hpp.

§ add() [2/3]

template<typename T1 , typename T2 , int R, int C>
Eigen::Matrix<typename boost::math::tools::promote_args<T1, T2>::type, R, C> stan::math::add ( const Eigen::Matrix< T1, R, C > &  m,
const T2 &  c 
)
inline

Return the sum of the specified matrix and specified scalar.

Template Parameters
T1Scalar type of matrix.
T2Type of scalar.
Parameters
mMatrix.
cScalar.
Returns
The matrix plus the scalar.

Definition at line 50 of file add.hpp.

§ add() [3/3]

template<typename T1 , typename T2 , int R, int C>
Eigen::Matrix<typename boost::math::tools::promote_args<T1, T2>::type, R, C> stan::math::add ( const T1 &  c,
const Eigen::Matrix< T2, R, C > &  m 
)
inline

Return the sum of the specified scalar and specified matrix.

Template Parameters
T1Type of scalar.
T2Scalar type of matrix.
Parameters
cScalar.
mMatrix.
Returns
The scalar plus the matrix.

Definition at line 72 of file add.hpp.

§ add_initial_values()

void stan::math::add_initial_values ( const std::vector< var > &  y0,
std::vector< std::vector< var > > &  y 
)
inline

Increment the state derived from the coupled system in the with the original initial state.

This is necessary because the coupled system subtracts out the initial state in its representation when the initial state is unknown.

Parameters
[in]y0original initial values to add back into the coupled system.
[in,out]ystate of the coupled system on input, incremented with initial values on output.

Definition at line 33 of file coupled_ode_system.hpp.

§ append_col() [1/6]

template<typename T1 , typename T2 , int R1, int C1, int R2, int C2>
Eigen::Matrix<typename return_type<T1, T2>::type, Eigen::Dynamic, Eigen::Dynamic> stan::math::append_col ( const Eigen::Matrix< T1, R1, C1 > &  A,
const Eigen::Matrix< T2, R2, C2 > &  B 
)
inline

Return the result of appending the second argument matrix after the first argument matrix, that is, putting them side by side, with the first matrix followed by the second matrix.

The inputs can be (matrix, matrix), (matrix, vector), (vector, matrix), or (vector, vector) and the output is always a matrix.

Template Parameters
T1Scalar type of first matrix.
T2Scalar type of second matrix.
R1Row specification of first matrix.
C1Column specification of first matrix.
R2Row specification of second matrix.
C2Column specification of second matrix.
Parameters
AFirst matrix.
BSecond matrix.
Returns
Result of appending the first matrix followed by the second matrix side by side.

Definition at line 38 of file append_col.hpp.

§ append_col() [2/6]

template<typename T1 , typename T2 , int C1, int C2>
Eigen::Matrix<typename return_type<T1, T2>::type, 1, Eigen::Dynamic> stan::math::append_col ( const Eigen::Matrix< T1, 1, C1 > &  A,
const Eigen::Matrix< T2, 1, C2 > &  B 
)
inline

Return the result of concatenaing the first row vector followed by the second row vector side by side, with the result being a row vector.

This function applies to (row_vector, row_vector) and returns a row_vector.

Template Parameters
T1Scalar type of first row vector.
T2Scalar type of second row vector.
C1Column specification of first row vector.
C2Column specification of second row vector.
Parameters
AFirst vector.
BSecond vector
Returns
Result of appending the second row vector to the right of the first row vector.

Definition at line 83 of file append_col.hpp.

§ append_col() [3/6]

template<typename T , int R1, int C1, int R2, int C2>
Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> stan::math::append_col ( const Eigen::Matrix< T, R1, C1 > &  A,
const Eigen::Matrix< T, R2, C2 > &  B 
)
inline

Return the result of appending the second argument matrix after the first argument matrix, that is, putting them side by side, with the first matrix followed by the second matrix.

This is an overloaded template function for the case when both matrices have the same type.

The inputs can be (matrix, matrix), (matrix, vector), (vector, matrix), or (vector, vector), and the output is always a matrix.

Template Parameters
TScalar type of both matrices.
R1Row specification of first matrix.
C1Column specification of first matrix.
R2Row specification of second matrix.
C2Column specification of second matrix.
Parameters
AFirst matrix.
BSecond matrix.
Returns
Result of appending the first matrix followed by the second matrix side by side.

Definition at line 125 of file append_col.hpp.

§ append_col() [4/6]

template<typename T , int C1, int C2>
Eigen::Matrix<T, 1, Eigen::Dynamic> stan::math::append_col ( const Eigen::Matrix< T, 1, C1 > &  A,
const Eigen::Matrix< T, 1, C2 > &  B 
)
inline

Return the result of concatenaing the first row vector followed by the second row vector side by side, with the result being a row vector.

This function applies to (row_vector, row_vector) and returns a row_vector.

Template Parameters
TScalar type of both vectors.
C1Column specification of first row vector.
C2Column specification of second row vector.
Parameters
AFirst vector.
BSecond vector
Returns
Result of appending the second row vector to the right of the first row vector.

Definition at line 157 of file append_col.hpp.

§ append_col() [5/6]

template<typename T1 , typename T2 , int R, int C>
Eigen::Matrix<typename return_type<T1, T2>::type, 1, Eigen::Dynamic> stan::math::append_col ( const T1 &  A,
const Eigen::Matrix< T2, R, C > &  B 
)
inline

Return the result of stacking an scalar on top of the a row vector, with the result being a row vector.

This function applies to (scalar, row vector) and returns a row vector.

Template Parameters
T1Scalar type of the scalar
T2Scalar type of the row vector.
RRow specification of the row vector.
Parameters
Ascalar.
Brow vector.
Returns
Result of stacking the scalar on top of the row vector.

Definition at line 184 of file append_col.hpp.

§ append_col() [6/6]

template<typename T1 , typename T2 , int R, int C>
Eigen::Matrix<typename return_type<T1, T2>::type, 1, Eigen::Dynamic> stan::math::append_col ( const Eigen::Matrix< T1, R, C > &  A,
const T2 &  B 
)
inline

Return the result of stacking a row vector on top of the an scalar, with the result being a row vector.

This function applies to (row vector, scalar) and returns a row vector.

Template Parameters
T1Scalar type of the row vector.
T2Scalar type of the scalar
RRow specification of the row vector.
Parameters
Arow vector.
Bscalar.
Returns
Result of stacking the row vector on top of the scalar.

Definition at line 213 of file append_col.hpp.

§ append_row() [1/6]

template<typename T1 , typename T2 , int R1, int C1, int R2, int C2>
Eigen::Matrix<typename return_type<T1, T2>::type, Eigen::Dynamic, Eigen::Dynamic> stan::math::append_row ( const Eigen::Matrix< T1, R1, C1 > &  A,
const Eigen::Matrix< T2, R2, C2 > &  B 
)
inline

Return the result of stacking the rows of the first argument matrix on top of the second argument matrix.

The inputs can be (matrix, matrix), (matrix, row_vector), (row_vector, matrix), or (row_vector, row_vector), and the output is always a matrix.

Template Parameters
T1Scalar type of first matrix.
T2Scalar type of second matrix.
R1Row specification of first matrix.
C1Column specification of first matrix.
R2Row specification of second matrix.
C2Column specification of second matrix.
Parameters
AFirst matrix.
BSecond matrix.
Returns
Result of stacking first matrix on top of second.

Definition at line 36 of file append_row.hpp.

§ append_row() [2/6]

template<typename T1 , typename T2 , int R1, int R2>
Eigen::Matrix<typename return_type<T1, T2>::type, Eigen::Dynamic, 1> stan::math::append_row ( const Eigen::Matrix< T1, R1, 1 > &  A,
const Eigen::Matrix< T2, R2, 1 > &  B 
)
inline

Return the result of stacking the first vector on top of the second vector, with the result being a vector.

This function applies to (vector, vector) and returns a vector.

Template Parameters
T1Scalar type of first vector.
T2Scalar type of second vector.
R1Row specification of first vector.
R2Row specification of second vector.
Parameters
AFirst vector.
BSecond vector.
Returns
Result of stacking first vector on top of the second vector.

Definition at line 78 of file append_row.hpp.

§ append_row() [3/6]

template<typename T , int R1, int C1, int R2, int C2>
Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> stan::math::append_row ( const Eigen::Matrix< T, R1, C1 > &  A,
const Eigen::Matrix< T, R2, C2 > &  B 
)
inline

Return the result of stacking the rows of the first argument matrix on top of the second argument matrix.

This is an overload for the case when the scalar types of the two input matrix are the same.

The inputs can be (matrix, matrix), (matrix, row_vector), (row_vector, matrix), or (row_vector, row_vector), and the output is always a matrix.

Template Parameters
TScalar type of both matrices.
R1Row specification of first matrix.
C1Column specification of first matrix.
R2Row specification of second matrix.
C2Column specification of second matrix.
Parameters
AFirst matrix.
BSecond matrix.
Returns
Result of stacking first matrix on top of second.

Definition at line 118 of file append_row.hpp.

§ append_row() [4/6]

template<typename T , int R1, int R2>
Eigen::Matrix<T, Eigen::Dynamic, 1> stan::math::append_row ( const Eigen::Matrix< T, R1, 1 > &  A,
const Eigen::Matrix< T, R2, 1 > &  B 
)
inline

Return the result of stacking the first vector on top of the second vector, with the result being a vector.

This is an overloaded template function for the case where both inputs have the same scalar type.

This function applies to (vector, vector) and returns a vector.

Template Parameters
TScalar type of both vectors.
R1Row specification of first vector.
R2Row specification of second vector.
Parameters
AFirst vector.
BSecond vector.
Returns
Result of stacking first vector on top of the second vector.

Definition at line 151 of file append_row.hpp.

§ append_row() [5/6]

template<typename T1 , typename T2 , int R, int C>
Eigen::Matrix<typename return_type<T1, T2>::type, Eigen::Dynamic, 1> stan::math::append_row ( const T1 &  A,
const Eigen::Matrix< T2, R, C > &  B 
)
inline

Return the result of stacking an scalar on top of the a vector, with the result being a vector.

This function applies to (scalar, vector) and returns a vector.

Template Parameters
T1Scalar type of the scalar
T2Scalar type of the vector.
RRow specification of the vector.
Parameters
Ascalar.
Bvector.
Returns
Result of stacking the scalar on top of the vector.

Definition at line 177 of file append_row.hpp.

§ append_row() [6/6]

template<typename T1 , typename T2 , int R, int C>
Eigen::Matrix<typename return_type<T1, T2>::type, Eigen::Dynamic, 1> stan::math::append_row ( const Eigen::Matrix< T1, R, C > &  A,
const T2 &  B 
)
inline

Return the result of stacking a vector on top of the an scalar, with the result being a vector.

This function applies to (vector, scalar) and returns a vector.

Template Parameters
T1Scalar type of the vector.
T2Scalar type of the scalar
RRow specification of the vector.
Parameters
Avector.
Bscalar.
Returns
Result of stacking the vector on top of the scalar.

Definition at line 205 of file append_row.hpp.

§ as_bool() [1/2]

template<typename T >
bool stan::math::as_bool ( const T  x)
inline

Return 1 if the argument is unequal to zero and 0 otherwise.

Parameters
xValue.
Returns
1 if argument is equal to zero (or NaN) and 0 otherwise.

Definition at line 14 of file as_bool.hpp.

§ as_bool() [2/2]

int stan::math::as_bool ( const var v)
inline

Return 1 if the argument is unequal to zero and 0 otherwise.

Parameters
vValue.
Returns
1 if argument is equal to zero (or NaN) and 0 otherwise.

Definition at line 15 of file as_bool.hpp.

§ asin() [1/3]

template<typename T >
fvar<T> stan::math::asin ( const fvar< T > &  x)
inline

Definition at line 12 of file asin.hpp.

§ asin() [2/3]

template<typename T >
apply_scalar_unary<asin_fun, T>::return_t stan::math::asin ( const T &  x)
inline

Vectorized version of asin().

Parameters
xContainer of variables.
Template Parameters
TContainer type.
Returns
Arcsine of each variable in the container, in radians.

Definition at line 32 of file asin.hpp.

§ asin() [3/3]

var stan::math::asin ( const var a)
inline

Return the principal value of the arc sine, in radians, of the specified variable (cmath).

The derivative is defined by

$\frac{d}{dx} \arcsin x = \frac{1}{\sqrt{1 - x^2}}$.

\[ \mbox{asin}(x) = \begin{cases} \textrm{NaN} & \mbox{if } x < -1\\ \arcsin(x) & \mbox{if } -1\leq x\leq 1 \\ \textrm{NaN} & \mbox{if } x > 1\\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{asin}(x)}{\partial x} = \begin{cases} \textrm{NaN} & \mbox{if } x < -1\\ \frac{\partial\, \arcsin(x)}{\partial x} & \mbox{if } -1\leq x\leq 1 \\ \textrm{NaN} & \mbox{if } x < -1\\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \frac{\partial \, \arcsin(x)}{\partial x} = \frac{1}{\sqrt{1-x^2}} \]

Parameters
aVariable in range [-1, 1].
Returns
Arc sine of variable, in radians.

Definition at line 58 of file asin.hpp.

§ asinh() [1/5]

template<typename T >
fvar<T> stan::math::asinh ( const fvar< T > &  x)
inline

Definition at line 13 of file asinh.hpp.

§ asinh() [2/5]

double stan::math::asinh ( double  x)
inline

Return the inverse hyperbolic sine of the specified value.

Returns infinity for infinity argument and -infinity for -infinity argument.

Parameters
[in]xArgument.
Returns
Inverse hyperbolic sine of the argument.

Definition at line 18 of file asinh.hpp.

§ asinh() [3/5]

double stan::math::asinh ( int  x)
inline

Integer version of asinh.

Parameters
[in]xArgument.
Returns
Inverse hyperbolic sine of the argument.

Definition at line 28 of file asinh.hpp.

§ asinh() [4/5]

template<typename T >
apply_scalar_unary<asinh_fun, T>::return_t stan::math::asinh ( const T &  x)
inline

Vectorized version of asinh().

Template Parameters
TContainer type.
Parameters
xContainer.
Returns
Inverse hyperbolic sine of each value in the container.

Definition at line 33 of file asinh.hpp.

§ asinh() [5/5]

var stan::math::asinh ( const var a)
inline

The inverse hyperbolic sine function for variables (C99).

The derivative is defined by

$\frac{d}{dx} \mbox{asinh}(x) = \frac{x}{x^2 + 1}$.

\[ \mbox{asinh}(x) = \begin{cases} \sinh^{-1}(x) & \mbox{if } -\infty\leq x \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{asinh}(x)}{\partial x} = \begin{cases} \frac{\partial\, \sinh^{-1}(x)}{\partial x} & \mbox{if } -\infty\leq x\leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \sinh^{-1}(x)=\ln\left(x+\sqrt{x^2+1}\right) \]

\[ \frac{\partial \, \sinh^{-1}(x)}{\partial x} = \frac{1}{\sqrt{x^2+1}} \]

Parameters
aThe variable.
Returns
Inverse hyperbolic sine of the variable.

Definition at line 58 of file asinh.hpp.

§ assign() [1/5]

template<typename LHS , typename RHS >
void stan::math::assign ( LHS &  lhs,
const RHS &  rhs 
)
inline

Copy the right-hand side's value to the left-hand side variable.

The assign() function is overloaded. This instance will match arguments where the right-hand side is assignable to the left and they are not both std::vector or Eigen::Matrix types.

Template Parameters
LHSType of left-hand side.
RHSType of right-hand side.
Parameters
lhsLeft-hand side.
rhsRight-hand side.

Definition at line 48 of file assign.hpp.

§ assign() [2/5]

template<typename LHS , typename RHS , int R1, int C1, int R2, int C2>
void stan::math::assign ( Eigen::Matrix< LHS, R1, C1 > &  x,
const Eigen::Matrix< RHS, R2, C2 > &  y 
)
inline

Copy the right-hand side's value to the left-hand side variable.

The assign() function is overloaded. This instance will be called for arguments that are both Eigen::Matrix types, but whose shapes are not compatible. The shapes are specified in the row and column template parameters.

Template Parameters
LHSType of left-hand side matrix elements.
RHSType of right-hand side matrix elements.
R1Row shape of left-hand side matrix.
C1Column shape of left-hand side matrix.
R2Row shape of right-hand side matrix.
C2Column shape of right-hand side matrix.
Parameters
xLeft-hand side matrix.
yRight-hand side matrix.
Exceptions
std::invalid_argument

Definition at line 74 of file assign.hpp.

§ assign() [3/5]

template<typename LHS , typename RHS , int R, int C>
void stan::math::assign ( Eigen::Matrix< LHS, R, C > &  x,
const Eigen::Matrix< RHS, R, C > &  y 
)
inline

Copy the right-hand side's value to the left-hand side variable.

The assign() function is overloaded. This instance will be called for arguments that are both Eigen::Matrix types and whose shapes match. The shapes are specified in the row and column template parameters.

Template Parameters
LHSType of left-hand side matrix elements.
RHSType of right-hand side matrix elements.
RRow shape of both matrices.
CColumn shape of both mtarices.
Parameters
xLeft-hand side matrix.
yRight-hand side matrix.
Exceptions
std::invalid_argumentif sizes do not match.

Definition at line 110 of file assign.hpp.

§ assign() [4/5]

template<typename LHS , typename RHS , int R, int C>
void stan::math::assign ( Eigen::Block< LHS >  x,
const Eigen::Matrix< RHS, R, C > &  y 
)
inline

Copy the right-hand side's value to the left-hand side variable.

The assign() function is overloaded. This instance will be called for arguments that are both Eigen::Matrix types and whose shapes match. The shape of the right-hand side matrix is specified in the row and column shape template parameters.

Template Parameters
LHSType of matrix block elements.
RHSType of right-hand side matrix elements.
RRow shape for right-hand side matrix.
CColumn shape for right-hand side matrix.
Parameters
xLeft-hand side block view of matrix.
yRight-hand side matrix.
Exceptions
std::invalid_argumentif sizes do not match.

Definition at line 139 of file assign.hpp.

§ assign() [5/5]

template<typename LHS , typename RHS >
void stan::math::assign ( std::vector< LHS > &  x,
const std::vector< RHS > &  y 
)
inline

Copy the right-hand side's value to the left-hand side variable.

The assign() function is overloaded. This instance will be called for arguments that are both std::vector, and will call assign() element-by element.

For example, a std::vector<int> can be assigned to a std::vector<double> using this function.

Template Parameters
LHSType of left-hand side vector elements.
RHSType of right-hand side vector elements.
Parameters
xLeft-hand side vector.
yRight-hand side vector.
Exceptions
std::invalid_argumentif sizes do not match.

Definition at line 173 of file assign.hpp.

§ atan() [1/3]

template<typename T >
fvar<T> stan::math::atan ( const fvar< T > &  x)
inline

Definition at line 12 of file atan.hpp.

§ atan() [2/3]

template<typename T >
apply_scalar_unary<atan_fun, T>::return_t stan::math::atan ( const T &  x)
inline

Vectorized version of asinh().

Parameters
xContainer.
Template Parameters
TContainer type.
Returns
Arctan of each value in x, in radians.

Definition at line 32 of file atan.hpp.

§ atan() [3/3]

var stan::math::atan ( const var a)
inline

Return the principal value of the arc tangent, in radians, of the specified variable (cmath).

The derivative is defined by

$\frac{d}{dx} \arctan x = \frac{1}{1 + x^2}$.

\[ \mbox{atan}(x) = \begin{cases} \arctan(x) & \mbox{if } -\infty\leq x \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{atan}(x)}{\partial x} = \begin{cases} \frac{\partial\, \arctan(x)}{\partial x} & \mbox{if } -\infty\leq x\leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \frac{\partial \, \arctan(x)}{\partial x} = \frac{1}{x^2+1} \]

Parameters
aVariable in range [-1, 1].
Returns
Arc tangent of variable, in radians.

Definition at line 55 of file atan.hpp.

§ atan2() [1/6]

template<typename T >
fvar<T> stan::math::atan2 ( const fvar< T > &  x1,
const fvar< T > &  x2 
)
inline

Definition at line 12 of file atan2.hpp.

§ atan2() [2/6]

template<typename T >
fvar<T> stan::math::atan2 ( double  x1,
const fvar< T > &  x2 
)
inline

Definition at line 20 of file atan2.hpp.

§ atan2() [3/6]

template<typename T >
fvar<T> stan::math::atan2 ( const fvar< T > &  x1,
double  x2 
)
inline

Definition at line 27 of file atan2.hpp.

§ atan2() [4/6]

var stan::math::atan2 ( const var a,
const var b 
)
inline

Return the principal value of the arc tangent, in radians, of the first variable divided by the second (cmath).

The partial derivatives are defined by

$ \frac{\partial}{\partial x} \arctan \frac{x}{y} = \frac{y}{x^2 + y^2}$, and

$ \frac{\partial}{\partial y} \arctan \frac{x}{y} = \frac{-x}{x^2 + y^2}$.

Parameters
aNumerator variable.
bDenominator variable.
Returns
The arc tangent of the fraction, in radians.

Definition at line 62 of file atan2.hpp.

§ atan2() [5/6]

var stan::math::atan2 ( const var a,
double  b 
)
inline

Return the principal value of the arc tangent, in radians, of the first variable divided by the second scalar (cmath).

The derivative with respect to the variable is

$ \frac{d}{d x} \arctan \frac{x}{c} = \frac{c}{x^2 + c^2}$.

Parameters
aNumerator variable.
bDenominator scalar.
Returns
The arc tangent of the fraction, in radians.

Definition at line 78 of file atan2.hpp.

§ atan2() [6/6]

var stan::math::atan2 ( double  a,
const var b 
)
inline

Return the principal value of the arc tangent, in radians, of the first scalar divided by the second variable (cmath).

The derivative with respect to the variable is

$ \frac{\partial}{\partial y} \arctan \frac{c}{y} = \frac{-c}{c^2 + y^2}$.

\[ \mbox{atan2}(x, y) = \begin{cases} \arctan\left(\frac{x}{y}\right) & \mbox{if } -\infty\leq x \leq \infty, -\infty\leq y \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN or } y = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{atan2}(x, y)}{\partial x} = \begin{cases} \frac{y}{x^2+y^2} & \mbox{if } -\infty\leq x\leq \infty, -\infty\leq y \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN or } y = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{atan2}(x, y)}{\partial y} = \begin{cases} -\frac{x}{x^2+y^2} & \mbox{if } -\infty\leq x\leq \infty, -\infty\leq y \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN or } y = \textrm{NaN} \end{cases} \]

Parameters
aNumerator scalar.
bDenominator variable.
Returns
The arc tangent of the fraction, in radians.

Definition at line 119 of file atan2.hpp.

§ atanh() [1/5]

double stan::math::atanh ( double  x)
inline

Return the inverse hyperbolic tangent of the specified value.

An argument of -1 returns negative infinity and an argument of 1 returns infinity.

Parameters
[in]xArgument.
Returns
Inverse hyperbolic tangent of the argument.
Exceptions
std::domain_errorIf argument is not in [-1, 1].

Definition at line 19 of file atanh.hpp.

§ atanh() [2/5]

template<typename T >
fvar<T> stan::math::atanh ( const fvar< T > &  x)
inline

Return inverse hyperbolic tangent of specified value.

Template Parameters
Tscalar type of forward-mode autodiff variable argument.
Parameters
xArgument.
Returns
Inverse hyperbolic tangent of argument.
Exceptions
std::domain_errorif x < -1 or x > 1.

Definition at line 21 of file atanh.hpp.

§ atanh() [3/5]

double stan::math::atanh ( int  x)
inline

Integer version of atanh.

Parameters
[in]xArgument.
Returns
Inverse hyperbolic tangent of the argument.
Exceptions
std::domain_errorIf argument is less than 1.

Definition at line 30 of file atanh.hpp.

§ atanh() [4/5]

template<typename T >
apply_scalar_unary<atanh_fun, T>::return_t stan::math::atanh ( const T &  x)
inline

Return the elementwise application of atanh() to specified argument container.

The return type promotes the underlying scalar argument type to double if it is an integer, and otherwise is the argument type.

Template Parameters
TContainer type.
Parameters
xContainer.
Returns
Elementwise atanh of members of container.

Definition at line 39 of file atanh.hpp.

§ atanh() [5/5]

var stan::math::atanh ( const var a)
inline

The inverse hyperbolic tangent function for variables (C99).

The derivative is defined by

$\frac{d}{dx} \mbox{atanh}(x) = \frac{1}{1 - x^2}$.

\[ \mbox{atanh}(x) = \begin{cases} \textrm{NaN} & \mbox{if } x < -1\\ \tanh^{-1}(x) & \mbox{if } -1\leq x \leq 1 \\ \textrm{NaN} & \mbox{if } x > 1\\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{atanh}(x)}{\partial x} = \begin{cases} \textrm{NaN} & \mbox{if } x < -1\\ \frac{\partial\, \tanh^{-1}(x)}{\partial x} & \mbox{if } -1\leq x\leq 1 \\ \textrm{NaN} & \mbox{if } x > 1\\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \tanh^{-1}(x)=\frac{1}{2}\ln\left(\frac{1+x}{1-x}\right) \]

\[ \frac{\partial \, \tanh^{-1}(x)}{\partial x} = \frac{1}{1-x^2} \]

Parameters
aThe variable.
Returns
Inverse hyperbolic tangent of the variable.
Exceptions
std::domain_errorif a < -1 or a > 1

Definition at line 62 of file atanh.hpp.

§ autocorrelation() [1/2]

template<typename T >
void stan::math::autocorrelation ( const std::vector< T > &  y,
std::vector< T > &  ac,
Eigen::FFT< T > &  fft 
)

Write autocorrelation estimates for every lag for the specified input sequence into the specified result using the specified FFT engine.

The return vector be resized to the same length as the input sequence with lags given by array index.

The implementation involves a fast Fourier transform, followed by a normalization, followed by an inverse transform.

An FFT engine can be created for reuse for type double with:

    Eigen::FFT<double> fft;
Template Parameters
TScalar type.
Parameters
yInput sequence.
acAutocorrelations.
fftFFT engine instance.

Definition at line 52 of file autocorrelation.hpp.

§ autocorrelation() [2/2]

template<typename T >
void stan::math::autocorrelation ( const std::vector< T > &  y,
std::vector< T > &  ac 
)

Write autocorrelation estimates for every lag for the specified input sequence into the specified result.

The return vector be resized to the same length as the input sequence with lags given by array index.

The implementation involves a fast Fourier transform, followed by a normalization, followed by an inverse transform.

This method is just a light wrapper around the three-argument autocorrelation function

Template Parameters
TScalar type.
Parameters
yInput sequence.
acAutocorrelations.

Definition at line 120 of file autocorrelation.hpp.

§ autocovariance() [1/2]

template<typename T >
void stan::math::autocovariance ( const std::vector< T > &  y,
std::vector< T > &  acov,
Eigen::FFT< T > &  fft 
)

Write autocovariance estimates for every lag for the specified input sequence into the specified result using the specified FFT engine.

The return vector be resized to the same length as the input sequence with lags given by array index.

The implementation involves a fast Fourier transform, followed by a normalization, followed by an inverse transform.

An FFT engine can be created for reuse for type double with:

    Eigen::FFT<double> fft;
Template Parameters
TScalar type.
Parameters
yInput sequence.
acovAutocovariance.
fftFFT engine instance.

Definition at line 32 of file autocovariance.hpp.

§ autocovariance() [2/2]

template<typename T >
void stan::math::autocovariance ( const std::vector< T > &  y,
std::vector< T > &  acov 
)

Write autocovariance estimates for every lag for the specified input sequence into the specified result.

The return vector be resized to the same length as the input sequence with lags given by array index.

The implementation involves a fast Fourier transform, followed by a normalization, followed by an inverse transform.

This method is just a light wrapper around the three-argument autocovariance function

Template Parameters
TScalar type.
Parameters
yInput sequence.
acovAutocovariances.

Definition at line 60 of file autocovariance.hpp.

§ bernoulli_ccdf_log()

template<typename T_n , typename T_prob >
return_type<T_prob>::type stan::math::bernoulli_ccdf_log ( const T_n &  n,
const T_prob &  theta 
)

Definition at line 25 of file bernoulli_ccdf_log.hpp.

§ bernoulli_cdf()

template<typename T_n , typename T_prob >
return_type<T_prob>::type stan::math::bernoulli_cdf ( const T_n &  n,
const T_prob &  theta 
)

Definition at line 25 of file bernoulli_cdf.hpp.

§ bernoulli_cdf_log()

template<typename T_n , typename T_prob >
return_type<T_prob>::type stan::math::bernoulli_cdf_log ( const T_n &  n,
const T_prob &  theta 
)

Definition at line 25 of file bernoulli_cdf_log.hpp.

§ bernoulli_lccdf()

template<typename T_n , typename T_prob >
return_type<T_prob>::type stan::math::bernoulli_lccdf ( const T_n &  n,
const T_prob &  theta 
)

Definition at line 25 of file bernoulli_lccdf.hpp.

§ bernoulli_lcdf()

template<typename T_n , typename T_prob >
return_type<T_prob>::type stan::math::bernoulli_lcdf ( const T_n &  n,
const T_prob &  theta 
)

Definition at line 25 of file bernoulli_lcdf.hpp.

§ bernoulli_log() [1/2]

template<bool propto, typename T_n , typename T_prob >
return_type<T_prob>::type stan::math::bernoulli_log ( const T_n &  n,
const T_prob &  theta 
)

Definition at line 27 of file bernoulli_log.hpp.

§ bernoulli_log() [2/2]

template<typename T_y , typename T_prob >
return_type<T_prob>::type stan::math::bernoulli_log ( const T_y &  n,
const T_prob &  theta 
)
inline

Definition at line 107 of file bernoulli_log.hpp.

§ bernoulli_logit_log() [1/2]

template<bool propto, typename T_n , typename T_prob >
return_type<T_prob>::type stan::math::bernoulli_logit_log ( const T_n &  n,
const T_prob &  theta 
)

Definition at line 27 of file bernoulli_logit_log.hpp.

§ bernoulli_logit_log() [2/2]

template<typename T_n , typename T_prob >
return_type<T_prob>::type stan::math::bernoulli_logit_log ( const T_n &  n,
const T_prob &  theta 
)
inline

Definition at line 90 of file bernoulli_logit_log.hpp.

§ bernoulli_logit_lpmf() [1/2]

template<bool propto, typename T_n , typename T_prob >
return_type<T_prob>::type stan::math::bernoulli_logit_lpmf ( const T_n &  n,
const T_prob &  theta 
)

Definition at line 27 of file bernoulli_logit_lpmf.hpp.

§ bernoulli_logit_lpmf() [2/2]

template<typename T_n , typename T_prob >
return_type<T_prob>::type stan::math::bernoulli_logit_lpmf ( const T_n &  n,
const T_prob &  theta 
)
inline

Definition at line 90 of file bernoulli_logit_lpmf.hpp.

§ bernoulli_logit_rng()

template<class RNG >
int stan::math::bernoulli_logit_rng ( double  t,
RNG &  rng 
)
inline

A Bernoulli random number generator which takes as its argument the often more convenient logit-parametrization.

Template Parameters
RNGRandom number generator type.
Parameters
tlogit-transformed probability parameter.
rngpseudorandom number generator.
Returns
Bernoulli(logit^{-1}(t)) generated random number, either 0 or 1.

Definition at line 30 of file bernoulli_logit_rng.hpp.

§ bernoulli_lpmf() [1/2]

template<bool propto, typename T_n , typename T_prob >
return_type<T_prob>::type stan::math::bernoulli_lpmf ( const T_n &  n,
const T_prob &  theta 
)

Definition at line 27 of file bernoulli_lpmf.hpp.

§ bernoulli_lpmf() [2/2]

template<typename T_y , typename T_prob >
return_type<T_prob>::type stan::math::bernoulli_lpmf ( const T_y &  n,
const T_prob &  theta 
)
inline

Definition at line 107 of file bernoulli_lpmf.hpp.

§ bernoulli_rng()

template<class RNG >
int stan::math::bernoulli_rng ( double  theta,
RNG &  rng 
)
inline

Definition at line 21 of file bernoulli_rng.hpp.

§ bessel_first_kind() [1/3]

template<typename T >
fvar<T> stan::math::bessel_first_kind ( int  v,
const fvar< T > &  z 
)
inline

Definition at line 13 of file bessel_first_kind.hpp.

§ bessel_first_kind() [2/3]

var stan::math::bessel_first_kind ( int  v,
const var a 
)
inline

Definition at line 27 of file bessel_first_kind.hpp.

§ bessel_first_kind() [3/3]

template<typename T2 >
T2 stan::math::bessel_first_kind ( int  v,
const T2  z 
)
inline

\[ \mbox{bessel\_first\_kind}(v, x) = \begin{cases} J_v(x) & \mbox{if } -\infty\leq x \leq \infty \\[6pt] \textrm{error} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{bessel\_first\_kind}(v, x)}{\partial x} = \begin{cases} \frac{\partial\, J_v(x)}{\partial x} & \mbox{if } -\infty\leq x\leq \infty \\[6pt] \textrm{error} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ J_v(x)=\left(\frac{1}{2}x\right)^v \sum_{k=0}^\infty \frac{\left(-\frac{1}{4}x^2\right)^k}{k!\, \Gamma(v+k+1)} \]

\[ \frac{\partial \, J_v(x)}{\partial x} = \frac{v}{x}J_v(x)-J_{v+1}(x) \]

Definition at line 40 of file bessel_first_kind.hpp.

§ bessel_second_kind() [1/3]

template<typename T >
fvar<T> stan::math::bessel_second_kind ( int  v,
const fvar< T > &  z 
)
inline

Definition at line 13 of file bessel_second_kind.hpp.

§ bessel_second_kind() [2/3]

var stan::math::bessel_second_kind ( int  v,
const var a 
)
inline

Definition at line 27 of file bessel_second_kind.hpp.

§ bessel_second_kind() [3/3]

template<typename T2 >
T2 stan::math::bessel_second_kind ( int  v,
const T2  z 
)
inline

\[ \mbox{bessel\_second\_kind}(v, x) = \begin{cases} \textrm{error} & \mbox{if } x \leq 0 \\ Y_v(x) & \mbox{if } x > 0 \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{bessel\_second\_kind}(v, x)}{\partial x} = \begin{cases} \textrm{error} & \mbox{if } x \leq 0 \\ \frac{\partial\, Y_v(x)}{\partial x} & \mbox{if } x > 0 \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ Y_v(x)=\frac{J_v(x)\cos(v\pi)-J_{-v}(x)}{\sin(v\pi)} \]

\[ \frac{\partial \, Y_v(x)}{\partial x} = \frac{v}{x}Y_v(x)-Y_{v+1}(x) \]

Definition at line 40 of file bessel_second_kind.hpp.

§ beta_binomial_ccdf_log()

template<typename T_n , typename T_N , typename T_size1 , typename T_size2 >
return_type<T_size1, T_size2>::type stan::math::beta_binomial_ccdf_log ( const T_n &  n,
const T_N &  N,
const T_size1 &  alpha,
const T_size2 &  beta 
)

Definition at line 29 of file beta_binomial_ccdf_log.hpp.

§ beta_binomial_cdf()

template<typename T_n , typename T_N , typename T_size1 , typename T_size2 >
return_type<T_size1, T_size2>::type stan::math::beta_binomial_cdf ( const T_n &  n,
const T_N &  N,
const T_size1 &  alpha,
const T_size2 &  beta 
)

Definition at line 30 of file beta_binomial_cdf.hpp.

§ beta_binomial_cdf_log()

template<typename T_n , typename T_N , typename T_size1 , typename T_size2 >
return_type<T_size1, T_size2>::type stan::math::beta_binomial_cdf_log ( const T_n &  n,
const T_N &  N,
const T_size1 &  alpha,
const T_size2 &  beta 
)

Definition at line 29 of file beta_binomial_cdf_log.hpp.

§ beta_binomial_lccdf()

template<typename T_n , typename T_N , typename T_size1 , typename T_size2 >
return_type<T_size1, T_size2>::type stan::math::beta_binomial_lccdf ( const T_n &  n,
const T_N &  N,
const T_size1 &  alpha,
const T_size2 &  beta 
)

Definition at line 29 of file beta_binomial_lccdf.hpp.

§ beta_binomial_lcdf()

template<typename T_n , typename T_N , typename T_size1 , typename T_size2 >
return_type<T_size1, T_size2>::type stan::math::beta_binomial_lcdf ( const T_n &  n,
const T_N &  N,
const T_size1 &  alpha,
const T_size2 &  beta 
)

Definition at line 29 of file beta_binomial_lcdf.hpp.

§ beta_binomial_log() [1/2]

template<bool propto, typename T_n , typename T_N , typename T_size1 , typename T_size2 >
return_type<T_size1, T_size2>::type stan::math::beta_binomial_log ( const T_n &  n,
const T_N &  N,
const T_size1 &  alpha,
const T_size2 &  beta 
)

Definition at line 31 of file beta_binomial_log.hpp.

§ beta_binomial_log() [2/2]

template<typename T_n , typename T_N , typename T_size1 , typename T_size2 >
return_type<T_size1, T_size2>::type stan::math::beta_binomial_log ( const T_n &  n,
const T_N &  N,
const T_size1 &  alpha,
const T_size2 &  beta 
)

Definition at line 164 of file beta_binomial_log.hpp.

§ beta_binomial_lpmf() [1/2]

template<bool propto, typename T_n , typename T_N , typename T_size1 , typename T_size2 >
return_type<T_size1, T_size2>::type stan::math::beta_binomial_lpmf ( const T_n &  n,
const T_N &  N,
const T_size1 &  alpha,
const T_size2 &  beta 
)

Definition at line 31 of file beta_binomial_lpmf.hpp.

§ beta_binomial_lpmf() [2/2]

template<typename T_n , typename T_N , typename T_size1 , typename T_size2 >
return_type<T_size1, T_size2>::type stan::math::beta_binomial_lpmf ( const T_n &  n,
const T_N &  N,
const T_size1 &  alpha,
const T_size2 &  beta 
)

Definition at line 164 of file beta_binomial_lpmf.hpp.

§ beta_binomial_rng()

template<class RNG >
int stan::math::beta_binomial_rng ( int  N,
double  alpha,
double  beta,
RNG &  rng 
)
inline

Definition at line 24 of file beta_binomial_rng.hpp.

§ beta_ccdf_log()

template<typename T_y , typename T_scale_succ , typename T_scale_fail >
return_type<T_y, T_scale_succ, T_scale_fail>::type stan::math::beta_ccdf_log ( const T_y &  y,
const T_scale_succ &  alpha,
const T_scale_fail &  beta 
)

Definition at line 35 of file beta_ccdf_log.hpp.

§ beta_cdf()

template<typename T_y , typename T_scale_succ , typename T_scale_fail >
return_type<T_y, T_scale_succ, T_scale_fail>::type stan::math::beta_cdf ( const T_y &  y,
const T_scale_succ &  alpha,
const T_scale_fail &  beta 
)

Calculates the beta cumulative distribution function for the given variate and scale variables.

Parameters
yA scalar variate.
alphaPrior sample size.
betaPrior sample size.
Returns
The beta cdf evaluated at the specified arguments.
Template Parameters
T_yType of y.
T_scale_succType of alpha.
T_scale_failType of beta.

Definition at line 48 of file beta_cdf.hpp.

§ beta_cdf_log()

template<typename T_y , typename T_scale_succ , typename T_scale_fail >
return_type<T_y, T_scale_succ, T_scale_fail>::type stan::math::beta_cdf_log ( const T_y &  y,
const T_scale_succ &  alpha,
const T_scale_fail &  beta 
)

Definition at line 34 of file beta_cdf_log.hpp.

§ beta_lccdf()

template<typename T_y , typename T_scale_succ , typename T_scale_fail >
return_type<T_y, T_scale_succ, T_scale_fail>::type stan::math::beta_lccdf ( const T_y &  y,
const T_scale_succ &  alpha,
const T_scale_fail &  beta 
)

Definition at line 35 of file beta_lccdf.hpp.

§ beta_lcdf()

template<typename T_y , typename T_scale_succ , typename T_scale_fail >
return_type<T_y, T_scale_succ, T_scale_fail>::type stan::math::beta_lcdf ( const T_y &  y,
const T_scale_succ &  alpha,
const T_scale_fail &  beta 
)

Definition at line 34 of file beta_lcdf.hpp.

§ beta_log() [1/2]

template<bool propto, typename T_y , typename T_scale_succ , typename T_scale_fail >
return_type<T_y, T_scale_succ, T_scale_fail>::type stan::math::beta_log ( const T_y &  y,
const T_scale_succ &  alpha,
const T_scale_fail &  beta 
)

The log of the beta density for the specified scalar(s) given the specified sample size(s).

y, alpha, or beta can each either be scalar or a vector. Any vector inputs must be the same length.

The result log probability is defined to be the sum of the log probabilities for each observation/alpha/beta triple.

Prior sample sizes, alpha and beta, must be greater than 0.

Parameters
y(Sequence of) scalar(s).
alpha(Sequence of) prior sample size(s).
beta(Sequence of) prior sample size(s).
Returns
The log of the product of densities.
Template Parameters
T_yType of scalar outcome.
T_scale_succType of prior scale for successes.
T_scale_failType of prior scale for failures.

Definition at line 53 of file beta_log.hpp.

§ beta_log() [2/2]

template<typename T_y , typename T_scale_succ , typename T_scale_fail >
return_type<T_y, T_scale_succ, T_scale_fail>::type stan::math::beta_log ( const T_y &  y,
const T_scale_succ &  alpha,
const T_scale_fail &  beta 
)
inline

Definition at line 190 of file beta_log.hpp.

§ beta_lpdf() [1/2]

template<bool propto, typename T_y , typename T_scale_succ , typename T_scale_fail >
return_type<T_y, T_scale_succ, T_scale_fail>::type stan::math::beta_lpdf ( const T_y &  y,
const T_scale_succ &  alpha,
const T_scale_fail &  beta 
)

The log of the beta density for the specified scalar(s) given the specified sample size(s).

y, alpha, or beta can each either be scalar or a vector. Any vector inputs must be the same length.

The result log probability is defined to be the sum of the log probabilities for each observation/alpha/beta triple.

Prior sample sizes, alpha and beta, must be greater than 0.

Parameters
y(Sequence of) scalar(s).
alpha(Sequence of) prior sample size(s).
beta(Sequence of) prior sample size(s).
Returns
The log of the product of densities.
Template Parameters
T_yType of scalar outcome.
T_scale_succType of prior scale for successes.
T_scale_failType of prior scale for failures.

Definition at line 53 of file beta_lpdf.hpp.

§ beta_lpdf() [2/2]

template<typename T_y , typename T_scale_succ , typename T_scale_fail >
return_type<T_y, T_scale_succ, T_scale_fail>::type stan::math::beta_lpdf ( const T_y &  y,
const T_scale_succ &  alpha,
const T_scale_fail &  beta 
)
inline

Definition at line 190 of file beta_lpdf.hpp.

§ beta_rng()

template<class RNG >
double stan::math::beta_rng ( double  alpha,
double  beta,
RNG &  rng 
)
inline

Definition at line 30 of file beta_rng.hpp.

§ binary_log_loss() [1/3]

template<typename T >
fvar<T> stan::math::binary_log_loss ( int  y,
const fvar< T > &  y_hat 
)
inline

Definition at line 13 of file binary_log_loss.hpp.

§ binary_log_loss() [2/3]

template<typename T >
boost::math::tools::promote_args<T>::type stan::math::binary_log_loss ( int  y,
const T  y_hat 
)
inline

Returns the log loss function for binary classification with specified reference and response values.

The log loss function for prediction $\hat{y} \in [0, 1]$ given outcome $y \in \{ 0, 1 \}$ is

$\mbox{logloss}(1, \hat{y}) = -\log \hat{y} $, and

$\mbox{logloss}(0, \hat{y}) = -\log (1 - \hat{y}) $.

Parameters
yReference value in { 0 , 1 }.
y_hatResponse value in [0, 1].
Returns
Log loss for response given reference value.

Definition at line 26 of file binary_log_loss.hpp.

§ binary_log_loss() [3/3]

var stan::math::binary_log_loss ( int  y,
const var y_hat 
)
inline

The log loss function for variables (stan).

See binary_log_loss() for the double-based version.

The derivative with respect to the variable $\hat{y}$ is

$\frac{d}{d\hat{y}} \mbox{logloss}(1, \hat{y}) = - \frac{1}{\hat{y}}$, and

$\frac{d}{d\hat{y}} \mbox{logloss}(0, \hat{y}) = \frac{1}{1 - \hat{y}}$.

\[ \mbox{binary\_log\_loss}(y, \hat{y}) = \begin{cases} y \log \hat{y} + (1 - y) \log (1 - \hat{y}) & \mbox{if } 0\leq \hat{y}\leq 1, y\in\{ 0, 1 \}\\[6pt] \textrm{NaN} & \mbox{if } \hat{y} = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{binary\_log\_loss}(y, \hat{y})}{\partial \hat{y}} = \begin{cases} \frac{y}{\hat{y}}-\frac{1-y}{1-\hat{y}} & \mbox{if } 0\leq \hat{y}\leq 1, y\in\{ 0, 1 \}\\[6pt] \textrm{NaN} & \mbox{if } \hat{y} = \textrm{NaN} \end{cases} \]

Parameters
yReference value.
y_hatResponse variable.
Returns
Log loss of response versus reference value.

Definition at line 68 of file binary_log_loss.hpp.

§ binomial_ccdf_log()

template<typename T_n , typename T_N , typename T_prob >
return_type<T_prob>::type stan::math::binomial_ccdf_log ( const T_n &  n,
const T_N &  N,
const T_prob &  theta 
)

Definition at line 32 of file binomial_ccdf_log.hpp.

§ binomial_cdf()

template<typename T_n , typename T_N , typename T_prob >
return_type<T_prob>::type stan::math::binomial_cdf ( const T_n &  n,
const T_N &  N,
const T_prob &  theta 
)

Definition at line 32 of file binomial_cdf.hpp.

§ binomial_cdf_log()

template<typename T_n , typename T_N , typename T_prob >
return_type<T_prob>::type stan::math::binomial_cdf_log ( const T_n &  n,
const T_N &  N,
const T_prob &  theta 
)

Definition at line 32 of file binomial_cdf_log.hpp.

§ binomial_coefficient_log() [1/4]

template<typename T >
fvar<T> stan::math::binomial_coefficient_log ( const fvar< T > &  x1,
const fvar< T > &  x2 
)
inline

Definition at line 15 of file binomial_coefficient_log.hpp.

§ binomial_coefficient_log() [2/4]

template<typename T >
fvar<T> stan::math::binomial_coefficient_log ( const fvar< T > &  x1,
double  x2 
)
inline

Definition at line 44 of file binomial_coefficient_log.hpp.

§ binomial_coefficient_log() [3/4]

template<typename T_N , typename T_n >
boost::math::tools::promote_args<T_N, T_n>::type stan::math::binomial_coefficient_log ( const T_N  N,
const T_n  n 
)
inline

Return the log of the binomial coefficient for the specified arguments.

The binomial coefficient, ${N \choose n}$, read "N choose n", is defined for $0 \leq n \leq N$ by

${N \choose n} = \frac{N!}{n! (N-n)!}$.

This function uses Gamma functions to define the log and generalize the arguments to continuous N and n.

$ \log {N \choose n} = \log \ \Gamma(N+1) - \log \Gamma(n+1) - \log \Gamma(N-n+1)$.

\[ \mbox{binomial\_coefficient\_log}(x, y) = \begin{cases} \textrm{error} & \mbox{if } y > x \textrm{ or } y < 0\\ \ln\Gamma(x+1) & \mbox{if } 0\leq y \leq x \\ \quad -\ln\Gamma(y+1)& \\ \quad -\ln\Gamma(x-y+1)& \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN or } y = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{binomial\_coefficient\_log}(x, y)}{\partial x} = \begin{cases} \textrm{error} & \mbox{if } y > x \textrm{ or } y < 0\\ \Psi(x+1) & \mbox{if } 0\leq y \leq x \\ \quad -\Psi(x-y+1)& \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN or } y = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{binomial\_coefficient\_log}(x, y)}{\partial y} = \begin{cases} \textrm{error} & \mbox{if } y > x \textrm{ or } y < 0\\ -\Psi(y+1) & \mbox{if } 0\leq y \leq x \\ \quad +\Psi(x-y+1)& \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN or } y = \textrm{NaN} \end{cases} \]

Parameters
Ntotal number of objects.
nnumber of objects chosen.
Returns
log (N choose n).

Definition at line 61 of file binomial_coefficient_log.hpp.

§ binomial_coefficient_log() [4/4]

template<typename T >
fvar<T> stan::math::binomial_coefficient_log ( double  x1,
const fvar< T > &  x2 
)
inline

Definition at line 67 of file binomial_coefficient_log.hpp.

§ binomial_lccdf()

template<typename T_n , typename T_N , typename T_prob >
return_type<T_prob>::type stan::math::binomial_lccdf ( const T_n &  n,
const T_N &  N,
const T_prob &  theta 
)

Definition at line 32 of file binomial_lccdf.hpp.

§ binomial_lcdf()

template<typename T_n , typename T_N , typename T_prob >
return_type<T_prob>::type stan::math::binomial_lcdf ( const T_n &  n,
const T_N &  N,
const T_prob &  theta 
)

Definition at line 32 of file binomial_lcdf.hpp.

§ binomial_log() [1/2]

template<bool propto, typename T_n , typename T_N , typename T_prob >
return_type<T_prob>::type stan::math::binomial_log ( const T_n &  n,
const T_N &  N,
const T_prob &  theta 
)

Definition at line 36 of file binomial_log.hpp.

§ binomial_log() [2/2]

template<typename T_n , typename T_N , typename T_prob >
return_type<T_prob>::type stan::math::binomial_log ( const T_n &  n,
const T_N &  N,
const T_prob &  theta 
)
inline

Definition at line 111 of file binomial_log.hpp.

§ binomial_logit_log() [1/2]

template<bool propto, typename T_n , typename T_N , typename T_prob >
return_type<T_prob>::type stan::math::binomial_logit_log ( const T_n &  n,
const T_N &  N,
const T_prob &  alpha 
)

Definition at line 37 of file binomial_logit_log.hpp.

§ binomial_logit_log() [2/2]

template<typename T_n , typename T_N , typename T_prob >
return_type<T_prob>::type stan::math::binomial_logit_log ( const T_n &  n,
const T_N &  N,
const T_prob &  alpha 
)
inline

Definition at line 117 of file binomial_logit_log.hpp.

§ binomial_logit_lpmf() [1/2]

template<bool propto, typename T_n , typename T_N , typename T_prob >
return_type<T_prob>::type stan::math::binomial_logit_lpmf ( const T_n &  n,
const T_N &  N,
const T_prob &  alpha 
)

Definition at line 37 of file binomial_logit_lpmf.hpp.

§ binomial_logit_lpmf() [2/2]

template<typename T_n , typename T_N , typename T_prob >
return_type<T_prob>::type stan::math::binomial_logit_lpmf ( const T_n &  n,
const T_N &  N,
const T_prob &  alpha 
)
inline

Definition at line 117 of file binomial_logit_lpmf.hpp.

§ binomial_lpmf() [1/2]

template<bool propto, typename T_n , typename T_N , typename T_prob >
return_type<T_prob>::type stan::math::binomial_lpmf ( const T_n &  n,
const T_N &  N,
const T_prob &  theta 
)

Definition at line 36 of file binomial_lpmf.hpp.

§ binomial_lpmf() [2/2]

template<typename T_n , typename T_N , typename T_prob >
return_type<T_prob>::type stan::math::binomial_lpmf ( const T_n &  n,
const T_N &  N,
const T_prob &  theta 
)
inline

Definition at line 111 of file binomial_lpmf.hpp.

§ binomial_rng()

template<class RNG >
int stan::math::binomial_rng ( int  N,
double  theta,
RNG &  rng 
)
inline

Definition at line 28 of file binomial_rng.hpp.

§ block()

template<typename T >
Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> stan::math::block ( const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &  m,
size_t  i,
size_t  j,
size_t  nrows,
size_t  ncols 
)
inline

Return a nrows x ncols submatrix starting at (i-1, j-1).

Parameters
mMatrix.
iStarting row.
jStarting column.
nrowsNumber of rows in block.
ncolsNumber of columns in block.
Exceptions
std::out_of_rangeif either index is out of range.

Definition at line 24 of file block.hpp.

§ calculate_chain()

double stan::math::calculate_chain ( double  x,
double  val 
)
inline

Definition at line 9 of file calculate_chain.hpp.

§ categorical_log() [1/4]

template<bool propto, typename T_prob >
boost::math::tools::promote_args<T_prob>::type stan::math::categorical_log ( int  n,
const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &  theta 
)

Definition at line 24 of file categorical_log.hpp.

§ categorical_log() [2/4]

template<typename T_prob >
boost::math::tools::promote_args<T_prob>::type stan::math::categorical_log ( const typename math::index_type< Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > >::type  n,
const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &  theta 
)
inline

Definition at line 44 of file categorical_log.hpp.

§ categorical_log() [3/4]

template<bool propto, typename T_prob >
boost::math::tools::promote_args<T_prob>::type stan::math::categorical_log ( const std::vector< int > &  ns,
const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &  theta 
)

Definition at line 54 of file categorical_log.hpp.

§ categorical_log() [4/4]

template<typename T_prob >
boost::math::tools::promote_args<T_prob>::type stan::math::categorical_log ( const std::vector< int > &  ns,
const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &  theta 
)
inline

Definition at line 90 of file categorical_log.hpp.

§ categorical_logit_log() [1/4]

template<bool propto, typename T_prob >
boost::math::tools::promote_args<T_prob>::type stan::math::categorical_logit_log ( int  n,
const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &  beta 
)

Definition at line 21 of file categorical_logit_log.hpp.

§ categorical_logit_log() [2/4]

template<typename T_prob >
boost::math::tools::promote_args<T_prob>::type stan::math::categorical_logit_log ( int  n,
const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &  beta 
)
inline

Definition at line 40 of file categorical_logit_log.hpp.

§ categorical_logit_log() [3/4]

template<bool propto, typename T_prob >
boost::math::tools::promote_args<T_prob>::type stan::math::categorical_logit_log ( const std::vector< int > &  ns,
const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &  beta 
)

Definition at line 49 of file categorical_logit_log.hpp.

§ categorical_logit_log() [4/4]

template<typename T_prob >
boost::math::tools::promote_args<T_prob>::type stan::math::categorical_logit_log ( const std::vector< int > &  ns,
const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &  beta 
)
inline

Definition at line 79 of file categorical_logit_log.hpp.

§ categorical_logit_lpmf() [1/4]

template<bool propto, typename T_prob >
boost::math::tools::promote_args<T_prob>::type stan::math::categorical_logit_lpmf ( int  n,
const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &  beta 
)

Definition at line 21 of file categorical_logit_lpmf.hpp.

§ categorical_logit_lpmf() [2/4]

template<typename T_prob >
boost::math::tools::promote_args<T_prob>::type stan::math::categorical_logit_lpmf ( int  n,
const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &  beta 
)
inline

Definition at line 40 of file categorical_logit_lpmf.hpp.

§ categorical_logit_lpmf() [3/4]

template<bool propto, typename T_prob >
boost::math::tools::promote_args<T_prob>::type stan::math::categorical_logit_lpmf ( const std::vector< int > &  ns,
const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &  beta 
)

Definition at line 49 of file categorical_logit_lpmf.hpp.

§ categorical_logit_lpmf() [4/4]

template<typename T_prob >
boost::math::tools::promote_args<T_prob>::type stan::math::categorical_logit_lpmf ( const std::vector< int > &  ns,
const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &  beta 
)
inline

Definition at line 79 of file categorical_logit_lpmf.hpp.

§ categorical_lpmf() [1/4]

template<bool propto, typename T_prob >
boost::math::tools::promote_args<T_prob>::type stan::math::categorical_lpmf ( int  n,
const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &  theta 
)

Definition at line 24 of file categorical_lpmf.hpp.

§ categorical_lpmf() [2/4]

template<typename T_prob >
boost::math::tools::promote_args<T_prob>::type stan::math::categorical_lpmf ( const typename math::index_type< Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > >::type  n,
const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &  theta 
)
inline

Definition at line 44 of file categorical_lpmf.hpp.

§ categorical_lpmf() [3/4]

template<bool propto, typename T_prob >
boost::math::tools::promote_args<T_prob>::type stan::math::categorical_lpmf ( const std::vector< int > &  ns,
const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &  theta 
)

Definition at line 54 of file categorical_lpmf.hpp.

§ categorical_lpmf() [4/4]

template<typename T_prob >
boost::math::tools::promote_args<T_prob>::type stan::math::categorical_lpmf ( const std::vector< int > &  ns,
const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &  theta 
)
inline

Definition at line 90 of file categorical_lpmf.hpp.

§ categorical_rng()

template<class RNG >
int stan::math::categorical_rng ( const Eigen::Matrix< double, Eigen::Dynamic, 1 > &  theta,
RNG &  rng 
)
inline

Definition at line 19 of file categorical_rng.hpp.

§ cauchy_ccdf_log()

template<typename T_y , typename T_loc , typename T_scale >
return_type<T_y, T_loc, T_scale>::type stan::math::cauchy_ccdf_log ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma 
)

Definition at line 25 of file cauchy_ccdf_log.hpp.

§ cauchy_cdf()

template<typename T_y , typename T_loc , typename T_scale >
return_type<T_y, T_loc, T_scale>::type stan::math::cauchy_cdf ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma 
)

Calculates the cauchy cumulative distribution function for the given variate, location, and scale.

$\frac{1}{\pi}\arctan\left(\frac{y-\mu}{\sigma}\right) + \frac{1}{2}$

Parameters
yA scalar variate.
muThe location parameter.
sigmaThe scale parameter.
Returns

Definition at line 37 of file cauchy_cdf.hpp.

§ cauchy_cdf_log()

template<typename T_y , typename T_loc , typename T_scale >
return_type<T_y, T_loc, T_scale>::type stan::math::cauchy_cdf_log ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma 
)

Definition at line 25 of file cauchy_cdf_log.hpp.

§ cauchy_lccdf()

template<typename T_y , typename T_loc , typename T_scale >
return_type<T_y, T_loc, T_scale>::type stan::math::cauchy_lccdf ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma 
)

Definition at line 25 of file cauchy_lccdf.hpp.

§ cauchy_lcdf()

template<typename T_y , typename T_loc , typename T_scale >
return_type<T_y, T_loc, T_scale>::type stan::math::cauchy_lcdf ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma 
)

Definition at line 25 of file cauchy_lcdf.hpp.

§ cauchy_log() [1/2]

template<bool propto, typename T_y , typename T_loc , typename T_scale >
return_type<T_y, T_loc, T_scale>::type stan::math::cauchy_log ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma 
)

The log of the Cauchy density for the specified scalar(s) given the specified location parameter(s) and scale parameter(s).

y, mu, or sigma can each either be scalar a vector. Any vector inputs must be the same length.

The result log probability is defined to be the sum of the log probabilities for each observation/mu/sigma triple.

Parameters
y(Sequence of) scalar(s).
mu(Sequence of) location(s).
sigma(Sequence of) scale(s).
Returns
The log of the product of densities.
Template Parameters
T_yType of scalar outcome.
T_locType of location.
T_scaleType of scale.

Definition at line 44 of file cauchy_log.hpp.

§ cauchy_log() [2/2]

template<typename T_y , typename T_loc , typename T_scale >
return_type<T_y, T_loc, T_scale>::type stan::math::cauchy_log ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma 
)
inline

Definition at line 130 of file cauchy_log.hpp.

§ cauchy_lpdf() [1/2]

template<bool propto, typename T_y , typename T_loc , typename T_scale >
return_type<T_y, T_loc, T_scale>::type stan::math::cauchy_lpdf ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma 
)

The log of the Cauchy density for the specified scalar(s) given the specified location parameter(s) and scale parameter(s).

y, mu, or sigma can each either be scalar a vector. Any vector inputs must be the same length.

The result log probability is defined to be the sum of the log probabilities for each observation/mu/sigma triple.

Parameters
y(Sequence of) scalar(s).
mu(Sequence of) location(s).
sigma(Sequence of) scale(s).
Returns
The log of the product of densities.
Template Parameters
T_yType of scalar outcome.
T_locType of location.
T_scaleType of scale.

Definition at line 44 of file cauchy_lpdf.hpp.

§ cauchy_lpdf() [2/2]

template<typename T_y , typename T_loc , typename T_scale >
return_type<T_y, T_loc, T_scale>::type stan::math::cauchy_lpdf ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma 
)
inline

Definition at line 130 of file cauchy_lpdf.hpp.

§ cauchy_rng()

template<class RNG >
double stan::math::cauchy_rng ( double  mu,
double  sigma,
RNG &  rng 
)
inline

Definition at line 21 of file cauchy_rng.hpp.

§ cbrt() [1/5]

template<typename T >
fvar<T> stan::math::cbrt ( const fvar< T > &  x)
inline

Return cube root of specified argument.

Template Parameters
TScalar type of autodiff variable.
Parameters
xArgument.
Returns
Cube root of argument.

Definition at line 18 of file cbrt.hpp.

§ cbrt() [2/5]

double stan::math::cbrt ( double  x)
inline

Return the cube root of the specified value.

Parameters
[in]xArgument.
Returns
Cube root of the argument.
Exceptions
std::domain_errorIf argument is negative.

Definition at line 20 of file cbrt.hpp.

§ cbrt() [3/5]

template<typename T >
apply_scalar_unary<cbrt_fun, T>::return_t stan::math::cbrt ( const T &  x)
inline

Vectorized version of cbrt().

Parameters
xContainer of variables.
Template Parameters
TContainer type.
Returns
Cube root of each value in x.

Definition at line 32 of file cbrt.hpp.

§ cbrt() [4/5]

double stan::math::cbrt ( int  x)
inline

Integer version of cbrt.

Parameters
[in]xArgument.
Returns
Cube root of the argument.
Exceptions
std::domain_errorIf argument is less than 1.

Definition at line 35 of file cbrt.hpp.

§ cbrt() [5/5]

var stan::math::cbrt ( const var a)
inline

Returns the cube root of the specified variable (C99).

The derivative is

$\frac{d}{dx} x^{1/3} = \frac{1}{3 x^{2/3}}$.

\[ \mbox{cbrt}(x) = \begin{cases} \sqrt[3]{x} & \mbox{if } -\infty\leq x \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{cbrt}(x)}{\partial x} = \begin{cases} \frac{1}{3x^{2/3}} & \mbox{if } -\infty\leq x\leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

Parameters
aSpecified variable.
Returns
Cube root of the variable.

Definition at line 49 of file cbrt.hpp.

§ ceil() [1/3]

template<typename T >
fvar<T> stan::math::ceil ( const fvar< T > &  x)
inline

Definition at line 11 of file ceil.hpp.

§ ceil() [2/3]

template<typename T >
apply_scalar_unary<ceil_fun, T>::return_t stan::math::ceil ( const T &  x)
inline

Vectorized version of ceil().

Parameters
xContainer.
Template Parameters
TContainer type.
Returns
Least integer >= each value in x.

Definition at line 32 of file ceil.hpp.

§ ceil() [3/3]

var stan::math::ceil ( const var a)
inline

Return the ceiling of the specified variable (cmath).

The derivative of the ceiling function is defined and zero everywhere but at integers, and we set them to zero for convenience,

$\frac{d}{dx} {\lceil x \rceil} = 0$.

The ceiling function rounds up. For double values, this is the smallest integral value that is not less than the specified value. Although this function is not differentiable because it is discontinuous at integral values, its gradient is returned as zero everywhere.

\[ \mbox{ceil}(x) = \begin{cases} \lceil x\rceil & \mbox{if } -\infty\leq x \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{ceil}(x)}{\partial x} = \begin{cases} 0 & \mbox{if } -\infty\leq x\leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

Parameters
aInput variable.
Returns
Ceiling of the variable.

Definition at line 60 of file ceil.hpp.

§ check_bounded()

template<typename T_y , typename T_low , typename T_high >
void stan::math::check_bounded ( const char *  function,
const char *  name,
const T_y &  y,
const T_low &  low,
const T_high &  high 
)
inline

Check if the value is between the low and high values, inclusively.

Template Parameters
T_yType of value
T_lowType of low value
T_highType of high value
Parameters
functionFunction name (for error messages)
nameVariable name (for error messages)
yValue to check
lowLow bound
highHigh bound
Exceptions
<code>std::domain_error</code>otherwise. This also throws if any of the arguments are NaN.

Definition at line 90 of file check_bounded.hpp.

§ check_cholesky_factor()

template<typename T_y >
void stan::math::check_cholesky_factor ( const char *  function,
const char *  name,
const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &  y 
)
inline

Check if the specified matrix is a valid Cholesky factor.

A Cholesky factor is a lower triangular matrix whose diagonal elements are all positive. Note that Cholesky factors need not be square, but require at least as many rows M as columns N (i.e., M >= N).

Template Parameters
T_yType of elements of Cholesky factor
Parameters
functionFunction name (for error messages)
nameVariable name (for error messages)
yMatrix to test
Exceptions
<code>std::domain_error</code>if y is not a valid Choleksy factor, if number of rows is less than the number of columns, if there are 0 columns, or if any element in matrix is NaN

Definition at line 32 of file check_cholesky_factor.hpp.

§ check_cholesky_factor_corr()

template<typename T_y >
void stan::math::check_cholesky_factor_corr ( const char *  function,
const char *  name,
const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &  y 
)

Check if the specified matrix is a valid Cholesky factor of a correlation matrix.

A Cholesky factor is a lower triangular matrix whose diagonal elements are all positive. Note that Cholesky factors need not be square, but require at least as many rows M as columns N (i.e., M >= N).

Tolerance is specified by math::CONSTRAINT_TOLERANCE.

Template Parameters
T_yType of elements of Cholesky factor
Parameters
functionFunction name (for error messages)
nameVariable name (for error messages)
yMatrix to test
Exceptions
<code>std::domain_error</code>if y is not a valid Choleksy factor, if number of rows is less than the number of columns, if there are 0 columns, or if any element in matrix is NaN

Definition at line 35 of file check_cholesky_factor_corr.hpp.

§ check_column_index()

template<typename T_y , int R, int C>
void stan::math::check_column_index ( const char *  function,
const char *  name,
const Eigen::Matrix< T_y, R, C > &  y,
size_t  i 
)
inline

Check if the specified index is a valid column of the matrix.

By default, this is a 1-indexed check (as opposed to 0-indexed). Behavior can be changed by setting stan::error_index::value. This function will throw an std::out_of_range exception if the index is out of bounds.

Template Parameters
T_yType of scalar.
RNumber of rows of the matrix
CNumber of columns of the matrix
Parameters
functionFunction name (for error messages)
nameVariable name (for error messages)
yMatrix
iIndex to check
Exceptions
std::out_of_rangeif index is an invalid column index

Definition at line 35 of file check_column_index.hpp.

§ check_consistent_size()

template<typename T >
void stan::math::check_consistent_size ( const char *  function,
const char *  name,
const T &  x,
size_t  expected_size 
)
inline

Check if the dimension of x is consistent, which is defined to be expected_size if x is a vector or 1 if x is not a vector.

Template Parameters
TType of value
Parameters
functionFunction name (for error messages)
nameVariable name (for error messages)
xVariable to check for consistent size
expected_sizeExpected size if x is a vector
Exceptions
<code>invalid_argument</code>if the size is inconsistent

Definition at line 27 of file check_consistent_size.hpp.

§ check_consistent_sizes() [1/4]

template<typename T1 , typename T2 >
void stan::math::check_consistent_sizes ( const char *  function,
const char *  name1,
const T1 &  x1,
const char *  name2,
const T2 &  x2 
)
inline

Check if the dimension of x1 is consistent with x2.

Consistent size is defined as having the same size if vector-like or being a scalar.

Template Parameters
T1Type of x1
T2Type of x2
Parameters
functionFunction name (for error messages)
name1Variable name (for error messages)
x1Variable to check for consistent size
name2Variable name (for error messages)
x2Variable to check for consistent size
Exceptions
<code>invalid_argument</code>if sizes are inconsistent

Definition at line 30 of file check_consistent_sizes.hpp.

§ check_consistent_sizes() [2/4]

template<typename T1 , typename T2 , typename T3 >
void stan::math::check_consistent_sizes ( const char *  function,
const char *  name1,
const T1 &  x1,
const char *  name2,
const T2 &  x2,
const char *  name3,
const T3 &  x3 
)
inline

Check if the dimension of x1, x2, and x3 are consistent.

Consistent size is defined as having the same size if vector-like or being a scalar.

Template Parameters
T1Type of x1
T2Type of x2
T3Type of x3
Parameters
functionFunction name (for error messages)
name1Variable name (for error messages)
x1Variable to check for consistent size
name2Variable name (for error messages)
x2Variable to check for consistent size
name3Variable name (for error messages)
x3Variable to check for consistent size
Exceptions
<code>invalid_argument</code>if sizes are inconsistent

Definition at line 64 of file check_consistent_sizes.hpp.

§ check_consistent_sizes() [3/4]

template<typename T1 , typename T2 , typename T3 , typename T4 >
void stan::math::check_consistent_sizes ( const char *  function,
const char *  name1,
const T1 &  x1,
const char *  name2,
const T2 &  x2,
const char *  name3,
const T3 &  x3,
const char *  name4,
const T4 &  x4 
)
inline

Check if the dimension of x1, x2, x3, and x4 are consistent.

Consistent size is defined as having the same size if vector-like or being a scalar.

Template Parameters
T1Type of x1
T2Type of x2
T3Type of x3
T4Type of x4
Parameters
functionFunction name (for error messages)
name1Variable name (for error messages)
x1Variable to check for consistent size
name2Variable name (for error messages)
x2Variable to check for consistent size
name3Variable name (for error messages)
x3Variable to check for consistent size
name4Variable name (for error messages)
x4Variable to check for consistent size
Exceptions
<code>invalid_argument</code>if sizes are inconsistent

Definition at line 104 of file check_consistent_sizes.hpp.

§ check_consistent_sizes() [4/4]

template<typename T1 , typename T2 , typename T3 , typename T4 , typename T5 >
void stan::math::check_consistent_sizes ( const char *  function,
const char *  name1,
const T1 &  x1,
const char *  name2,
const T2 &  x2,
const char *  name3,
const T3 &  x3,
const char *  name4,
const T4 &  x4,
const char *  name5,
const T5 &  x5 
)
inline

Definition at line 125 of file check_consistent_sizes.hpp.

§ check_corr_matrix()

template<typename T_y >
void stan::math::check_corr_matrix ( const char *  function,
const char *  name,
const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &  y 
)
inline

Check if the specified matrix is a valid correlation matrix.

A valid correlation matrix is symmetric, has a unit diagonal (all 1 values), and has all values between -1 and 1 (inclusive).

This function throws exceptions if the variable is not a valid correlation matrix.

Template Parameters
T_yType of scalar
Parameters
functionName of the function this was called from
nameName of the variable
yMatrix to test
Exceptions
<code>std::invalid_argument</code>if the matrix is not square or if the matrix is 0x0
<code>std::domain_error</code>if the matrix is non-symmetric, diagonals not near 1, not positive definite, or any of the elements nan.

Definition at line 44 of file check_corr_matrix.hpp.

§ check_cov_matrix()

template<typename T_y >
void stan::math::check_cov_matrix ( const char *  function,
const char *  name,
const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &  y 
)
inline

Check if the specified matrix is a valid covariance matrix.

A valid covariance matrix is a square, symmetric matrix that is positive definite.

Template Parameters
TType of scalar.
Parameters
functionFunction name (for error messages)
nameVariable name (for error messages)
yMatrix to test
Exceptions
<code>std::invalid_argument</code>if the matrix is not square or if the matrix is 0x0
<code>std::domain_error</code>if the matrix is not symmetric, if the matrix is not positive definite, or if any element of the matrix is nan

Definition at line 30 of file check_cov_matrix.hpp.

§ check_finite()

template<typename T_y >
void stan::math::check_finite ( const char *  function,
const char *  name,
const T_y &  y 
)
inline

Check if y is finite.

This function is vectorized and will check each element of y.

Template Parameters
T_yType of y
Parameters
functionFunction name (for error messages)
nameVariable name (for error messages)
yVariable to check
Exceptions
<code>domain_error</code>if y is infinity, -infinity, or NaN.

Definition at line 57 of file check_finite.hpp.

§ check_greater()

template<typename T_y , typename T_low >
void stan::math::check_greater ( const char *  function,
const char *  name,
const T_y &  y,
const T_low &  low 
)
inline

Check if y is strictly greater than low.

This function is vectorized and will check each element of y against each element of low.

Template Parameters
T_yType of y
T_lowType of lower bound
Parameters
functionFunction name (for error messages)
nameVariable name (for error messages)
yVariable to check
lowLower bound
Exceptions
<code>domain_error</code>if y is not greater than low or if any element of y or low is NaN.

Definition at line 78 of file check_greater.hpp.

§ check_greater_or_equal()

template<typename T_y , typename T_low >
void stan::math::check_greater_or_equal ( const char *  function,
const char *  name,
const T_y &  y,
const T_low &  low 
)
inline

Check if y is greater or equal than low.

This function is vectorized and will check each element of y against each element of low.

Template Parameters
T_yType of y
T_lowType of lower bound
Parameters
functionFunction name (for error messages)
nameVariable name (for error messages)
yVariable to check
lowLower bound
Exceptions
<code>domain_error</code>if y is not greater or equal to low or if any element of y or low is NaN.

Definition at line 78 of file check_greater_or_equal.hpp.

§ check_ldlt_factor()

template<typename T , int R, int C>
void stan::math::check_ldlt_factor ( const char *  function,
const char *  name,
LDLT_factor< T, R, C > &  A 
)
inline

Check if the argument is a valid LDLT_factor.

LDLT_factor can be constructed in an invalid state, so it must be checked. A invalid LDLT_factor is constructed from a non positive definite matrix.

Template Parameters
TType of scalar
RRows of the matrix
CColumns of the matrix
Parameters
functionFunction name (for error messages)
nameVariable name (for error messages)
ALDLT_factor to check for validity.
Exceptions
<code>std::domain_error</code>the LDLT_factor was created improperly (A.success() == false)

Definition at line 33 of file check_ldlt_factor.hpp.

§ check_less()

template<typename T_y , typename T_high >
void stan::math::check_less ( const char *  function,
const char *  name,
const T_y &  y,
const T_high &  high 
)
inline

Check if y is strictly less than high.

This function is vectorized and will check each element of y against each element of high.

Template Parameters
T_yType of y
T_highType of upper bound
Parameters
functionFunction name (for error messages)
nameVariable name (for error messages)
yVariable to check
highUpper bound
Exceptions
<code>domain_error</code>if y is not less than low or if any element of y or high is NaN.

Definition at line 78 of file check_less.hpp.

§ check_less_or_equal()

template<typename T_y , typename T_high >
void stan::math::check_less_or_equal ( const char *  function,
const char *  name,
const T_y &  y,
const T_high &  high 
)
inline

Check if y is less or equal to high.

This function is vectorized and will check each element of y against each element of high.

Template Parameters
T_yType of y
T_highType of upper bound
Parameters
functionFunction name (for error messages)
nameVariable name (for error messages)
yVariable to check
highUpper bound
Exceptions
<code>std::domain_error</code>if y is not less than or equal to low or if any element of y or high is NaN.

Definition at line 78 of file check_less_or_equal.hpp.

§ check_lower_triangular()

template<typename T_y >
void stan::math::check_lower_triangular ( const char *  function,
const char *  name,
const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &  y 
)
inline

Check if the specified matrix is lower triangular.

A matrix x is not lower triangular if there is a non-zero entry x[m, n] with m < n. This function only inspects the upper triangular portion of the matrix, not including the diagonal.

Template Parameters
TType of scalar of the matrix
Parameters
functionFunction name (for error messages)
nameVariable name (for error messages)
yMatrix to test
Exceptions
<code>std::domain_error</code>if the matrix is not lower triangular or if any element in the upper triangular portion is NaN

Definition at line 32 of file check_lower_triangular.hpp.

§ check_matching_dims()

template<typename T1 , typename T2 , int R1, int C1, int R2, int C2>
void stan::math::check_matching_dims ( const char *  function,
const char *  name1,
const Eigen::Matrix< T1, R1, C1 > &  y1,
const char *  name2,
const Eigen::Matrix< T2, R2, C2 > &  y2 
)
inline

Check if the two matrices are of the same size.

This function checks not only the runtime sizes, but the static sizes as well. For example, a 4x1 matrix is not the same as a vector with 4 elements.

Template Parameters
T1Scalar type of the first matrix
T2Scalar type of the second matrix
R1Rows specified at compile time of the first matrix
C1Columns specified at compile time of the first matrix
R2Rows specified at compile time of the second matrix
C2Columns specified at compile time of the second matrix
Parameters
functionFunction name (for error messages)
name1Variable name for the first matrix (for error messages)
y1First matrix
name2Variable name for the second matrix (for error messages)
y2Second matrix
Exceptions
<code>std::invalid_argument</code>if the dimensions of the matrices do not match

Definition at line 36 of file check_matching_dims.hpp.

§ check_matching_sizes()

template<typename T_y1 , typename T_y2 >
void stan::math::check_matching_sizes ( const char *  function,
const char *  name1,
const T_y1 &  y1,
const char *  name2,
const T_y2 &  y2 
)
inline

Check if two structures at the same size.

This function only checks the runtime sizes for variables that implement a size() method.

Template Parameters
T_y1Type of the first variable
T_y2Type of the second variable
Parameters
functionFunction name (for error messages)
name1First variable name (for error messages)
y1First variable
name2Second variable name (for error messages)
y2Second variable
Exceptions
<code>std::invalid_argument</code>if the sizes do not match

Definition at line 28 of file check_matching_sizes.hpp.

§ check_multiplicable()

template<typename T1 , typename T2 >
void stan::math::check_multiplicable ( const char *  function,
const char *  name1,
const T1 &  y1,
const char *  name2,
const T2 &  y2 
)
inline

Check if the matrices can be multiplied.

This checks the runtime sizes to determine whether the two matrices are multiplicable. This allows Eigen matrices, vectors, and row vectors to be checked.

Template Parameters
T1Type of first matrix
T2Type of second matrix
Parameters
functionFunction name (for error messages)
name1Variable name for the first matrix (for error messages)
y1First matrix
name2Variable name for the second matrix (for error messages)
y2Second matrix
Exceptions
<code>std::invalid_argument</code>if the matrices are not multiplicable or if either matrix is size 0 for either rows or columns

Definition at line 31 of file check_multiplicable.hpp.

§ check_nonnegative()

template<typename T_y >
void stan::math::check_nonnegative ( const char *  function,
const char *  name,
const T_y &  y 
)
inline

Check if y is non-negative.

This function is vectorized and will check each element of y.

Template Parameters
T_yType of y
Parameters
functionFunction name (for error messages)
nameVariable name (for error messages)
yVariable to check
Exceptions
<code>domain_error</code>if y is negative or if any element of y is NaN.

Definition at line 61 of file check_nonnegative.hpp.

§ check_nonzero_size()

template<typename T_y >
void stan::math::check_nonzero_size ( const char *  function,
const char *  name,
const T_y &  y 
)
inline

Check if the specified matrix/vector is of non-zero size.

Throws a std:invalid_argument otherwise. The message will indicate that the variable name "has size 0".

Template Parameters
T_yType of container
Parameters
functionFunction name (for error messages)
nameVariable name (for error messages)
yContainer to test. This will accept matrices and vectors
Exceptions
<code>std::invalid_argument</code>if the specified matrix/vector has zero size

Definition at line 27 of file check_nonzero_size.hpp.

§ check_not_nan()

template<typename T_y >
void stan::math::check_not_nan ( const char *  function,
const char *  name,
const T_y &  y 
)
inline

Check if y is not NaN.

This function is vectorized and will check each element of y. If any element is NaN, this function will throw an exception.

Template Parameters
T_yType of y
Parameters
functionFunction name (for error messages)
nameVariable name (for error messages)
yVariable to check
Exceptions
<code>domain_error</code>if any element of y is NaN.

Definition at line 57 of file check_not_nan.hpp.

§ check_ordered() [1/2]

template<typename T_y >
void stan::math::check_ordered ( const char *  function,
const char *  name,
const std::vector< T_y > &  y 
)

Check if the specified vector is sorted into strictly increasing order.

Template Parameters
T_yType of scalar
Parameters
functionFunction name (for error messages)
nameVariable name (for error messages)
ystd::vector to test
Exceptions
<code>std::domain_error</code>if the vector elements are not ordered, if there are duplicated values, or if any element is NaN.

Definition at line 29 of file check_ordered.hpp.

§ check_ordered() [2/2]

template<typename T_y >
void stan::math::check_ordered ( const char *  function,
const char *  name,
const Eigen::Matrix< T_y, Eigen::Dynamic, 1 > &  y 
)

Check if the specified vector is sorted into strictly increasing order.

Template Parameters
T_yType of scalar
Parameters
functionFunction name (for error messages)
nameVariable name (for error messages)
yVector to test
Exceptions
<code>std::domain_error</code>if the vector elements are not ordered, if there are duplicated values, or if any element is NaN.

Definition at line 30 of file check_ordered.hpp.

§ check_pos_definite() [1/3]

template<typename T_y >
void stan::math::check_pos_definite ( const char *  function,
const char *  name,
const Eigen::Matrix< T_y, -1, -1 > &  y 
)
inline

Check if the specified square, symmetric matrix is positive definite.

Template Parameters
T_yType of scalar of the matrix
Parameters
functionFunction name (for error messages)
nameVariable name (for error messages)
yMatrix to test
Exceptions
<code>std::invalid_argument</code>if the matrix is not square or if the matrix has 0 size.
<code>std::domain_error</code>if the matrix is not symmetric, if it is not positive definite, or if any element is NaN.

Definition at line 33 of file check_pos_definite.hpp.

§ check_pos_definite() [2/3]

template<typename Derived >
void stan::math::check_pos_definite ( const char *  function,
const char *  name,
const Eigen::LDLT< Derived > &  cholesky 
)
inline

Check if the specified LDLT transform of a matrix is positive definite.

Template Parameters
DerivedDerived type of the Eigen::LDLT transform.
Parameters
functionFunction name (for error messages)
nameVariable name (for error messages)
choleskyEigen::LDLT to test, whose progenitor must not have any NaN elements
Exceptions
<code>std::domain_error</code>if the matrix is not positive definite.

Definition at line 61 of file check_pos_definite.hpp.

§ check_pos_definite() [3/3]

template<typename Derived >
void stan::math::check_pos_definite ( const char *  function,
const char *  name,
const Eigen::LLT< Derived > &  cholesky 
)
inline

Check if the specified LLT decomposition transform resulted in Eigen::Success

Template Parameters
DerivedDerived type of the Eigen::LLT transform.
Parameters
functionFunction name (for error messages)
nameVariable name (for error messages)
choleskyEigen::LLT to test, whose progenitor must not have any NaN elements
Exceptions
<code>std::domain_error</code>if the diagonal of the L matrix is not positive.

Definition at line 84 of file check_pos_definite.hpp.

§ check_pos_semidefinite()

template<typename T_y >
void stan::math::check_pos_semidefinite ( const char *  function,
const char *  name,
const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &  y 
)
inline

Check if the specified matrix is positive definite.

Template Parameters
T_yscalar type of the matrix
Parameters
functionFunction name (for error messages)
nameVariable name (for error messages)
yMatrix to test
Exceptions
<code>std::invalid_argument</code>if the matrix is not square or if the matrix has 0 size.
<code>std::domain_error</code>if the matrix is not symmetric, or if it is not positive semi-definite, or if any element of the matrix is NaN.

Definition at line 34 of file check_pos_semidefinite.hpp.

§ check_positive()

template<typename T_y >
void stan::math::check_positive ( const char *  function,
const char *  name,
const T_y &  y 
)
inline

Check if y is positive.

This function is vectorized and will check each element of y.

Template Parameters
T_yType of y
Parameters
functionFunction name (for error messages)
nameVariable name (for error messages)
yVariable to check
Exceptions
<code>domain_error</code>if y is negative or zero or if any element of y is NaN.

Definition at line 63 of file check_positive.hpp.

§ check_positive_finite()

template<typename T_y >
void stan::math::check_positive_finite ( const char *  function,
const char *  name,
const T_y &  y 
)
inline

Check if y is positive and finite.

This function is vectorized and will check each element of y.

Template Parameters
T_yType of y
Parameters
functionFunction name (for error messages)
nameVariable name (for error messages)
yVariable to check
Exceptions
<code>domain_error</code>if any element of y is not positive or if any element of y is NaN.

Definition at line 26 of file check_positive_finite.hpp.

§ check_positive_ordered()

template<typename T_y >
void stan::math::check_positive_ordered ( const char *  function,
const char *  name,
const Eigen::Matrix< T_y, Eigen::Dynamic, 1 > &  y 
)

Check if the specified vector contains non-negative values and is sorted into strictly increasing order.

Parameters
functionFunction name (for error messages)
nameVariable name (for error messages)
yVector to test
Exceptions
<code>std::domain_error</code>if the vector contains non-positive values, if the values are not ordered, if there are duplicated values, or if any element is NaN.

Definition at line 29 of file check_positive_ordered.hpp.

§ check_positive_size()

void stan::math::check_positive_size ( const char *  function,
const char *  name,
const char *  expr,
int  size 
)
inline

Check if size is positive.

Parameters
functionFunction name (for error messages)
nameVariable name (for error messages)
exprExpression for the dimension size (for error messages)
sizeSize value to check
Exceptions
<code>std::invalid_argument</code>if size is zero or negative.

Definition at line 22 of file check_positive_size.hpp.

§ check_range() [1/3]

void stan::math::check_range ( const char *  function,
const char *  name,
int  max,
int  index,
int  nested_level,
const char *  error_msg 
)
inline

Check if specified index is within range.

This check is 1-indexed by default. This behavior can be changed by setting stan::error_index::value.

Parameters
functionFunction name (for error messages)
nameVariable name (for error messages)
maxMaximum size of the variable
indexIndex to check
nested_levelNested level (for error messages)
error_msgAdditional error message (for error messages)
Exceptions
<code>std::out_of_range</code>if the index is not in range

Definition at line 28 of file check_range.hpp.

§ check_range() [2/3]

void stan::math::check_range ( const char *  function,
const char *  name,
int  max,
int  index,
const char *  error_msg 
)
inline

Check if specified index is within range.

This check is 1-indexed by default. This behavior can be changed by setting stan::error_index::value.

Parameters
functionFunction name (for error messages)
nameVariable name (for error messages)
maxMaximum size of the variable
indexIndex to check
error_msgAdditional error message (for error messages)
Exceptions
<code>std::out_of_range</code>if the index is not in range

Definition at line 59 of file check_range.hpp.

§ check_range() [3/3]

void stan::math::check_range ( const char *  function,
const char *  name,
int  max,
int  index 
)
inline

Check if specified index is within range.

This check is 1-indexed by default. This behavior can be changed by setting stan::error_index::value.

Parameters
functionFunction name (for error messages)
nameVariable name (for error messages)
maxMaximum size of the variable
indexIndex to check
Exceptions
<code>std::out_of_range</code>if the index is not in range

Definition at line 84 of file check_range.hpp.

§ check_row_index()

template<typename T_y , int R, int C>
void stan::math::check_row_index ( const char *  function,
const char *  name,
const Eigen::Matrix< T_y, R, C > &  y,
size_t  i 
)
inline

Check if the specified index is a valid row of the matrix.

This check is 1-indexed by default. This behavior can be changed by setting stan::error_index::value.

Template Parameters
TScalar type
RCompile time rows
CCompile time columns
Parameters
functionFunction name (for error messages)
nameVariable name (for error messages)
yMatrix to test
iis index
Exceptions
<code>std::out_of_range</code>if the index is out of range.

Definition at line 30 of file check_row_index.hpp.

§ check_simplex()

template<typename T_prob >
void stan::math::check_simplex ( const char *  function,
const char *  name,
const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &  theta 
)

Check if the specified vector is simplex.

To be a simplex, all values must be greater than or equal to 0 and the values must sum to 1.

A valid simplex is one where the sum of hte elements is equal to 1. This function tests that the sum is within the tolerance specified by CONSTRAINT_TOLERANCE. This function only accepts Eigen vectors, statically typed vectors, not general matrices with 1 column.

Template Parameters
T_probScalar type of the vector
Parameters
functionFunction name (for error messages)
nameVariable name (for error messages)
thetaVector to test.
Exceptions
<code>std::invalid_argument</code>if theta is a 0-vector.
<code>std::domain_error</code>if the vector is not a simplex or if any element is NaN.

Definition at line 39 of file check_simplex.hpp.

§ check_size_match() [1/2]

template<typename T_size1 , typename T_size2 >
void stan::math::check_size_match ( const char *  function,
const char *  name_i,
T_size1  i,
const char *  name_j,
T_size2  j 
)
inline

Check if the provided sizes match.

Template Parameters
T_size1Type of size 1
T_size2Type of size 2
Parameters
functionFunction name (for error messages)
name_iVariable name 1 (for error messages)
iSize 1
name_jVariable name 2 (for error messages)
jSize 2
Exceptions
<code>std::invalid_argument</code>if the sizes do not match

Definition at line 29 of file check_size_match.hpp.

§ check_size_match() [2/2]

template<typename T_size1 , typename T_size2 >
void stan::math::check_size_match ( const char *  function,
const char *  expr_i,
const char *  name_i,
T_size1  i,
const char *  expr_j,
const char *  name_j,
T_size2  j 
)
inline

Check if the provided sizes match.

Template Parameters
T_size1Type of size 1
T_size2Type of size 2
Parameters
functionFunction name (for error messages)
expr_iExpression for variable name 1 (for error messages)
name_iVariable name 1 (for error messages)
iSize 1
expr_jExpression for variable name 2 (for error messages)
name_jVariable name 2 (for error messages)
jSize 2
Exceptions
<code>std::invalid_argument</code>if the sizes do not match

Definition at line 63 of file check_size_match.hpp.

§ check_spsd_matrix()

template<typename T_y >
void stan::math::check_spsd_matrix ( const char *  function,
const char *  name,
const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &  y 
)
inline

Check if the specified matrix is a square, symmetric, and positive semi-definite.

Template Parameters
TScalar type of the matrix
Parameters
functionFunction name (for error messages)
nameVariable name (for error messages)
yMatrix to test
Exceptions
<code>std::invalid_argument</code>if the matrix is not square or if the matrix is 0x0
<code>std::domain_error</code>if the matrix is not symmetric or if the matrix is not positive semi-definite

Definition at line 29 of file check_spsd_matrix.hpp.

§ check_square()

template<typename T_y >
void stan::math::check_square ( const char *  function,
const char *  name,
const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &  y 
)
inline

Check if the specified matrix is square.

This check allows 0x0 matrices.

Template Parameters
TType of scalar.
Parameters
functionFunction name (for error messages)
nameVariable name (for error messages)
yMatrix to test
Exceptions
<code>std::invalid_argument</code>if the matrix is not square

Definition at line 27 of file check_square.hpp.

§ check_std_vector_index()

template<typename T >
void stan::math::check_std_vector_index ( const char *  function,
const char *  name,
const std::vector< T > &  y,
int  i 
)
inline

Check if the specified index is valid in std vector.

This check is 1-indexed by default. This behavior can be changed by setting stan::error_index::value.

Template Parameters
TScalar type
Parameters
functionFunction name (for error messages)
nameVariable name (for error messages)
ystd::vector to test
iIndex
Exceptions
<code>std::out_of_range</code>if the index is out of range.

Definition at line 29 of file check_std_vector_index.hpp.

§ check_symmetric()

template<typename T_y >
void stan::math::check_symmetric ( const char *  function,
const char *  name,
const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &  y 
)
inline

Check if the specified matrix is symmetric.

The error message is either 0 or 1 indexed, specified by stan::error_index::value.

Template Parameters
T_yType of scalar.
Parameters
functionFunction name (for error messages)
nameVariable name (for error messages)
yMatrix to test
Exceptions
<code>std::invalid_argument</code>if the matrix is not square.
<code>std::domain_error</code>if any element not on the main diagonal is NaN

Definition at line 35 of file check_symmetric.hpp.

§ check_unit_vector()

template<typename T_prob >
void stan::math::check_unit_vector ( const char *  function,
const char *  name,
const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &  theta 
)

Check if the specified vector is unit vector.

A valid unit vector is one where the square of the elements summed is equal to 1. This function tests that the sum is within the tolerance specified by CONSTRAINT_TOLERANCE. This function only accepts Eigen vectors, statically typed vectors, not general matrices with 1 column.

Template Parameters
T_probScalar type of the vector
Parameters
functionFunction name (for error messages)
nameVariable name (for error messages)
thetaVector to test.
Exceptions
<code>std::invalid_argument</code>if theta is a 0-vector.
<code>std::domain_error</code>if the vector is not a unit vector or if any element is NaN.

Definition at line 34 of file check_unit_vector.hpp.

§ check_vector()

template<typename T , int R, int C>
void stan::math::check_vector ( const char *  function,
const char *  name,
const Eigen::Matrix< T, R, C > &  x 
)
inline

Check if the matrix is either a row vector or column vector.

This function checks the runtime size of the matrix to check whether it is a row or column vector.

Template Parameters
TScalar type of the matrix
RCompile time rows of the matrix
CCompile time columns of the matrix
Parameters
functionFunction name (for error messages)
nameVariable name (for error messages)
xMatrix
Exceptions
<code>std::invalid_argument</code>if x is not a row or column vector.

Definition at line 32 of file check_vector.hpp.

§ chi_square_ccdf_log()

template<typename T_y , typename T_dof >
return_type<T_y, T_dof>::type stan::math::chi_square_ccdf_log ( const T_y &  y,
const T_dof &  nu 
)

Definition at line 29 of file chi_square_ccdf_log.hpp.

§ chi_square_cdf()

template<typename T_y , typename T_dof >
return_type<T_y, T_dof>::type stan::math::chi_square_cdf ( const T_y &  y,
const T_dof &  nu 
)

Calculates the chi square cumulative distribution function for the given variate and degrees of freedom.

y A scalar variate. nu Degrees of freedom.

Returns
The cdf of the chi square distribution

Definition at line 38 of file chi_square_cdf.hpp.

§ chi_square_cdf_log()

template<typename T_y , typename T_dof >
return_type<T_y, T_dof>::type stan::math::chi_square_cdf_log ( const T_y &  y,
const T_dof &  nu 
)

Definition at line 29 of file chi_square_cdf_log.hpp.

§ chi_square_lccdf()

template<typename T_y , typename T_dof >
return_type<T_y, T_dof>::type stan::math::chi_square_lccdf ( const T_y &  y,
const T_dof &  nu 
)

Definition at line 29 of file chi_square_lccdf.hpp.

§ chi_square_lcdf()

template<typename T_y , typename T_dof >
return_type<T_y, T_dof>::type stan::math::chi_square_lcdf ( const T_y &  y,
const T_dof &  nu 
)

Definition at line 29 of file chi_square_lcdf.hpp.

§ chi_square_log() [1/2]

template<bool propto, typename T_y , typename T_dof >
return_type<T_y, T_dof>::type stan::math::chi_square_log ( const T_y &  y,
const T_dof &  nu 
)

The log of a chi-squared density for y with the specified degrees of freedom parameter.

The degrees of freedom prarameter must be greater than 0. y must be greater than or equal to 0.

\begin{eqnarray*} y &\sim& \chi^2_\nu \\ \log (p (y \, |\, \nu)) &=& \log \left( \frac{2^{-\nu / 2}}{\Gamma (\nu / 2)} y^{\nu / 2 - 1} \exp^{- y / 2} \right) \\ &=& - \frac{\nu}{2} \log(2) - \log (\Gamma (\nu / 2)) + (\frac{\nu}{2} - 1) \log(y) - \frac{y}{2} \\ & & \mathrm{ where } \; y \ge 0 \end{eqnarray*}

Parameters
yA scalar variable.
nuDegrees of freedom.
Exceptions
std::domain_errorif nu is not greater than or equal to 0
std::domain_errorif y is not greater than or equal to 0.
Template Parameters
T_yType of scalar.
T_dofType of degrees of freedom.

Definition at line 48 of file chi_square_log.hpp.

§ chi_square_log() [2/2]

template<typename T_y , typename T_dof >
return_type<T_y, T_dof>::type stan::math::chi_square_log ( const T_y &  y,
const T_dof &  nu 
)
inline

Definition at line 134 of file chi_square_log.hpp.

§ chi_square_lpdf() [1/2]

template<bool propto, typename T_y , typename T_dof >
return_type<T_y, T_dof>::type stan::math::chi_square_lpdf ( const T_y &  y,
const T_dof &  nu 
)

The log of a chi-squared density for y with the specified degrees of freedom parameter.

The degrees of freedom prarameter must be greater than 0. y must be greater than or equal to 0.

\begin{eqnarray*} y &\sim& \chi^2_\nu \\ \log (p (y \, |\, \nu)) &=& \log \left( \frac{2^{-\nu / 2}}{\Gamma (\nu / 2)} y^{\nu / 2 - 1} \exp^{- y / 2} \right) \\ &=& - \frac{\nu}{2} \log(2) - \log (\Gamma (\nu / 2)) + (\frac{\nu}{2} - 1) \log(y) - \frac{y}{2} \\ & & \mathrm{ where } \; y \ge 0 \end{eqnarray*}

Parameters
yA scalar variable.
nuDegrees of freedom.
Exceptions
std::domain_errorif nu is not greater than or equal to 0
std::domain_errorif y is not greater than or equal to 0.
Template Parameters
T_yType of scalar.
T_dofType of degrees of freedom.

Definition at line 48 of file chi_square_lpdf.hpp.

§ chi_square_lpdf() [2/2]

template<typename T_y , typename T_dof >
return_type<T_y, T_dof>::type stan::math::chi_square_lpdf ( const T_y &  y,
const T_dof &  nu 
)
inline

Definition at line 134 of file chi_square_lpdf.hpp.

§ chi_square_rng()

template<class RNG >
double stan::math::chi_square_rng ( double  nu,
RNG &  rng 
)
inline

Definition at line 23 of file chi_square_rng.hpp.

§ cholesky_corr_constrain() [1/2]

template<typename T >
Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> stan::math::cholesky_corr_constrain ( const Eigen::Matrix< T, Eigen::Dynamic, 1 > &  y,
int  K 
)

Definition at line 17 of file cholesky_corr_constrain.hpp.

§ cholesky_corr_constrain() [2/2]

template<typename T >
Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> stan::math::cholesky_corr_constrain ( const Eigen::Matrix< T, Eigen::Dynamic, 1 > &  y,
int  K,
T &  lp 
)

Definition at line 52 of file cholesky_corr_constrain.hpp.

§ cholesky_corr_free()

template<typename T >
Eigen::Matrix<T, Eigen::Dynamic, 1> stan::math::cholesky_corr_free ( const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &  x)

Definition at line 16 of file cholesky_corr_free.hpp.

§ cholesky_decompose() [1/2]

template<typename T >
Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> stan::math::cholesky_decompose ( const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &  m)

Return the lower-triangular Cholesky factor (i.e., matrix square root) of the specified square, symmetric matrix.

The return value $L$ will be a lower-traingular matrix such that the original matrix $A$ is given by

$A = L \times L^T$.

Parameters
mSymmetrix matrix.
Returns
Square root of matrix.
Exceptions
std::domain_errorif m is not a symmetric matrix or if m is not positive definite (if m has more than 0 elements)

Definition at line 25 of file cholesky_decompose.hpp.

§ cholesky_decompose() [2/2]

Eigen::Matrix<var, -1, -1> stan::math::cholesky_decompose ( const Eigen::Matrix< var, -1, -1 > &  A)
inline

Definition at line 131 of file cholesky_decompose.hpp.

§ cholesky_factor_constrain() [1/2]

template<typename T >
Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> stan::math::cholesky_factor_constrain ( const Eigen::Matrix< T, Eigen::Dynamic, 1 > &  x,
int  M,
int  N 
)

Return the Cholesky factor of the specified size read from the specified vector.

A total of (N choose 2) + N + (M - N) * N elements are required to read an M by N Cholesky factor.

Template Parameters
TType of scalars in matrix
Parameters
xVector of unconstrained values
MNumber of rows
NNumber of columns
Returns
Cholesky factor

Definition at line 28 of file cholesky_factor_constrain.hpp.

§ cholesky_factor_constrain() [2/2]

template<typename T >
Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> stan::math::cholesky_factor_constrain ( const Eigen::Matrix< T, Eigen::Dynamic, 1 > &  x,
int  M,
int  N,
T &  lp 
)

Return the Cholesky factor of the specified size read from the specified vector and increment the specified log probability reference with the log Jacobian adjustment of the transform.

A total of (N choose 2) + N + N * (M - N) free parameters are required to read an M by N Cholesky factor.

Template Parameters
TType of scalars in matrix
Parameters
xVector of unconstrained values
MNumber of rows
NNumber of columns
lpLog probability that is incremented with the log Jacobian
Returns
Cholesky factor

Definition at line 73 of file cholesky_factor_constrain.hpp.

§ cholesky_factor_free()

template<typename T >
Eigen::Matrix<T, Eigen::Dynamic, 1> stan::math::cholesky_factor_free ( const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &  y)

Return the unconstrained vector of parameters correspdonding to the specified Cholesky factor.

A Cholesky factor must be lower triangular and have positive diagonal elements.

Parameters
yCholesky factor.
Returns
Unconstrained parameters for Cholesky factor.
Exceptions
std::domain_errorIf the matrix is not a Cholesky factor.

Definition at line 23 of file cholesky_factor_free.hpp.

§ choose()

int stan::math::choose ( int  n,
int  k 
)
inline

Return the binomial coefficient for the specified integer arguments.

The binomial coefficient, ${n \choose k}$, read "n choose k", is defined for $0 \leq k \leq n$ (otherwise return 0) by

${n \choose k} = \frac{n!}{k! (n-k)!}$.

Parameters
ntotal number of objects
knumber of objects chosen
Returns
n choose k or 0 iff k > n
Exceptions
std::domain_errorif either argument is negative or the result will not fit in an int type

Definition at line 27 of file choose.hpp.

§ col()

template<typename T >
Eigen::Matrix<T, Eigen::Dynamic, 1> stan::math::col ( const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &  m,
size_t  j 
)
inline

Return the specified column of the specified matrix using start-at-1 indexing.

This is equivalent to calling m.col(i - 1) and assigning the resulting template expression to a column vector.

Parameters
mMatrix.
jColumn index (count from 1).
Returns
Specified column of the matrix.
Exceptions
std::out_of_rangeif j is out of range.

Definition at line 25 of file col.hpp.

§ cols()

template<typename T , int R, int C>
int stan::math::cols ( const Eigen::Matrix< T, R, C > &  m)
inline

Return the number of columns in the specified matrix, vector, or row vector.

Template Parameters
TType of matrix entries.
RRow type of matrix.
CColumn type of matrix.
Parameters
[in]mInput matrix, vector, or row vector.
Returns
Number of columns.

Definition at line 20 of file cols.hpp.

§ columns_dot_product() [1/5]

template<typename T , int R1, int C1, int R2, int C2>
Eigen::Matrix<fvar<T>, 1, C1> stan::math::columns_dot_product ( const Eigen::Matrix< fvar< T >, R1, C1 > &  v1,
const Eigen::Matrix< fvar< T >, R2, C2 > &  v2 
)
inline

Definition at line 18 of file columns_dot_product.hpp.

§ columns_dot_product() [2/5]

template<int R1, int C1, int R2, int C2>
Eigen::Matrix<double, 1, C1> stan::math::columns_dot_product ( const Eigen::Matrix< double, R1, C1 > &  v1,
const Eigen::Matrix< double, R2, C2 > &  v2 
)
inline

Returns the dot product of the specified vectors.

Parameters
v1First vector.
v2Second vector.
Returns
Dot product of the vectors.
Exceptions
std::domain_errorIf the vectors are not the same size or if they are both not vector dimensioned.

Definition at line 22 of file columns_dot_product.hpp.

§ columns_dot_product() [3/5]

template<typename T1 , int R1, int C1, typename T2 , int R2, int C2>
boost::enable_if_c<boost::is_same<T1, var>::value || boost::is_same<T2, var>::value, Eigen::Matrix<var, 1, C1> >::type stan::math::columns_dot_product ( const Eigen::Matrix< T1, R1, C1 > &  v1,
const Eigen::Matrix< T2, R2, C2 > &  v2 
)
inline

Definition at line 25 of file columns_dot_product.hpp.

§ columns_dot_product() [4/5]

template<typename T , int R1, int C1, int R2, int C2>
Eigen::Matrix<fvar<T>, 1, C1> stan::math::columns_dot_product ( const Eigen::Matrix< fvar< T >, R1, C1 > &  v1,
const Eigen::Matrix< double, R2, C2 > &  v2 
)
inline

Definition at line 35 of file columns_dot_product.hpp.

§ columns_dot_product() [5/5]

template<typename T , int R1, int C1, int R2, int C2>
Eigen::Matrix<fvar<T>, 1, C1> stan::math::columns_dot_product ( const Eigen::Matrix< double, R1, C1 > &  v1,
const Eigen::Matrix< fvar< T >, R2, C2 > &  v2 
)
inline

Definition at line 52 of file columns_dot_product.hpp.

§ columns_dot_self() [1/3]

template<typename T , int R, int C>
Eigen::Matrix<fvar<T>, 1, C> stan::math::columns_dot_self ( const Eigen::Matrix< fvar< T >, R, C > &  x)
inline

Definition at line 15 of file columns_dot_self.hpp.

§ columns_dot_self() [2/3]

template<typename T , int R, int C>
Eigen::Matrix<T, 1, C> stan::math::columns_dot_self ( const Eigen::Matrix< T, R, C > &  x)
inline

Returns the dot product of each column of a matrix with itself.

Parameters
xMatrix.
Template Parameters
Tscalar type

Definition at line 16 of file columns_dot_self.hpp.

§ columns_dot_self() [3/3]

template<int R, int C>
Eigen::Matrix<var, 1, C> stan::math::columns_dot_self ( const Eigen::Matrix< var, R, C > &  x)
inline

Returns the dot product of each column of a matrix with itself.

Parameters
xMatrix.
Template Parameters
Tscalar type

Definition at line 22 of file columns_dot_self.hpp.

§ corr_constrain() [1/2]

template<typename T >
T stan::math::corr_constrain ( const T  x)
inline

Return the result of transforming the specified scalar to have a valid correlation value between -1 and 1 (inclusive).

The transform used is the hyperbolic tangent function,

$f(x) = \tanh x = \frac{\exp(2x) - 1}{\exp(2x) + 1}$.

Parameters
xScalar input.
Returns
Result of transforming the input to fall between -1 and 1.
Template Parameters
TType of scalar.

Definition at line 24 of file corr_constrain.hpp.

§ corr_constrain() [2/2]

template<typename T >
T stan::math::corr_constrain ( const T  x,
T &  lp 
)
inline

Return the result of transforming the specified scalar to have a valid correlation value between -1 and 1 (inclusive).

The transform used is as specified for corr_constrain(T). The log absolute Jacobian determinant is

$\log | \frac{d}{dx} \tanh x | = \log (1 - \tanh^2 x)$.

Template Parameters
TType of scalar.

Definition at line 42 of file corr_constrain.hpp.

§ corr_free()

template<typename T >
T stan::math::corr_free ( const T  y)
inline

Return the unconstrained scalar that when transformed to a valid correlation produces the specified value.

This function inverts the transform defined for corr_constrain(T), which is the inverse hyperbolic tangent,

$ f^{-1}(y) = \mbox{atanh}\, y = \frac{1}{2} \log \frac{y + 1}{y - 1}$.

Parameters
yCorrelation scalar input.
Returns
Free scalar that transforms to the specified input.
Template Parameters
TType of scalar.

Definition at line 28 of file corr_free.hpp.

§ corr_matrix_constrain() [1/2]

template<typename T >
Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> stan::math::corr_matrix_constrain ( const Eigen::Matrix< T, Eigen::Dynamic, 1 > &  x,
typename math::index_type< Eigen::Matrix< T, Eigen::Dynamic, 1 > >::type  k 
)

Return the correlation matrix of the specified dimensionality derived from the specified vector of unconstrained values.

The input vector must be of length ${k \choose 2} = \frac{k(k-1)}{2}$. The values in the input vector represent unconstrained (partial) correlations among the dimensions.

The transform based on partial correlations is as specified in

  • Lewandowski, Daniel, Dorota Kurowicka, and Harry Joe. 2009. Generating random correlation matrices based on vines and extended onion method. Journal of Multivariate Analysis 100:1989–-2001.

The free vector entries are first constrained to be valid correlation values using corr_constrain(T).

Parameters
xVector of unconstrained partial correlations.
kDimensionality of returned correlation matrix.
Template Parameters
TType of scalar.
Exceptions
std::invalid_argumentif x is not a valid correlation matrix.

Definition at line 40 of file corr_matrix_constrain.hpp.

§ corr_matrix_constrain() [2/2]

template<typename T >
Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> stan::math::corr_matrix_constrain ( const Eigen::Matrix< T, Eigen::Dynamic, 1 > &  x,
typename math::index_type< Eigen::Matrix< T, Eigen::Dynamic, 1 > >::type  k,
T &  lp 
)

Return the correlation matrix of the specified dimensionality derived from the specified vector of unconstrained values.

The input vector must be of length ${k \choose 2} = \frac{k(k-1)}{2}$. The values in the input vector represent unconstrained (partial) correlations among the dimensions.

The transform is as specified for corr_matrix_constrain(Matrix, size_t); the paper it cites also defines the Jacobians for correlation inputs, which are composed with the correlation constrained Jacobians defined in corr_constrain(T, double) for this function.

Parameters
xVector of unconstrained partial correlations.
kDimensionality of returned correlation matrix.
lpLog probability reference to increment.
Template Parameters
TType of scalar.

Definition at line 78 of file corr_matrix_constrain.hpp.

§ corr_matrix_free()

template<typename T >
Eigen::Matrix<T, Eigen::Dynamic, 1> stan::math::corr_matrix_free ( const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &  y)

Return the vector of unconstrained partial correlations that define the specified correlation matrix when transformed.

The constraining transform is defined as for corr_matrix_constrain(Matrix, size_t). The inverse transform in this function is simpler in that it only needs to compute the $k \choose 2$ partial correlations and then free those.

Parameters
yThe correlation matrix to free.
Returns
Vector of unconstrained values that produce the specified correlation matrix when transformed.
Template Parameters
TType of scalar.
Exceptions
std::domain_errorif the correlation matrix has no elements or is not a square matrix.
std::runtime_errorif the correlation matrix cannot be factorized by factor_cov_matrix() or if the sds returned by factor_cov_matrix() on log scale are unconstrained.

Definition at line 38 of file corr_matrix_free.hpp.

§ cos() [1/3]

template<typename T >
fvar<T> stan::math::cos ( const fvar< T > &  x)
inline

Definition at line 13 of file cos.hpp.

§ cos() [2/3]

template<typename T >
apply_scalar_unary<cos_fun, T>::return_t stan::math::cos ( const T &  x)
inline

Vectorized version of cos().

Parameters
xContainer of angles in radians.
Template Parameters
TContainer type.
Returns
Cosine of each value in x.

Definition at line 32 of file cos.hpp.

§ cos() [3/3]

var stan::math::cos ( const var a)
inline

Return the cosine of a radian-scaled variable (cmath).

The derivative is defined by

$\frac{d}{dx} \cos x = - \sin x$.

\[ \mbox{cos}(x) = \begin{cases} \cos(x) & \mbox{if } -\infty\leq x \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{cos}(x)}{\partial x} = \begin{cases} -\sin(x) & \mbox{if } -\infty\leq x\leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

Parameters
aVariable for radians of angle.
Returns
Cosine of variable.

Definition at line 49 of file cos.hpp.

§ cosh() [1/3]

template<typename T >
fvar<T> stan::math::cosh ( const fvar< T > &  x)
inline

Definition at line 13 of file cosh.hpp.

§ cosh() [2/3]

template<typename T >
apply_scalar_unary<cosh_fun, T>::return_t stan::math::cosh ( const T &  x)
inline

Vectorized version of cosh().

Parameters
xAngle in radians.
Template Parameters
TVariable type.
Returns
Hyberbolic cosine of x.

Definition at line 32 of file cosh.hpp.

§ cosh() [3/3]

var stan::math::cosh ( const var a)
inline

Return the hyperbolic cosine of the specified variable (cmath).

The derivative is defined by

$\frac{d}{dx} \cosh x = \sinh x$.

\[ \mbox{cosh}(x) = \begin{cases} \cosh(x) & \mbox{if } -\infty\leq x \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{cosh}(x)}{\partial x} = \begin{cases} \sinh(x) & \mbox{if } -\infty\leq x\leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

Parameters
aVariable.
Returns
Hyperbolic cosine of variable.

Definition at line 50 of file cosh.hpp.

§ cov_exp_quad() [1/4]

template<typename T_x , typename T_sigma , typename T_l >
Eigen::Matrix<typename stan::return_type<T_x, T_sigma, T_l>::type, Eigen::Dynamic, Eigen::Dynamic> stan::math::cov_exp_quad ( const std::vector< T_x > &  x,
const T_sigma &  sigma,
const T_l &  l 
)
inline

Returns a squared exponential kernel.

Template Parameters
T_xtype of std::vector of elements
T_sigmatype of sigma
T_ltype of length scale
Parameters
xstd::vector of elements that can be used in square distance. This function assumes each element of x is the same size.
sigmastandard deviation
llength scale
Returns
squared distance
Exceptions
std::domain_errorif sigma <= 0, l <= 0, or x is nan or infinite

Definition at line 37 of file cov_exp_quad.hpp.

§ cov_exp_quad() [2/4]

template<typename T_x1 , typename T_x2 , typename T_sigma , typename T_l >
Eigen::Matrix<typename stan::return_type<T_x1, T_x2, T_sigma, T_l>::type, Eigen::Dynamic, Eigen::Dynamic> stan::math::cov_exp_quad ( const std::vector< T_x1 > &  x1,
const std::vector< T_x2 > &  x2,
const T_sigma &  sigma,
const T_l &  l 
)
inline

Returns a squared exponential kernel.

Template Parameters
T_x1type of first std::vector of elements
T_x2type of second std::vector of elements
T_sigmatype of sigma
T_ltype of length scale
Parameters
x1std::vector of elements that can be used in square distance
x2std::vector of elements that can be used in square distance
sigmastandard deviation
llength scale
Returns
squared distance
Exceptions
std::domain_errorif sigma <= 0, l <= 0, or x is nan or infinite

Definition at line 89 of file cov_exp_quad.hpp.

§ cov_exp_quad() [3/4]

template<typename T_x >
boost::enable_if_c<boost::is_same<typename scalar_type<T_x>::type, double>::value, Eigen::Matrix<var, -1, -1> >::type stan::math::cov_exp_quad ( const std::vector< T_x > &  x,
const var sigma,
const var l 
)
inline

Returns a squared exponential kernel.

Parameters
xstd::vector input that can be used in square distance Assumes each element of x is the same size
sigmastandard deviation
llength scale
Returns
squared distance
Exceptions
std::domain_errorif sigma <= 0, l <= 0, or x is nan or infinite

Definition at line 212 of file cov_exp_quad.hpp.

§ cov_exp_quad() [4/4]

template<typename T_x >
boost::enable_if_c<boost::is_same<typename scalar_type<T_x>::type, double>::value, Eigen::Matrix<var, -1, -1> >::type stan::math::cov_exp_quad ( const std::vector< T_x > &  x,
double  sigma,
const var l 
)
inline

Returns a squared exponential kernel.

Parameters
xstd::vector input that can be used in square distance Assumes each element of x is the same size
sigmastandard deviation
llength scale
Returns
squared distance
Exceptions
std::domain_errorif sigma <= 0, l <= 0, or x is nan or infinite

Definition at line 259 of file cov_exp_quad.hpp.

§ cov_matrix_constrain() [1/2]

template<typename T >
Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> stan::math::cov_matrix_constrain ( const Eigen::Matrix< T, Eigen::Dynamic, 1 > &  x,
typename math::index_type< Eigen::Matrix< T, Eigen::Dynamic, 1 > >::type  K 
)

Return the symmetric, positive-definite matrix of dimensions K by K resulting from transforming the specified finite vector of size K plus (K choose 2).

See cov_matrix_free() for the inverse transform.

Parameters
xThe vector to convert to a covariance matrix.
KThe number of rows and columns of the resulting covariance matrix.
Exceptions
std::invalid_argumentif (x.size() != K + (K choose 2)).

Definition at line 29 of file cov_matrix_constrain.hpp.

§ cov_matrix_constrain() [2/2]

template<typename T >
Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> stan::math::cov_matrix_constrain ( const Eigen::Matrix< T, Eigen::Dynamic, 1 > &  x,
typename math::index_type< Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > >::type  K,
T &  lp 
)

Return the symmetric, positive-definite matrix of dimensions K by K resulting from transforming the specified finite vector of size K plus (K choose 2).

See cov_matrix_free() for the inverse transform.

Parameters
xThe vector to convert to a covariance matrix.
KThe dimensions of the resulting covariance matrix.
lpReference
Exceptions
std::domain_errorif (x.size() != K + (K choose 2)).

Definition at line 66 of file cov_matrix_constrain.hpp.

§ cov_matrix_constrain_lkj() [1/2]

template<typename T >
Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> stan::math::cov_matrix_constrain_lkj ( const Eigen::Matrix< T, Eigen::Dynamic, 1 > &  x,
size_t  k 
)

Return the covariance matrix of the specified dimensionality derived from constraining the specified vector of unconstrained values.

The input vector must be of length $k \choose 2 + k$. The first $k \choose 2$ values in the input represent unconstrained (partial) correlations and the last $k$ are unconstrained standard deviations of the dimensions.

The transform scales the correlation matrix transform defined in corr_matrix_constrain(Matrix, size_t) with the constrained deviations.

Parameters
xInput vector of unconstrained partial correlations and standard deviations.
kDimensionality of returned covariance matrix.
Returns
Covariance matrix derived from the unconstrained partial correlations and deviations.
Template Parameters
TType of scalar.

Definition at line 33 of file cov_matrix_constrain_lkj.hpp.

§ cov_matrix_constrain_lkj() [2/2]

template<typename T >
Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> stan::math::cov_matrix_constrain_lkj ( const Eigen::Matrix< T, Eigen::Dynamic, 1 > &  x,
size_t  k,
T &  lp 
)

Return the covariance matrix of the specified dimensionality derived from constraining the specified vector of unconstrained values and increment the specified log probability reference with the log absolute Jacobian determinant.

The transform is defined as for cov_matrix_constrain(Matrix, size_t).

The log absolute Jacobian determinant is derived by composing the log absolute Jacobian determinant for the underlying correlation matrix as defined in cov_matrix_constrain(Matrix, size_t, T&) with the Jacobian of the transfrom of the correlation matrix into a covariance matrix by scaling by standard deviations.

Parameters
xInput vector of unconstrained partial correlations and standard deviations.
kDimensionality of returned covariance matrix.
lpLog probability reference to increment.
Returns
Covariance matrix derived from the unconstrained partial correlations and deviations.
Template Parameters
TType of scalar.

Definition at line 72 of file cov_matrix_constrain_lkj.hpp.

§ cov_matrix_free()

template<typename T >
Eigen::Matrix<T, Eigen::Dynamic, 1> stan::math::cov_matrix_free ( const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &  y)

The covariance matrix derived from the symmetric view of the lower-triangular view of the K by K specified matrix is freed to return a vector of size K + (K choose 2).

This is the inverse of the cov_matrix_constrain() function so that for any finite vector x of size K

  • (K choose 2),

x == cov_matrix_free(cov_matrix_constrain(x, K)).

In order for this round-trip to work (and really for this function to work), the symmetric view of its lower-triangular view must be positive definite.

Parameters
yMatrix of dimensions K by K such that he symmetric view of the lower-triangular view is positive definite.
Returns
Vector of size K plus (K choose 2) in (-inf, inf) that produces
Exceptions
std::domain_errorif y is not square, has zero dimensionality, or has a non-positive diagonal element.

Definition at line 38 of file cov_matrix_free.hpp.

§ cov_matrix_free_lkj()

template<typename T >
Eigen::Matrix<T, Eigen::Dynamic, 1> stan::math::cov_matrix_free_lkj ( const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &  y)

Return the vector of unconstrained partial correlations and deviations that transform to the specified covariance matrix.

The constraining transform is defined as for cov_matrix_constrain(Matrix, size_t). The inverse first factors out the deviations, then applies the freeing transfrom of corr_matrix_free(Matrix&).

Parameters
yCovariance matrix to free.
Returns
Vector of unconstrained values that transforms to the specified covariance matrix.
Template Parameters
TType of scalar.
Exceptions
std::domain_errorif the correlation matrix has no elements or is not a square matrix.
std::runtime_errorif the correlation matrix cannot be factorized by factor_cov_matrix()

Definition at line 33 of file cov_matrix_free_lkj.hpp.

§ crossprod() [1/3]

matrix_v stan::math::crossprod ( const matrix_v M)
inline

Returns the result of pre-multiplying a matrix by its own transpose.

Parameters
MMatrix to multiply.
Returns
Transpose of M times M

Definition at line 17 of file crossprod.hpp.

§ crossprod() [2/3]

template<typename T , int R, int C>
Eigen::Matrix<fvar<T>, C, C> stan::math::crossprod ( const Eigen::Matrix< fvar< T >, R, C > &  m)
inline

Definition at line 17 of file crossprod.hpp.

§ crossprod() [3/3]

matrix_d stan::math::crossprod ( const matrix_d M)
inline

Returns the result of pre-multiplying a matrix by its own transpose.

Parameters
MMatrix to multiply.
Returns
Transpose of M times M

Definition at line 17 of file crossprod.hpp.

§ csr_matrix_times_vector()

template<typename T1 , typename T2 >
Eigen::Matrix<typename boost::math::tools::promote_args<T1, T2>::type, Eigen::Dynamic, 1> stan::math::csr_matrix_times_vector ( int  m,
int  n,
const Eigen::Matrix< T1, Eigen::Dynamic, 1 > &  w,
const std::vector< int > &  v,
const std::vector< int > &  u,
const Eigen::Matrix< T2, Eigen::Dynamic, 1 > &  b 
)
inline

Definition at line 79 of file csr_matrix_times_vector.hpp.

§ cumulative_sum() [1/2]

template<typename T >
std::vector<T> stan::math::cumulative_sum ( const std::vector< T > &  x)
inline

Return the cumulative sum of the specified vector.

The cumulative sum of a vector of values

is the
@code x[0], x[1] + x[2], ..., x[1] + , ..., + x[x.size()-1]
Template Parameters
TScalar type of vector.
Parameters
xVector of values.
Returns
Cumulative sum of values.

Definition at line 23 of file cumulative_sum.hpp.

§ cumulative_sum() [2/2]

template<typename T , int R, int C>
Eigen::Matrix<T, R, C> stan::math::cumulative_sum ( const Eigen::Matrix< T, R, C > &  m)
inline

Return the cumulative sum of the specified matrix.

The cumulative sum is of the same type as the input and has values defined by

x(0), x(1) + x(2), ..., x(1) + , ..., + x(x.size()-1)
Template Parameters
TScalar type of matrix.
RRow type of matrix.
CColumn type of matrix.
Parameters
mMatrix of values.
Returns
Cumulative sum of values.

Definition at line 49 of file cumulative_sum.hpp.

§ cvodes_check_flag()

void stan::math::cvodes_check_flag ( int  flag,
const std::string &  func_name 
)
inline

Definition at line 22 of file cvodes_utils.hpp.

§ cvodes_set_options()

void stan::math::cvodes_set_options ( void *  cvodes_mem,
double  rel_tol,
double  abs_tol,
long int  max_num_steps 
)
inline

Definition at line 30 of file cvodes_utils.hpp.

§ cvodes_silent_err_handler()

void stan::math::cvodes_silent_err_handler ( int  error_code,
const char *  module,
const char *  function,
char *  msg,
void *  eh_data 
)
inline

Definition at line 17 of file cvodes_utils.hpp.

§ decouple_ode_states() [1/2]

template<typename T_initial , typename T_param >
std::vector<std::vector<typename stan::return_type<T_initial, T_param>::type> > stan::math::decouple_ode_states ( const std::vector< std::vector< double > > &  y,
const std::vector< T_initial > &  y0,
const std::vector< T_param > &  theta 
)
inline

Takes sensitivity output from integrators and returns results in precomputed_gradients format.

Solution input vector size depends on requested sensitivities, which can be enabled for initials and parameters. For each sensitivity N states are computed. The input vector is expected to be ordered by states, i.e. first the N states, then optionally the N sensitivities for the initials (first the N states for the first initial and so on), finally the sensitivities for the M parameters follow optionally.

Template Parameters
T1_initialtype of scalars for initial values.
T2_paramtype of scalars for parameters.
Parameters
[in]youtput from integrator in column-major format as a coupled system output
[in]y0initial state.
[in]thetaparameters
Returns
a vector of states for each entry in y in Stan var format

Definition at line 37 of file decouple_ode_states.hpp.

§ decouple_ode_states() [2/2]

template<>
std::vector<std::vector<double> > stan::math::decouple_ode_states ( const std::vector< std::vector< double > > &  y,
const std::vector< double > &  y0,
const std::vector< double > &  theta 
)
inline

The decouple ODE states operation for the case of no sensitivities is equal to the indentity operation.

Parameters
[in]youtput from integrator
[in]y0initial state.
[in]thetaparameters
Returns
y

Definition at line 86 of file decouple_ode_states.hpp.

§ derivative()

template<typename T , typename F >
void stan::math::derivative ( const F &  f,
const T &  x,
T &  fx,
T &  dfx_dx 
)

Return the derivative of the specified univariate function at the specified argument.

Template Parameters
TArgument type
FFunction type
Parameters
[in]fFunction
[in]xArgument
[out]fxValue of function applied to argument
[out]dfx_dxValue of derivative

Definition at line 25 of file derivative.hpp.

§ determinant() [1/3]

template<typename T , int R, int C>
T stan::math::determinant ( const Eigen::Matrix< T, R, C > &  m)
inline

Returns the determinant of the specified square matrix.

Parameters
mSpecified matrix.
Returns
Determinant of the matrix.
Exceptions
std::domain_errorif matrix is not square.

Definition at line 18 of file determinant.hpp.

§ determinant() [2/3]

template<typename T , int R, int C>
fvar<T> stan::math::determinant ( const Eigen::Matrix< fvar< T >, R, C > &  m)
inline

Definition at line 21 of file determinant.hpp.

§ determinant() [3/3]

template<int R, int C>
var stan::math::determinant ( const Eigen::Matrix< var, R, C > &  m)
inline

Definition at line 66 of file determinant.hpp.

§ diag_matrix()

template<typename T >
Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> stan::math::diag_matrix ( const Eigen::Matrix< T, Eigen::Dynamic, 1 > &  v)
inline

Return a square diagonal matrix with the specified vector of coefficients as the diagonal values.

Parameters
[in]vSpecified vector.
Returns
Diagonal matrix with vector as diagonal values.

Definition at line 18 of file diag_matrix.hpp.

§ diag_post_multiply()

template<typename T1 , typename T2 , int R1, int C1, int R2, int C2>
Eigen::Matrix<typename boost::math::tools::promote_args<T1, T2>::type, R1, C1> stan::math::diag_post_multiply ( const Eigen::Matrix< T1, R1, C1 > &  m1,
const Eigen::Matrix< T2, R2, C2 > &  m2 
)

Definition at line 15 of file diag_post_multiply.hpp.

§ diag_pre_multiply()

template<typename T1 , typename T2 , int R1, int C1, int R2, int C2>
Eigen::Matrix<typename boost::math::tools::promote_args<T1, T2>::type, R2, C2> stan::math::diag_pre_multiply ( const Eigen::Matrix< T1, R1, C1 > &  m1,
const Eigen::Matrix< T2, R2, C2 > &  m2 
)

Definition at line 15 of file diag_pre_multiply.hpp.

§ diagonal()

template<typename T >
Eigen::Matrix<T, Eigen::Dynamic, 1> stan::math::diagonal ( const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &  m)
inline

Return a column vector of the diagonal elements of the specified matrix.

The matrix is not required to be square.

Parameters
mSpecified matrix.
Returns
Diagonal of the matrix.

Definition at line 18 of file diagonal.hpp.

§ digamma() [1/4]

template<typename T >
fvar<T> stan::math::digamma ( const fvar< T > &  x)
inline

Return the derivative of the log gamma function at the specified argument.

Template Parameters
Tscalar type of autodiff variable
Parameters
[in]xargument
Returns
derivative of the log gamma function at the specified argument

Definition at line 22 of file digamma.hpp.

§ digamma() [2/4]

var stan::math::digamma ( const var a)
inline

Definition at line 23 of file digamma.hpp.

§ digamma() [3/4]

template<typename T >
apply_scalar_unary<digamma_fun, T>::return_t stan::math::digamma ( const T &  x)
inline

Vectorized version of digamma().

Parameters
xContainer.
Template Parameters
TContainer type.
Returns
Digamma function applied to each value in x.
Exceptions
std::domain_errorif any value is a negative integer or 0

Definition at line 34 of file digamma.hpp.

§ digamma() [4/4]

double stan::math::digamma ( double  x)
inline

Return the derivative of the log gamma function at the specified value.

\[ \mbox{digamma}(x) = \begin{cases} \textrm{error} & \mbox{if } x\in \{\dots, -3, -2, -1, 0\}\\ \Psi(x) & \mbox{if } x\not\in \{\dots, -3, -2, -1, 0\}\\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{digamma}(x)}{\partial x} = \begin{cases} \textrm{error} & \mbox{if } x\in \{\dots, -3, -2, -1, 0\}\\ \frac{\partial\, \Psi(x)}{\partial x} & \mbox{if } x\not\in \{\dots, -3, -2, -1, 0\}\\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \Psi(x)=\frac{\Gamma'(x)}{\Gamma(x)} \]

\[ \frac{\partial \, \Psi(x)}{\partial x} = \frac{\Gamma''(x)\Gamma(x)-(\Gamma'(x))^2}{\Gamma^2(x)} \]

The design follows the standard C++ library in returning NaN rather than throwing exceptions.

Parameters
[in]xargument
Returns
derivative of log gamma function at argument

Definition at line 47 of file digamma.hpp.

§ dims() [1/4]

template<typename T >
void stan::math::dims ( const T &  x,
std::vector< int > &  result 
)
inline

Definition at line 13 of file dims.hpp.

§ dims() [2/4]

template<typename T , int R, int C>
void stan::math::dims ( const Eigen::Matrix< T, R, C > &  x,
std::vector< int > &  result 
)
inline

Definition at line 18 of file dims.hpp.

§ dims() [3/4]

template<typename T >
void stan::math::dims ( const std::vector< T > &  x,
std::vector< int > &  result 
)
inline

Definition at line 25 of file dims.hpp.

§ dims() [4/4]

template<typename T >
std::vector<int> stan::math::dims ( const T &  x)
inline

Definition at line 34 of file dims.hpp.

§ dirichlet_log() [1/2]

template<bool propto, typename T_prob , typename T_prior_sample_size >
boost::math::tools::promote_args<T_prob, T_prior_sample_size>::type stan::math::dirichlet_log ( const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &  theta,
const Eigen::Matrix< T_prior_sample_size, Eigen::Dynamic, 1 > &  alpha 
)

The log of the Dirichlet density for the given theta and a vector of prior sample sizes, alpha.

Each element of alpha must be greater than 0. Each element of theta must be greater than or 0. Theta sums to 1.

\begin{eqnarray*} \theta &\sim& \mbox{\sf{Dirichlet}} (\alpha_1, \ldots, \alpha_k) \\ \log (p (\theta \, |\, \alpha_1, \ldots, \alpha_k) ) &=& \log \left( \frac{\Gamma(\alpha_1 + \cdots + \alpha_k)}{\Gamma(\alpha_1) \cdots \Gamma(\alpha_k)} \theta_1^{\alpha_1 - 1} \cdots \theta_k^{\alpha_k - 1} \right) \\ &=& \log (\Gamma(\alpha_1 + \cdots + \alpha_k)) - \log(\Gamma(\alpha_1)) - \cdots - \log(\Gamma(\alpha_k)) + (\alpha_1 - 1) \log (\theta_1) + \cdots + (\alpha_k - 1) \log (\theta_k) \end{eqnarray*}

Parameters
thetaA scalar vector.
alphaPrior sample sizes.
Returns
The log of the Dirichlet density.
Exceptions
std::domain_errorif any element of alpha is less than or equal to 0.
std::domain_errorif any element of theta is less than 0.
std::domain_errorif the sum of theta is not 1.
Template Parameters
T_probType of scalar.
T_prior_sample_sizeType of prior sample sizes.

Definition at line 45 of file dirichlet_log.hpp.

§ dirichlet_log() [2/2]

template<typename T_prob , typename T_prior_sample_size >
boost::math::tools::promote_args<T_prob, T_prior_sample_size>::type stan::math::dirichlet_log ( const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &  theta,
const Eigen::Matrix< T_prior_sample_size, Eigen::Dynamic, 1 > &  alpha 
)
inline

Definition at line 74 of file dirichlet_log.hpp.

§ dirichlet_lpmf() [1/2]

template<bool propto, typename T_prob , typename T_prior_sample_size >
boost::math::tools::promote_args<T_prob, T_prior_sample_size>::type stan::math::dirichlet_lpmf ( const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &  theta,
const Eigen::Matrix< T_prior_sample_size, Eigen::Dynamic, 1 > &  alpha 
)

The log of the Dirichlet density for the given theta and a vector of prior sample sizes, alpha.

Each element of alpha must be greater than 0. Each element of theta must be greater than or 0. Theta sums to 1.

\begin{eqnarray*} \theta &\sim& \mbox{\sf{Dirichlet}} (\alpha_1, \ldots, \alpha_k) \\ \log (p (\theta \, |\, \alpha_1, \ldots, \alpha_k) ) &=& \log \left( \frac{\Gamma(\alpha_1 + \cdots + \alpha_k)}{\Gamma(\alpha_1) \cdots \Gamma(\alpha_k)} \theta_1^{\alpha_1 - 1} \cdots \theta_k^{\alpha_k - 1} \right) \\ &=& \log (\Gamma(\alpha_1 + \cdots + \alpha_k)) - \log(\Gamma(\alpha_1)) - \cdots - \log(\Gamma(\alpha_k)) + (\alpha_1 - 1) \log (\theta_1) + \cdots + (\alpha_k - 1) \log (\theta_k) \end{eqnarray*}

Parameters
thetaA scalar vector.
alphaPrior sample sizes.
Returns
The log of the Dirichlet density.
Exceptions
std::domain_errorif any element of alpha is less than or equal to 0.
std::domain_errorif any element of theta is less than 0.
std::domain_errorif the sum of theta is not 1.
Template Parameters
T_probType of scalar.
T_prior_sample_sizeType of prior sample sizes.

Definition at line 45 of file dirichlet_lpmf.hpp.

§ dirichlet_lpmf() [2/2]

template<typename T_prob , typename T_prior_sample_size >
boost::math::tools::promote_args<T_prob, T_prior_sample_size>::type stan::math::dirichlet_lpmf ( const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &  theta,
const Eigen::Matrix< T_prior_sample_size, Eigen::Dynamic, 1 > &  alpha 
)
inline

Definition at line 74 of file dirichlet_lpmf.hpp.

§ dirichlet_rng()

template<class RNG >
Eigen::VectorXd stan::math::dirichlet_rng ( const Eigen::Matrix< double, Eigen::Dynamic, 1 > &  alpha,
RNG &  rng 
)
inline

Return a draw from a Dirichlet distribution with specified parameters and pseudo-random number generator.

For prior counts greater than zero, the usual algorithm that draws gamma variates and normalizes is used.

For prior counts less than zero (i.e., parameters with value less than one), a log-scale version of the following algorithm is used to deal with underflow:

G. Marsaglia and W. Tsang. A simple method for generating gamma variables. ACM Transactions on Mathematical Software. 26(3):363–372, 2000.

Template Parameters
RNGType of pseudo-random number generator.
Parameters
alphaPrior count (plus 1) parameter for Dirichlet.
rngPseudo-random number generator.

Definition at line 45 of file dirichlet_rng.hpp.

§ distance()

template<typename T1 , int R1, int C1, typename T2 , int R2, int C2>
boost::math::tools::promote_args<T1, T2>::type stan::math::distance ( const Eigen::Matrix< T1, R1, C1 > &  v1,
const Eigen::Matrix< T2, R2, C2 > &  v2 
)
inline

Returns the distance between the specified vectors.

Parameters
v1First vector.
v2Second vector.
Returns
Dot product of the vectors.
Exceptions
std::domain_errorIf the vectors are not the same size or if they are both not vector dimensioned.

Definition at line 24 of file distance.hpp.

§ divide() [1/7]

template<typename T , int R, int C>
Eigen::Matrix<fvar<T>, R, C> stan::math::divide ( const Eigen::Matrix< fvar< T >, R, C > &  v,
const fvar< T > &  c 
)
inline

Definition at line 16 of file divide.hpp.

§ divide() [2/7]

template<typename T1 , typename T2 >
stan::return_type<T1, T2>::type stan::math::divide ( const T1 &  x,
const T2 &  y 
)
inline

Return the division of the first scalar by the second scalar.

Parameters
[in]xSpecified vector.
[in]ySpecified scalar.
Returns
Vector divided by the scalar.

Definition at line 22 of file divide.hpp.

§ divide() [3/7]

template<typename T1 , typename T2 , int R, int C>
Eigen::Matrix<var, R, C> stan::math::divide ( const Eigen::Matrix< T1, R, C > &  v,
const T2 &  c 
)
inline

Return the division of the specified column vector by the specified scalar.

Parameters
[in]vSpecified vector.
[in]cSpecified scalar.
Returns
Vector divided by the scalar.

Definition at line 23 of file divide.hpp.

§ divide() [4/7]

template<int R, int C, typename T >
boost::enable_if_c<boost::is_arithmetic<T>::value, Eigen::Matrix<double, R, C> >::type stan::math::divide ( const Eigen::Matrix< double, R, C > &  m,
c 
)
inline

Return specified matrix divided by specified scalar.

Template Parameters
RRow type for matrix.
CColumn type for matrix.
Parameters
mMatrix.
cScalar.
Returns
Matrix divided by scalar.

Definition at line 23 of file divide.hpp.

§ divide() [5/7]

int stan::math::divide ( int  x,
int  y 
)
inline

Definition at line 26 of file divide.hpp.

§ divide() [6/7]

template<typename T , int R, int C>
Eigen::Matrix<fvar<T>, R, C> stan::math::divide ( const Eigen::Matrix< fvar< T >, R, C > &  v,
double  c 
)
inline

Definition at line 27 of file divide.hpp.

§ divide() [7/7]

template<typename T , int R, int C>
Eigen::Matrix<fvar<T>, R, C> stan::math::divide ( const Eigen::Matrix< double, R, C > &  v,
const fvar< T > &  c 
)
inline

Definition at line 39 of file divide.hpp.

§ do_lkj_constant()

template<typename T_shape >
T_shape stan::math::do_lkj_constant ( const T_shape &  eta,
const unsigned int &  K 
)

Definition at line 53 of file lkj_corr_lpdf.hpp.

§ domain_error() [1/2]

template<typename T >
void stan::math::domain_error ( const char *  function,
const char *  name,
const T &  y,
const char *  msg1,
const char *  msg2 
)
inline

Throw a domain error with a consistently formatted message.

This is an abstraction for all Stan functions to use when throwing domain errors. This will allow us to change the behavior for all functions at once.

The message is: "<function>: <name> <msg1><y><msg2>"

Template Parameters
TType of variable.
Parameters
[in]functionName of the function.
[in]nameName of the variable.
[in]yVariable.
[in]msg1Message to print before the variable.
[in]msg2Message to print after the variable.
Exceptions
std::domain_errorAlways.

Definition at line 30 of file domain_error.hpp.

§ domain_error() [2/2]

template<typename T >
void stan::math::domain_error ( const char *  function,
const char *  name,
const T &  y,
const char *  msg1 
)
inline

Throw a domain error with a consistently formatted message.

This is an abstraction for all Stan functions to use when throwing domain errors. This will allow us to change the behavior for all functions at once.

The message is: * "<function>: <name> <msg1><y>"

Template Parameters
TType of variable.
Parameters
[in]functionName of the function.
[in]nameName of the variable.
[in]yVariable.
[in]msg1Message to print before the variable.
Exceptions
std::domain_errorAlways.

Definition at line 56 of file domain_error.hpp.

§ domain_error_vec() [1/2]

template<typename T >
void stan::math::domain_error_vec ( const char *  function,
const char *  name,
const T &  y,
size_t  i,
const char *  msg1,
const char *  msg2 
)
inline

Throw a domain error with a consistently formatted message.

This is an abstraction for all Stan functions to use when throwing domain errors. This will allow us to change the behavior for all functions at once. (We've already changed behavior mulitple times up to Stan v2.5.0.)

The message is: "<function>: <name>[<i+error_index>] <msg1><y>" where error_index is the value of stan::error_index::value which indicates whether the message should be 0 or 1 indexed.

Template Parameters
TType of variable
Parameters
functionName of the function
nameName of the variable
yVariable
iIndex
msg1Message to print before the variable
msg2Message to print after the variable
Exceptions
std::domain_error

Definition at line 37 of file domain_error_vec.hpp.

§ domain_error_vec() [2/2]

template<typename T >
void stan::math::domain_error_vec ( const char *  function,
const char *  name,
const T &  y,
size_t  i,
const char *  msg 
)
inline

Throw a domain error with a consistently formatted message.

This is an abstraction for all Stan functions to use when throwing domain errors. This will allow us to change the behavior for all functions at once. (We've already changed behavior mulitple times up to Stan v2.5.0.)

The message is: "<function>: <name>[<i+error_index>] <msg1><y>" where error_index is the value of stan::error_index::value which indicates whether the message should be 0 or 1 indexed.

Template Parameters
TType of variable
Parameters
functionName of the function
nameName of the variable
yVariable
iIndex
msgMessage to print before the variable
Exceptions
std::domain_error

Definition at line 72 of file domain_error_vec.hpp.

§ dot()

double stan::math::dot ( const std::vector< double > &  x,
const std::vector< double > &  y 
)
inline

Definition at line 10 of file dot.hpp.

§ dot_product() [1/18]

template<typename T , int R1, int C1, int R2, int C2>
fvar<T> stan::math::dot_product ( const Eigen::Matrix< fvar< T >, R1, C1 > &  v1,
const Eigen::Matrix< fvar< T >, R2, C2 > &  v2 
)
inline

Definition at line 18 of file dot_product.hpp.

§ dot_product() [2/18]

template<int R1, int C1, int R2, int C2>
double stan::math::dot_product ( const Eigen::Matrix< double, R1, C1 > &  v1,
const Eigen::Matrix< double, R2, C2 > &  v2 
)
inline

Returns the dot product of the specified vectors.

Parameters
v1First vector.
v2Second vector.
Returns
Dot product of the vectors.
Exceptions
std::domain_errorIf the vectors are not the same size or if they are both not vector dimensioned.

Definition at line 22 of file dot_product.hpp.

§ dot_product() [3/18]

template<typename T , int R1, int C1, int R2, int C2>
fvar<T> stan::math::dot_product ( const Eigen::Matrix< fvar< T >, R1, C1 > &  v1,
const Eigen::Matrix< double, R2, C2 > &  v2 
)
inline

Definition at line 33 of file dot_product.hpp.

§ dot_product() [4/18]

double stan::math::dot_product ( const double *  v1,
const double *  v2,
size_t  length 
)
inline

Returns the dot product of the specified arrays of doubles.

Parameters
v1First array.
v2Second array.
lengthLength of both arrays.

Definition at line 35 of file dot_product.hpp.

§ dot_product() [5/18]

template<typename T , int R1, int C1, int R2, int C2>
fvar<T> stan::math::dot_product ( const Eigen::Matrix< double, R1, C1 > &  v1,
const Eigen::Matrix< fvar< T >, R2, C2 > &  v2 
)
inline

Definition at line 48 of file dot_product.hpp.

§ dot_product() [6/18]

double stan::math::dot_product ( const std::vector< double > &  v1,
const std::vector< double > &  v2 
)
inline

Returns the dot product of the specified arrays of doubles.

Parameters
v1First array.
v2Second array.
Exceptions
std::domain_errorif the vectors are not the same size.

Definition at line 48 of file dot_product.hpp.

§ dot_product() [7/18]

template<typename T , int R1, int C1, int R2, int C2>
fvar<T> stan::math::dot_product ( const Eigen::Matrix< fvar< T >, R1, C1 > &  v1,
const Eigen::Matrix< fvar< T >, R2, C2 > &  v2,
size_type length 
)
inline

Definition at line 63 of file dot_product.hpp.

§ dot_product() [8/18]

template<typename T , int R1, int C1, int R2, int C2>
fvar<T> stan::math::dot_product ( const Eigen::Matrix< fvar< T >, R1, C1 > &  v1,
const Eigen::Matrix< double, R2, C2 > &  v2,
size_type length 
)
inline

Definition at line 78 of file dot_product.hpp.

§ dot_product() [9/18]

template<typename T , int R1, int C1, int R2, int C2>
fvar<T> stan::math::dot_product ( const Eigen::Matrix< double, R1, C1 > &  v1,
const Eigen::Matrix< fvar< T >, R2, C2 > &  v2,
size_type length 
)
inline

Definition at line 93 of file dot_product.hpp.

§ dot_product() [10/18]

template<typename T >
fvar<T> stan::math::dot_product ( const std::vector< fvar< T > > &  v1,
const std::vector< fvar< T > > &  v2 
)
inline

Definition at line 108 of file dot_product.hpp.

§ dot_product() [11/18]

template<typename T >
fvar<T> stan::math::dot_product ( const std::vector< double > &  v1,
const std::vector< fvar< T > > &  v2 
)
inline

Definition at line 120 of file dot_product.hpp.

§ dot_product() [12/18]

template<typename T >
fvar<T> stan::math::dot_product ( const std::vector< fvar< T > > &  v1,
const std::vector< double > &  v2 
)
inline

Definition at line 132 of file dot_product.hpp.

§ dot_product() [13/18]

template<typename T >
fvar<T> stan::math::dot_product ( const std::vector< fvar< T > > &  v1,
const std::vector< fvar< T > > &  v2,
size_type length 
)
inline

Definition at line 144 of file dot_product.hpp.

§ dot_product() [14/18]

template<typename T >
fvar<T> stan::math::dot_product ( const std::vector< double > &  v1,
const std::vector< fvar< T > > &  v2,
size_type length 
)
inline

Definition at line 156 of file dot_product.hpp.

§ dot_product() [15/18]

template<typename T >
fvar<T> stan::math::dot_product ( const std::vector< fvar< T > > &  v1,
const std::vector< double > &  v2,
size_type length 
)
inline

Definition at line 168 of file dot_product.hpp.

§ dot_product() [16/18]

template<typename T1 , int R1, int C1, typename T2 , int R2, int C2>
boost::enable_if_c<boost::is_same<T1, var>::value || boost::is_same<T2, var>::value, var>::type stan::math::dot_product ( const Eigen::Matrix< T1, R1, C1 > &  v1,
const Eigen::Matrix< T2, R2, C2 > &  v2 
)
inline

Returns the dot product.

Parameters
[in]v1First column vector.
[in]v2Second column vector.
Returns
Dot product of the vectors.
Exceptions
std::domain_errorif length of v1 is not equal to length of v2.

Definition at line 209 of file dot_product.hpp.

§ dot_product() [17/18]

template<typename T1 , typename T2 >
boost::enable_if_c<boost::is_same<T1, var>::value || boost::is_same<T2, var>::value, var>::type stan::math::dot_product ( const T1 *  v1,
const T2 *  v2,
size_t  length 
)
inline

Returns the dot product.

Parameters
[in]v1First array.
[in]v2Second array.
[in]lengthLength of both arrays.
Returns
Dot product of the arrays.

Definition at line 230 of file dot_product.hpp.

§ dot_product() [18/18]

template<typename T1 , typename T2 >
boost::enable_if_c<boost::is_same<T1, var>::value || boost::is_same<T2, var>::value, var>::type stan::math::dot_product ( const std::vector< T1 > &  v1,
const std::vector< T2 > &  v2 
)
inline

Returns the dot product.

Parameters
[in]v1First vector.
[in]v2Second vector.
Returns
Dot product of the vectors.
Exceptions
std::domain_errorif sizes of v1 and v2 do not match.

Definition at line 246 of file dot_product.hpp.

§ dot_self() [1/4]

double stan::math::dot_self ( const std::vector< double > &  x)
inline

Definition at line 10 of file dot_self.hpp.

§ dot_self() [2/4]

template<typename T , int R, int C>
fvar<T> stan::math::dot_self ( const Eigen::Matrix< fvar< T >, R, C > &  v)
inline

Definition at line 16 of file dot_self.hpp.

§ dot_self() [3/4]

template<int R, int C>
double stan::math::dot_self ( const Eigen::Matrix< double, R, C > &  v)
inline

Returns the dot product of the specified vector with itself.

Parameters
vVector.
Template Parameters
Rnumber of rows or Eigen::Dynamic for dynamic
Cnumber of rows or Eigen::Dyanmic for dynamic
Exceptions
std::domain_errorIf v is not vector dimensioned.

Definition at line 18 of file dot_self.hpp.

§ dot_self() [4/4]

template<int R, int C>
var stan::math::dot_self ( const Eigen::Matrix< var, R, C > &  v)
inline

Returns the dot product of a vector with itself.

Parameters
[in]vVector.
Returns
Dot product of the vector with itself.
Template Parameters
Rnumber of rows or Eigen::Dynamic for dynamic; one of R or C must be 1
Cnumber of rows or Eigen::Dyanmic for dynamic; one of R or C must be 1

Definition at line 80 of file dot_self.hpp.

§ double_exponential_ccdf_log()

template<typename T_y , typename T_loc , typename T_scale >
return_type<T_y, T_loc, T_scale>::type stan::math::double_exponential_ccdf_log ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma 
)

Definition at line 25 of file double_exponential_ccdf_log.hpp.

§ double_exponential_cdf()

template<typename T_y , typename T_loc , typename T_scale >
return_type<T_y, T_loc, T_scale>::type stan::math::double_exponential_cdf ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma 
)

Calculates the double exponential cumulative density function.

$ f(y|\mu, \sigma) = \begin{cases} \ \frac{1}{2} \exp\left(\frac{y-\mu}{\sigma}\right), \mbox{if } y < \mu \\ 1 - \frac{1}{2} \exp\left(-\frac{y-\mu}{\sigma}\right), \mbox{if } y \ge \mu \ \end{cases}$

Parameters
yA scalar variate.
muThe location parameter.
sigmaThe scale parameter.
Returns
The cumulative density function.

Definition at line 39 of file double_exponential_cdf.hpp.

§ double_exponential_cdf_log()

template<typename T_y , typename T_loc , typename T_scale >
return_type<T_y, T_loc, T_scale>::type stan::math::double_exponential_cdf_log ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma 
)

Definition at line 25 of file double_exponential_cdf_log.hpp.

§ double_exponential_lccdf()

template<typename T_y , typename T_loc , typename T_scale >
return_type<T_y, T_loc, T_scale>::type stan::math::double_exponential_lccdf ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma 
)

Definition at line 25 of file double_exponential_lccdf.hpp.

§ double_exponential_lcdf()

template<typename T_y , typename T_loc , typename T_scale >
return_type<T_y, T_loc, T_scale>::type stan::math::double_exponential_lcdf ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma 
)

Definition at line 25 of file double_exponential_lcdf.hpp.

§ double_exponential_log() [1/2]

template<bool propto, typename T_y , typename T_loc , typename T_scale >
return_type<T_y, T_loc, T_scale>::type stan::math::double_exponential_log ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma 
)

Definition at line 30 of file double_exponential_log.hpp.

§ double_exponential_log() [2/2]

template<typename T_y , typename T_loc , typename T_scale >
return_type<T_y, T_loc, T_scale>::type stan::math::double_exponential_log ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma 
)

Definition at line 114 of file double_exponential_log.hpp.

§ double_exponential_lpdf() [1/2]

template<bool propto, typename T_y , typename T_loc , typename T_scale >
return_type<T_y, T_loc, T_scale>::type stan::math::double_exponential_lpdf ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma 
)

Definition at line 30 of file double_exponential_lpdf.hpp.

§ double_exponential_lpdf() [2/2]

template<typename T_y , typename T_loc , typename T_scale >
return_type<T_y, T_loc, T_scale>::type stan::math::double_exponential_lpdf ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma 
)

Definition at line 114 of file double_exponential_lpdf.hpp.

§ double_exponential_rng()

template<class RNG >
double stan::math::double_exponential_rng ( double  mu,
double  sigma,
RNG &  rng 
)
inline

Definition at line 22 of file double_exponential_rng.hpp.

§ e()

double stan::math::e ( )
inline

Return the base of the natural logarithm.

Returns
Base of natural logarithm.

Definition at line 94 of file constants.hpp.

§ eigenvalues_sym()

template<typename T >
Eigen::Matrix<T, Eigen::Dynamic, 1> stan::math::eigenvalues_sym ( const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &  m)

Return the eigenvalues of the specified symmetric matrix in descending order of magnitude.

This function is more efficient than the general eigenvalues function for symmetric matrices.

See eigen_decompose() for more information.

Parameters
mSpecified matrix.
Returns
Eigenvalues of matrix.

Definition at line 22 of file eigenvalues_sym.hpp.

§ eigenvectors_sym()

template<typename T >
Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> stan::math::eigenvectors_sym ( const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &  m)

Definition at line 13 of file eigenvectors_sym.hpp.

§ elt_divide() [1/3]

template<typename T1 , typename T2 , int R, int C>
Eigen::Matrix<typename boost::math::tools::promote_args<T1, T2>::type, R, C> stan::math::elt_divide ( const Eigen::Matrix< T1, R, C > &  m1,
const Eigen::Matrix< T2, R, C > &  m2 
)

Return the elementwise division of the specified matrices.

Template Parameters
T1Type of scalars in first matrix.
T2Type of scalars in second matrix.
RRow type of both matrices.
CColumn type of both matrices.
Parameters
m1First matrix
m2Second matrix
Returns
Elementwise division of matrices.

Definition at line 25 of file elt_divide.hpp.

§ elt_divide() [2/3]

template<typename T1 , typename T2 , int R, int C>
Eigen::Matrix<typename boost::math::tools::promote_args<T1, T2>::type, R, C> stan::math::elt_divide ( const Eigen::Matrix< T1, R, C > &  m,
T2  s 
)

Return the elementwise division of the specified matrix by the specified scalar.

Template Parameters
T1Type of scalars in the matrix.
T2Type of the scalar.
RRow type of the matrix.
CColumn type of the matrix.
Parameters
mmatrix
sscalar
Returns
Elementwise division of a scalar by matrix.

Definition at line 49 of file elt_divide.hpp.

§ elt_divide() [3/3]

template<typename T1 , typename T2 , int R, int C>
Eigen::Matrix<typename boost::math::tools::promote_args<T1, T2>::type, R, C> stan::math::elt_divide ( T1  s,
const Eigen::Matrix< T2, R, C > &  m 
)

Return the elementwise division of the specified scalar by the specified matrix.

Template Parameters
T1Type of the scalar.
T2Type of scalars in the matrix.
RRow type of the matrix.
CColumn type of the matrix.
Parameters
sscalar
mmatrix
Returns
Elementwise division of a scalar by matrix.

Definition at line 67 of file elt_divide.hpp.

§ elt_multiply()

template<typename T1 , typename T2 , int R, int C>
Eigen::Matrix<typename boost::math::tools::promote_args<T1, T2>::type, R, C> stan::math::elt_multiply ( const Eigen::Matrix< T1, R, C > &  m1,
const Eigen::Matrix< T2, R, C > &  m2 
)

Return the elementwise multiplication of the specified matrices.

Template Parameters
T1Type of scalars in first matrix.
T2Type of scalars in second matrix.
RRow type of both matrices.
CColumn type of both matrices.
Parameters
m1First matrix
m2Second matrix
Returns
Elementwise product of matrices.

Definition at line 25 of file elt_multiply.hpp.

§ empty_nested()

static bool stan::math::empty_nested ( )
inlinestatic

Return true if there is no nested autodiff being executed.

Definition at line 12 of file empty_nested.hpp.

§ erf() [1/5]

template<typename T >
fvar<T> stan::math::erf ( const fvar< T > &  x)
inline

Definition at line 14 of file erf.hpp.

§ erf() [2/5]

double stan::math::erf ( double  x)
inline

Return the error function of the specified value.

\[ \mbox{erf}(x) = \frac{2}{\sqrt{\pi}} \int_0^x e^{-t^2} dt \]

Parameters
[in]xArgument.
Returns
Error function of the argument.

Definition at line 22 of file erf.hpp.

§ erf() [3/5]

template<typename T >
apply_scalar_unary<erf_fun, T>::return_t stan::math::erf ( const T &  x)
inline

Vectorized version of erf().

Template Parameters
TContainer type.
Parameters
xContainer.
Returns
Error function applied to each value in x.

Definition at line 34 of file erf.hpp.

§ erf() [4/5]

double stan::math::erf ( int  x)
inline

Return the error function of the specified argument.

This version is required to disambiguate erf(int).

Parameters
[in]xArgument.
Returns
Error function of the argument.

Definition at line 35 of file erf.hpp.

§ erf() [5/5]

var stan::math::erf ( const var a)
inline

The error function for variables (C99).

The derivative is

$\frac{d}{dx} \mbox{erf}(x) = \frac{2}{\sqrt{\pi}} \exp(-x^2)$.

\[ \mbox{erf}(x) = \begin{cases} \operatorname{erf}(x) & \mbox{if } -\infty\leq x \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{erf}(x)}{\partial x} = \begin{cases} \frac{\partial\, \operatorname{erf}(x)}{\partial x} & \mbox{if } -\infty\leq x\leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \operatorname{erf}(x)=\frac{2}{\sqrt{\pi}}\int_0^x e^{-t^2}dt \]

\[ \frac{\partial \, \operatorname{erf}(x)}{\partial x} = \frac{2}{\sqrt{\pi}} e^{-x^2} \]

Parameters
aThe variable.
Returns
Error function applied to the variable.

Definition at line 60 of file erf.hpp.

§ erfc() [1/5]

template<typename T >
fvar<T> stan::math::erfc ( const fvar< T > &  x)
inline

Definition at line 14 of file erfc.hpp.

§ erfc() [2/5]

double stan::math::erfc ( double  x)
inline

Return the complementary error function of the specified value.

\[ \mbox{erfc}(x) = 1 - \frac{2}{\sqrt{\pi}} \int_0^x e^{-t^2} dt \]

Parameters
[in]xArgument.
Returns
Complementary error function of the argument.

Definition at line 22 of file erfc.hpp.

§ erfc() [3/5]

template<typename T >
apply_scalar_unary<erfc_fun, T>::return_t stan::math::erfc ( const T &  x)
inline

Vectorized version of erfc().

Parameters
xContainer.
Template Parameters
TContainer type.
Returns
Complementary error function applied to each value in x.

Definition at line 32 of file erfc.hpp.

§ erfc() [4/5]

double stan::math::erfc ( int  x)
inline

Return the error function of the specified argument.

This version is required to disambiguate erf(int).

Parameters
[in]xArgument.
Returns
Complementary error function value of the argument.

Definition at line 35 of file erfc.hpp.

§ erfc() [5/5]

var stan::math::erfc ( const var a)
inline

The complementary error function for variables (C99).

The derivative is

$\frac{d}{dx} \mbox{erfc}(x) = - \frac{2}{\sqrt{\pi}} \exp(-x^2)$.

\[ \mbox{erfc}(x) = \begin{cases} \operatorname{erfc}(x) & \mbox{if } -\infty\leq x \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{erfc}(x)}{\partial x} = \begin{cases} \frac{\partial\, \operatorname{erfc}(x)}{\partial x} & \mbox{if } -\infty\leq x\leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \operatorname{erfc}(x)=\frac{2}{\sqrt{\pi}}\int_x^\infty e^{-t^2}dt \]

\[ \frac{\partial \, \operatorname{erfc}(x)}{\partial x} = -\frac{2}{\sqrt{\pi}} e^{-x^2} \]

Parameters
aThe variable.
Returns
Complementary error function applied to the variable.

Definition at line 60 of file erfc.hpp.

§ exp() [1/4]

template<typename T >
fvar<T> stan::math::exp ( const fvar< T > &  x)
inline

Definition at line 10 of file exp.hpp.

§ exp() [2/4]

double stan::math::exp ( int  x)
inline

Return the natural exponential of the specified argument.

This version is required to disambiguate exp(int).

Parameters
[in]xArgument.
Returns
Natural exponential of argument.

Definition at line 16 of file exp.hpp.

§ exp() [3/4]

template<typename T >
apply_scalar_unary<exp_fun, T>::return_t stan::math::exp ( const T &  x)
inline

Return the elementwise exponentiation of the specified argument, which may be a scalar or any Stan container of numeric scalars.

The return type is the same as the argument type.

Template Parameters
TArgument type.
Parameters
[in]xArgument.
Returns
Elementwise application of exponentiation to the argument.

Definition at line 41 of file exp.hpp.

§ exp() [4/4]

var stan::math::exp ( const var a)
inline

Return the exponentiation of the specified variable (cmath).

\[ \mbox{exp}(x) = \begin{cases} e^x & \mbox{if } -\infty\leq x \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{exp}(x)}{\partial x} = \begin{cases} e^x & \mbox{if } -\infty\leq x\leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

Parameters
aVariable to exponentiate.
Returns
Exponentiated variable.

Definition at line 44 of file exp.hpp.

§ exp2() [1/5]

template<typename T >
fvar<T> stan::math::exp2 ( const fvar< T > &  x)
inline

Definition at line 14 of file exp2.hpp.

§ exp2() [2/5]

double stan::math::exp2 ( double  y)
inline

Return the exponent base 2 of the specified argument (C99, C++11).

The exponent base 2 function is defined by

exp2(y) = pow(2.0, y).

Parameters
yargument.
Returns
exponent base 2 of argument.

Definition at line 21 of file exp2.hpp.

§ exp2() [3/5]

double stan::math::exp2 ( int  y)
inline

Return the exponent base 2 of the specified argument (C99, C++11).

Parameters
yargument
Returns
exponent base 2 of argument

Definition at line 33 of file exp2.hpp.

§ exp2() [4/5]

template<typename T >
apply_scalar_unary<exp2_fun, T>::return_t stan::math::exp2 ( const T &  x)
inline

Return the elementwise application of exp2() to specified argument container.

The return type promotes the underlying scalar argument type to double if it is an integer, and otherwise is the argument type.

Template Parameters
TContainer type.
Parameters
xContainer.
Returns
Elementwise exp2 of members of container.

Definition at line 39 of file exp2.hpp.

§ exp2() [5/5]

var stan::math::exp2 ( const var a)
inline

Exponentiation base 2 function for variables (C99).

The derivative is

$\frac{d}{dx} 2^x = (\log 2) 2^x$.

\[ \mbox{exp2}(x) = \begin{cases} 2^x & \mbox{if } -\infty\leq x \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{exp2}(x)}{\partial x} = \begin{cases} 2^x\ln2 & \mbox{if } -\infty\leq x\leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

Parameters
aThe variable.
Returns
Two to the power of the specified variable.

Definition at line 50 of file exp2.hpp.

§ exp_mod_normal_ccdf_log()

template<typename T_y , typename T_loc , typename T_scale , typename T_inv_scale >
return_type<T_y, T_loc, T_scale, T_inv_scale>::type stan::math::exp_mod_normal_ccdf_log ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma,
const T_inv_scale &  lambda 
)

Definition at line 25 of file exp_mod_normal_ccdf_log.hpp.

§ exp_mod_normal_cdf()

template<typename T_y , typename T_loc , typename T_scale , typename T_inv_scale >
return_type<T_y, T_loc, T_scale, T_inv_scale>::type stan::math::exp_mod_normal_cdf ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma,
const T_inv_scale &  lambda 
)

Definition at line 25 of file exp_mod_normal_cdf.hpp.

§ exp_mod_normal_cdf_log()

template<typename T_y , typename T_loc , typename T_scale , typename T_inv_scale >
return_type<T_y, T_loc, T_scale, T_inv_scale>::type stan::math::exp_mod_normal_cdf_log ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma,
const T_inv_scale &  lambda 
)

Definition at line 25 of file exp_mod_normal_cdf_log.hpp.

§ exp_mod_normal_lccdf()

template<typename T_y , typename T_loc , typename T_scale , typename T_inv_scale >
return_type<T_y, T_loc, T_scale, T_inv_scale>::type stan::math::exp_mod_normal_lccdf ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma,
const T_inv_scale &  lambda 
)

Definition at line 25 of file exp_mod_normal_lccdf.hpp.

§ exp_mod_normal_lcdf()

template<typename T_y , typename T_loc , typename T_scale , typename T_inv_scale >
return_type<T_y, T_loc, T_scale, T_inv_scale>::type stan::math::exp_mod_normal_lcdf ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma,
const T_inv_scale &  lambda 
)

Definition at line 25 of file exp_mod_normal_lcdf.hpp.

§ exp_mod_normal_log() [1/2]

template<bool propto, typename T_y , typename T_loc , typename T_scale , typename T_inv_scale >
return_type<T_y, T_loc, T_scale, T_inv_scale>::type stan::math::exp_mod_normal_log ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma,
const T_inv_scale &  lambda 
)

Definition at line 25 of file exp_mod_normal_log.hpp.

§ exp_mod_normal_log() [2/2]

template<typename T_y , typename T_loc , typename T_scale , typename T_inv_scale >
return_type<T_y, T_loc, T_scale, T_inv_scale>::type stan::math::exp_mod_normal_log ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma,
const T_inv_scale &  lambda 
)
inline

Definition at line 125 of file exp_mod_normal_log.hpp.

§ exp_mod_normal_lpdf() [1/2]

template<bool propto, typename T_y , typename T_loc , typename T_scale , typename T_inv_scale >
return_type<T_y, T_loc, T_scale, T_inv_scale>::type stan::math::exp_mod_normal_lpdf ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma,
const T_inv_scale &  lambda 
)

Definition at line 25 of file exp_mod_normal_lpdf.hpp.

§ exp_mod_normal_lpdf() [2/2]

template<typename T_y , typename T_loc , typename T_scale , typename T_inv_scale >
return_type<T_y, T_loc, T_scale, T_inv_scale>::type stan::math::exp_mod_normal_lpdf ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma,
const T_inv_scale &  lambda 
)
inline

Definition at line 125 of file exp_mod_normal_lpdf.hpp.

§ exp_mod_normal_rng()

template<class RNG >
double stan::math::exp_mod_normal_rng ( double  mu,
double  sigma,
double  lambda,
RNG &  rng 
)
inline

Definition at line 24 of file exp_mod_normal_rng.hpp.

§ expm1() [1/5]

template<typename T >
fvar<T> stan::math::expm1 ( const fvar< T > &  x)
inline

Definition at line 12 of file expm1.hpp.

§ expm1() [2/5]

double stan::math::expm1 ( double  x)
inline

Return the natural exponentiation of x minus one.

Returns infinity for infinity argument and -infinity for -infinity argument.

Parameters
[in]xArgument.
Returns
Natural exponentiation of argument minus one.

Definition at line 18 of file expm1.hpp.

§ expm1() [3/5]

double stan::math::expm1 ( int  x)
inline

Integer version of expm1.

Parameters
[in]xArgument.
Returns
Natural exponentiation of argument minus one.

Definition at line 28 of file expm1.hpp.

§ expm1() [4/5]

template<typename T >
apply_scalar_unary<expm1_fun, T>::return_t stan::math::expm1 ( const T &  x)
inline

Vectorized version of expm1().

Parameters
xContainer.
Template Parameters
TContainer type.
Returns
Natural exponential of each value in x minus one.

Definition at line 32 of file expm1.hpp.

§ expm1() [5/5]

var stan::math::expm1 ( const var a)
inline

The exponentiation of the specified variable minus 1 (C99).

The derivative is given by

$\frac{d}{dx} \exp(a) - 1 = \exp(a)$.

\[ \mbox{expm1}(x) = \begin{cases} e^x-1 & \mbox{if } -\infty\leq x \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{expm1}(x)}{\partial x} = \begin{cases} e^x & \mbox{if } -\infty\leq x\leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

Parameters
aThe variable.
Returns
Two to the power of the specified variable.

Definition at line 49 of file expm1.hpp.

§ exponential_ccdf_log()

template<typename T_y , typename T_inv_scale >
return_type<T_y, T_inv_scale>::type stan::math::exponential_ccdf_log ( const T_y &  y,
const T_inv_scale &  beta 
)

Definition at line 26 of file exponential_ccdf_log.hpp.

§ exponential_cdf()

template<typename T_y , typename T_inv_scale >
return_type<T_y, T_inv_scale>::type stan::math::exponential_cdf ( const T_y &  y,
const T_inv_scale &  beta 
)

Calculates the exponential cumulative distribution function for the given y and beta.

Inverse scale parameter must be greater than 0. y must be greater than or equal to 0.

Parameters
yA scalar variable.
betaInverse scale parameter.
Template Parameters
T_yType of scalar.
T_inv_scaleType of inverse scale.

Definition at line 39 of file exponential_cdf.hpp.

§ exponential_cdf_log()

template<typename T_y , typename T_inv_scale >
return_type<T_y, T_inv_scale>::type stan::math::exponential_cdf_log ( const T_y &  y,
const T_inv_scale &  beta 
)

Definition at line 27 of file exponential_cdf_log.hpp.

§ exponential_lccdf()

template<typename T_y , typename T_inv_scale >
return_type<T_y, T_inv_scale>::type stan::math::exponential_lccdf ( const T_y &  y,
const T_inv_scale &  beta 
)

Definition at line 26 of file exponential_lccdf.hpp.

§ exponential_lcdf()

template<typename T_y , typename T_inv_scale >
return_type<T_y, T_inv_scale>::type stan::math::exponential_lcdf ( const T_y &  y,
const T_inv_scale &  beta 
)

Definition at line 27 of file exponential_lcdf.hpp.

§ exponential_log() [1/2]

template<bool propto, typename T_y , typename T_inv_scale >
return_type<T_y, T_inv_scale>::type stan::math::exponential_log ( const T_y &  y,
const T_inv_scale &  beta 
)

The log of an exponential density for y with the specified inverse scale parameter.

Inverse scale parameter must be greater than 0. y must be greater than or equal to 0.

\begin{eqnarray*} y &\sim& \mbox{\sf{Expon}}(\beta) \\ \log (p (y \, |\, \beta) ) &=& \log \left( \beta \exp^{-\beta y} \right) \\ &=& \log (\beta) - \beta y \\ & & \mathrm{where} \; y > 0 \end{eqnarray*}

Parameters
yA scalar variable.
betaInverse scale parameter.
Exceptions
std::domain_errorif beta is not greater than 0.
std::domain_errorif y is not greater than or equal to 0.
Template Parameters
T_yType of scalar.
T_inv_scaleType of inverse scale.

Definition at line 53 of file exponential_log.hpp.

§ exponential_log() [2/2]

template<typename T_y , typename T_inv_scale >
return_type<T_y, T_inv_scale>::type stan::math::exponential_log ( const T_y &  y,
const T_inv_scale &  beta 
)
inline

Definition at line 103 of file exponential_log.hpp.

§ exponential_lpdf() [1/2]

template<bool propto, typename T_y , typename T_inv_scale >
return_type<T_y, T_inv_scale>::type stan::math::exponential_lpdf ( const T_y &  y,
const T_inv_scale &  beta 
)

The log of an exponential density for y with the specified inverse scale parameter.

Inverse scale parameter must be greater than 0. y must be greater than or equal to 0.

\begin{eqnarray*} y &\sim& \mbox{\sf{Expon}}(\beta) \\ \log (p (y \, |\, \beta) ) &=& \log \left( \beta \exp^{-\beta y} \right) \\ &=& \log (\beta) - \beta y \\ & & \mathrm{where} \; y > 0 \end{eqnarray*}

Parameters
yA scalar variable.
betaInverse scale parameter.
Exceptions
std::domain_errorif beta is not greater than 0.
std::domain_errorif y is not greater than or equal to 0.
Template Parameters
T_yType of scalar.
T_inv_scaleType of inverse scale.

Definition at line 53 of file exponential_lpdf.hpp.

§ exponential_lpdf() [2/2]

template<typename T_y , typename T_inv_scale >
return_type<T_y, T_inv_scale>::type stan::math::exponential_lpdf ( const T_y &  y,
const T_inv_scale &  beta 
)
inline

Definition at line 103 of file exponential_lpdf.hpp.

§ exponential_rng()

template<class RNG >
double stan::math::exponential_rng ( double  beta,
RNG &  rng 
)
inline

Definition at line 23 of file exponential_rng.hpp.

§ F32()

template<typename T >
T stan::math::F32 ( a,
b,
c,
d,
e,
z,
precision = 1e-6 
)

Definition at line 10 of file F32.hpp.

§ fabs() [1/3]

template<typename T >
fvar<T> stan::math::fabs ( const fvar< T > &  x)
inline

Definition at line 15 of file fabs.hpp.

§ fabs() [2/3]

template<typename T >
apply_scalar_unary<fabs_fun, T>::return_t stan::math::fabs ( const T &  x)
inline

Vectorized version of fabs().

Parameters
xContainer.
Template Parameters
TContainer type.
Returns
Absolute value of each value in x.

Definition at line 34 of file fabs.hpp.

§ fabs() [3/3]

var stan::math::fabs ( const var a)
inline

Return the absolute value of the variable (cmath).

Choosing an arbitrary value at the non-differentiable point 0,

$\frac{d}{dx}|x| = \mbox{sgn}(x)$.

where $\mbox{sgn}(x)$ is the signum function, taking values -1 if $x < 0$, 0 if $x == 0$, and 1 if $x == 1$.

The function abs() provides the same behavior, with abs() defined in stdlib.h and fabs() defined in cmath. The derivative is 0 if the input is 0.

Returns std::numeric_limits<double>::quiet_NaN() for NaN inputs.

\[ \mbox{fabs}(x) = \begin{cases} |x| & \mbox{if } -\infty\leq x\leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{fabs}(x)}{\partial x} = \begin{cases} -1 & \mbox{if } x < 0 \\ 0 & \mbox{if } x = 0 \\ 1 & \mbox{if } x > 0 \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

Parameters
aInput variable.
Returns
Absolute value of variable.

Definition at line 49 of file fabs.hpp.

§ factor_cov_matrix()

template<typename T >
bool stan::math::factor_cov_matrix ( const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &  Sigma,
Eigen::Array< T, Eigen::Dynamic, 1 > &  CPCs,
Eigen::Array< T, Eigen::Dynamic, 1 > &  sds 
)

This function is intended to make starting values, given a covariance matrix Sigma.

The transformations are hard coded as log for standard deviations and Fisher transformations (atanh()) of CPCs

Parameters
[in]Sigmacovariance matrix
[out]CPCsfill this unbounded (does not resize)
[out]sdsfill this unbounded (does not resize)
Returns
false if any of the diagonals of Sigma are 0

Definition at line 25 of file factor_cov_matrix.hpp.

§ factor_U()

template<typename T >
void stan::math::factor_U ( const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &  U,
Eigen::Array< T, Eigen::Dynamic, 1 > &  CPCs 
)

This function is intended to make starting values, given a unit upper-triangular matrix U such that U'DU is a correlation matrix.

Parameters
USigma matrix
CPCsfill this unbounded

Definition at line 27 of file factor_U.hpp.

§ falling_factorial() [1/7]

template<typename T >
fvar<T> stan::math::falling_factorial ( const fvar< T > &  x,
const fvar< T > &  n 
)
inline

Definition at line 14 of file falling_factorial.hpp.

§ falling_factorial() [2/7]

template<typename T >
fvar<T> stan::math::falling_factorial ( const fvar< T > &  x,
double  n 
)
inline

Definition at line 28 of file falling_factorial.hpp.

§ falling_factorial() [3/7]

template<typename T >
fvar<T> stan::math::falling_factorial ( double  x,
const fvar< T > &  n 
)
inline

Definition at line 40 of file falling_factorial.hpp.

§ falling_factorial() [4/7]

template<typename T1 , typename T2 >
boost::math::tools::promote_args<T1, T2>::type stan::math::falling_factorial ( const T1  x,
const T2  n 
)
inline

\[ \mbox{falling\_factorial}(x, n) = \begin{cases} \textrm{error} & \mbox{if } x \leq 0\\ (x)_n & \mbox{if } x > 0 \textrm{ and } -\infty \leq n \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN or } n = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{falling\_factorial}(x, n)}{\partial x} = \begin{cases} \textrm{error} & \mbox{if } x \leq 0\\ \frac{\partial\, (x)_n}{\partial x} & \mbox{if } x > 0 \textrm{ and } -\infty \leq n \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN or } n = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{falling\_factorial}(x, n)}{\partial n} = \begin{cases} \textrm{error} & \mbox{if } x \leq 0\\ \frac{\partial\, (x)_n}{\partial n} & \mbox{if } x > 0 \textrm{ and } -\infty \leq n \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN or } n = \textrm{NaN} \end{cases} \]

\[ (x)_n=\frac{\Gamma(x+1)}{\Gamma(x-n+1)} \]

\[ \frac{\partial \, (x)_n}{\partial x} = (x)_n\Psi(x+1) \]

\[ \frac{\partial \, (x)_n}{\partial n} = -(x)_n\Psi(n+1) \]

Definition at line 54 of file falling_factorial.hpp.

§ falling_factorial() [5/7]

var stan::math::falling_factorial ( const var a,
double  b 
)
inline

Definition at line 56 of file falling_factorial.hpp.

§ falling_factorial() [6/7]

var stan::math::falling_factorial ( const var a,
const var b 
)
inline

Definition at line 61 of file falling_factorial.hpp.

§ falling_factorial() [7/7]

var stan::math::falling_factorial ( double  a,
const var b 
)
inline

Definition at line 66 of file falling_factorial.hpp.

§ fdim() [1/7]

template<typename T >
fvar<T> stan::math::fdim ( const fvar< T > &  x,
const fvar< T > &  y 
)
inline

Return the positive difference of the specified values (C++11).

Template Parameters
TScalar type of autodiff variables.
Parameters
xFirst argument.
ySecond argument.
Returns
Return the differences of the arguments if it is positive and 0 otherwise.

Definition at line 20 of file fdim.hpp.

§ fdim() [2/7]

template<typename T1 , typename T2 >
boost::math::tools::promote_args<T1, T2>::type stan::math::fdim ( T1  x,
T2  y 
)
inline

Return the positive difference of the specified values (C++11).

The function is defined by

fdim(x, y) = (x > y) ? (x - y) : 0.

Parameters
xFirst value.
ySecond value.
Returns
max(x- y, 0)

Definition at line 24 of file fdim.hpp.

§ fdim() [3/7]

template<typename T >
fvar<T> stan::math::fdim ( const fvar< T > &  x,
double  y 
)
inline

Return the positive difference of the specified values (C++11).

Template Parameters
TScalar type of autodiff variables.
Parameters
xFirst argument.
ySecond argument.
Returns
Return the differences of the arguments if it is positive and 0 otherwise.

Definition at line 38 of file fdim.hpp.

§ fdim() [4/7]

template<typename T >
fvar<T> stan::math::fdim ( double  x,
const fvar< T > &  y 
)
inline

Return the positive difference of the specified values (C++11).

Template Parameters
TScalar type of autodiff variables.
Parameters
xFirst argument.
ySecond argument.
Returns
Return the differences of the arguments if it is positive and 0 otherwise.

Definition at line 55 of file fdim.hpp.

§ fdim() [5/7]

var stan::math::fdim ( const var a,
const var b 
)
inline

Return the positive difference between the first variable's the value and the second's (C99, C++11).

The function values and deriatives are defined by

\[ \mbox{fdim}(x, y) = \begin{cases} x-y & \mbox{if } x > y \\[6pt] 0 & \mbox{otherwise} \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN or } y = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{fdim}(x, y)}{\partial x} = \begin{cases} 1 & \mbox{if } x > y \\[6pt] 0 & \mbox{otherwise} \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN or } y = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{fdim}(x, y)}{\partial y} = \begin{cases} -1 & \mbox{if } x > y \\[6pt] 0 & \mbox{otherwise} \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN or } y = \textrm{NaN} \end{cases} \]

Parameters
aFirst variable.
bSecond variable.
Returns
The positive difference between the first and second variable.

Definition at line 94 of file fdim.hpp.

§ fdim() [6/7]

var stan::math::fdim ( double  a,
const var b 
)
inline

Return the positive difference between the first value and the value of the second variable (C99, C++11).

See fdim(var, var) for definitions of values and derivatives.

Parameters
aFirst value.
bSecond variable.
Returns
The positive difference between the first and second arguments.

Definition at line 113 of file fdim.hpp.

§ fdim() [7/7]

var stan::math::fdim ( const var a,
double  b 
)
inline

Return the positive difference between the first variable's value and the second value (C99, C++11).

See fdim(var, var) for definitions of values and derivatives.

Parameters
aFirst value.
bSecond variable.
Returns
The positive difference between the first and second arguments.

Definition at line 131 of file fdim.hpp.

§ fill() [1/3]

template<typename T , typename S >
void stan::math::fill ( T &  x,
const S &  y 
)

Fill the specified container with the specified value.

This base case simply assigns the value to the container.

Template Parameters
TType of reference container.
SType of value.
Parameters
xContainer.
yValue.

Definition at line 18 of file fill.hpp.

§ fill() [2/3]

template<typename T , typename S >
void stan::math::fill ( std::vector< T > &  x,
const S &  y 
)

Fill the specified container with the specified value.

Each container in the specified standard vector is filled recursively by calling fill.

Template Parameters
TType of container in vector.
SType of value.
Parameters
[in]xContainer.
[in,out]yValue.

Definition at line 22 of file fill.hpp.

§ fill() [3/3]

template<typename T , int R, int C, typename S >
void stan::math::fill ( Eigen::Matrix< T, R, C > &  x,
const S &  y 
)

Fill the specified container with the specified value.

The specified matrix is filled by element.

Template Parameters
TType of scalar for matrix container.
RRow type of matrix.
CColumn type of matrix.
SType of value.
Parameters
xContainer.
yValue.

Definition at line 22 of file fill.hpp.

§ finite_diff_grad_hessian()

template<typename F >
void stan::math::finite_diff_grad_hessian ( const F &  f,
const Eigen::Matrix< double, -1, 1 > &  x,
double &  fx,
Eigen::Matrix< double, -1, -1 > &  hess,
std::vector< Eigen::Matrix< double, -1, -1 > > &  grad_hess_fx,
double  epsilon = 1e-04 
)

Calculate the value and the gradient of the hessian of the specified function at the specified argument using second-order autodiff and first-order finite difference.

The functor must implement

double operator()(const Eigen::Matrix<double, Eigen::Dynamic, 1>&)

Reference:

De Levie: An improved numerical approximation for the first derivative, page 3

4 calls to the function, f.

Template Parameters
FType of function
Parameters
[in]fFunction
[in]xArgument to function
[out]fxFunction applied to argument
[out]hessHessian matrix
[out]grad_hess_fxgradient of Hessian of function at argument
[in]epsilonperturbation size

Definition at line 42 of file finite_diff_grad_hessian.hpp.

§ finite_diff_gradient()

template<typename F >
void stan::math::finite_diff_gradient ( const F &  f,
const Eigen::Matrix< double, -1, 1 > &  x,
double &  fx,
Eigen::Matrix< double, -1, 1 > &  grad_fx,
double  epsilon = 1e-03 
)

Calculate the value and the gradient of the specified function at the specified argument using finite difference.

The functor must implement

double operator()(const Eigen::Matrix<double, Eigen::Dynamic, 1>&)

Error should be on order of epsilon ^ 6. The reference for this algorithm is:

De Levie: An improved numerical approximation for the first derivative, page 3

This function involves 6 calls to f.

Template Parameters
FType of function
Parameters
[in]fFunction
[in]xArgument to function
[out]fxFunction applied to argument
[out]grad_fxGradient of function at argument
[in]epsilonperturbation size

Definition at line 38 of file finite_diff_gradient.hpp.

§ finite_diff_hess_helper()

template<typename F >
double stan::math::finite_diff_hess_helper ( const F &  f,
const Eigen::Matrix< double, Eigen::Dynamic, 1 > &  x,
int  lambda,
double  epsilon = 1e-03 
)

Definition at line 12 of file finite_diff_hessian.hpp.

§ finite_diff_hessian()

template<typename F >
void stan::math::finite_diff_hessian ( const F &  f,
const Eigen::Matrix< double, -1, 1 > &  x,
double &  fx,
Eigen::Matrix< double, -1, 1 > &  grad_fx,
Eigen::Matrix< double, -1, -1 > &  hess_fx,
double  epsilon = 1e-03 
)

Calculate the value and the Hessian of the specified function at the specified argument using second-order finite difference.

The functor must implement

double operator()(const Eigen::Matrix<double, Eigen::Dynamic, 1>&)

Error should be on order of epsilon ^ 4, with 4 calls to the function f.

Reference: Eberly: Derivative Approximation by Finite Differences Page 6

Template Parameters
FType of function
Parameters
[in]fFunction
[in]xArgument to function
[out]fxFunction applied to argument
[out]grad_fxGradient of function at argument
[out]hess_fxHessian of function at argument
[in]epsilonperturbation size

Definition at line 66 of file finite_diff_hessian.hpp.

§ floor() [1/3]

template<typename T >
fvar<T> stan::math::floor ( const fvar< T > &  x)
inline

Definition at line 11 of file floor.hpp.

§ floor() [2/3]

template<typename T >
apply_scalar_unary<floor_fun, T>::return_t stan::math::floor ( const T &  x)
inline

Vectorized version of floor().

Parameters
xContainer.
Template Parameters
TContainer type.
Returns
Greatest integer <= each value in x.

Definition at line 32 of file floor.hpp.

§ floor() [3/3]

var stan::math::floor ( const var a)
inline

Return the floor of the specified variable (cmath).

The derivative of the floor function is defined and zero everywhere but at integers, so we set these derivatives to zero for convenience,

$\frac{d}{dx} {\lfloor x \rfloor} = 0$.

The floor function rounds down. For double values, this is the largest integral value that is not greater than the specified value. Although this function is not differentiable because it is discontinuous at integral values, its gradient is returned as zero everywhere.

\[ \mbox{floor}(x) = \begin{cases} \lfloor x \rfloor & \mbox{if } -\infty\leq x \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{floor}(x)}{\partial x} = \begin{cases} 0 & \mbox{if } -\infty\leq x\leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

Parameters
aInput variable.
Returns
Floor of the variable.

Definition at line 60 of file floor.hpp.

§ fma() [1/15]

template<typename T1 , typename T2 , typename T3 >
boost::math::tools::promote_args<T1, T2, T3>::type stan::math::fma ( const T1 &  x,
const T2 &  y,
const T3 &  z 
)
inline

Return the product of the first two arguments plus the third argument.

Warning: This does not delegate to the high-precision platform-specific fma() implementation.

Parameters
xFirst argument.
ySecond argument.
zThird argument.
Returns
The product of the first two arguments plus the third argument.

Definition at line 24 of file fma.hpp.

§ fma() [2/15]

template<typename T1 , typename T2 , typename T3 >
fvar<typename stan::return_type<T1, T2, T3>::type> stan::math::fma ( const fvar< T1 > &  x1,
const fvar< T2 > &  x2,
const fvar< T3 > &  x3 
)
inline

The fused multiply-add operation (C99).

This double-based operation delegates to fma.

The function is defined by

fma(a, b, c) = (a * b) + c.

\[ \mbox{fma}(x, y, z) = \begin{cases} x\cdot y+z & \mbox{if } -\infty\leq x, y, z \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{fma}(x, y, z)}{\partial x} = \begin{cases} y & \mbox{if } -\infty\leq x, y, z \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{fma}(x, y, z)}{\partial y} = \begin{cases} x & \mbox{if } -\infty\leq x, y, z \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{fma}(x, y, z)}{\partial z} = \begin{cases} 1 & \mbox{if } -\infty\leq x, y, z \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

Parameters
x1First value.
x2Second value.
x3Third value.
Returns
Product of the first two values plus the third.

Definition at line 61 of file fma.hpp.

§ fma() [3/15]

template<typename T1 , typename T2 , typename T3 >
fvar<typename stan::return_type<T1, T2, T3>::type> stan::math::fma ( const T1 &  x1,
const fvar< T2 > &  x2,
const fvar< T3 > &  x3 
)
inline

See all-var input signature for details on the function and derivatives.

Definition at line 73 of file fma.hpp.

§ fma() [4/15]

template<typename T1 , typename T2 , typename T3 >
fvar<typename stan::return_type<T1, T2, T3>::type> stan::math::fma ( const fvar< T1 > &  x1,
const T2 &  x2,
const fvar< T3 > &  x3 
)
inline

See all-var input signature for details on the function and derivatives.

Definition at line 84 of file fma.hpp.

§ fma() [5/15]

template<typename T1 , typename T2 , typename T3 >
fvar<typename stan::return_type<T1, T2, T3>::type> stan::math::fma ( const fvar< T1 > &  x1,
const fvar< T2 > &  x2,
const T3 &  x3 
)
inline

See all-var input signature for details on the function and derivatives.

Definition at line 95 of file fma.hpp.

§ fma() [6/15]

template<typename T1 , typename T2 , typename T3 >
fvar<typename stan::return_type<T1, T2, T3>::type> stan::math::fma ( const T1 &  x1,
const T2 &  x2,
const fvar< T3 > &  x3 
)
inline

See all-var input signature for details on the function and derivatives.

Definition at line 106 of file fma.hpp.

§ fma() [7/15]

template<typename T1 , typename T2 , typename T3 >
fvar<typename stan::return_type<T1, T2, T3>::type> stan::math::fma ( const fvar< T1 > &  x1,
const T2 &  x2,
const T3 &  x3 
)
inline

See all-var input signature for details on the function and derivatives.

Definition at line 117 of file fma.hpp.

§ fma() [8/15]

var stan::math::fma ( const var a,
const var b,
const var c 
)
inline

The fused multiply-add function for three variables (C99).

This function returns the product of the first two arguments plus the third argument.

The partial derivatives are

$\frac{\partial}{\partial x} (x * y) + z = y$, and

$\frac{\partial}{\partial y} (x * y) + z = x$, and

$\frac{\partial}{\partial z} (x * y) + z = 1$.

Parameters
aFirst multiplicand.
bSecond multiplicand.
cSummand.
Returns
Product of the multiplicands plus the summand, ($a * $b) + $c.

Definition at line 120 of file fma.hpp.

§ fma() [9/15]

template<typename T1 , typename T2 , typename T3 >
fvar<typename stan::return_type<T1, T2, T3>::type> stan::math::fma ( const T1 &  x1,
const fvar< T2 > &  x2,
const T3 &  x3 
)
inline

See all-var input signature for details on the function and derivatives.

Definition at line 128 of file fma.hpp.

§ fma() [10/15]

var stan::math::fma ( const var a,
const var b,
double  c 
)
inline

The fused multiply-add function for two variables and a value (C99).

This function returns the product of the first two arguments plus the third argument.

The partial derivatives are

$\frac{\partial}{\partial x} (x * y) + c = y$, and

$\frac{\partial}{\partial y} (x * y) + c = x$.

Parameters
aFirst multiplicand.
bSecond multiplicand.
cSummand.
Returns
Product of the multiplicands plus the summand, ($a * $b) + $c.

Definition at line 140 of file fma.hpp.

§ fma() [11/15]

var stan::math::fma ( const var a,
double  b,
const var c 
)
inline

The fused multiply-add function for a variable, value, and variable (C99).

This function returns the product of the first two arguments plus the third argument.

The partial derivatives are

$\frac{\partial}{\partial x} (x * c) + z = c$, and

$\frac{\partial}{\partial z} (x * c) + z = 1$.

Parameters
aFirst multiplicand.
bSecond multiplicand.
cSummand.
Returns
Product of the multiplicands plus the summand, ($a * $b) + $c.

Definition at line 160 of file fma.hpp.

§ fma() [12/15]

var stan::math::fma ( const var a,
double  b,
double  c 
)
inline

The fused multiply-add function for a variable and two values (C99).

This function returns the product of the first two arguments plus the third argument.

The double-based version ::fma(double, double, double) is defined in <cmath>.

The derivative is

$\frac{d}{d x} (x * c) + d = c$.

Parameters
aFirst multiplicand.
bSecond multiplicand.
cSummand.
Returns
Product of the multiplicands plus the summand, ($a * $b) + $c.

Definition at line 181 of file fma.hpp.

§ fma() [13/15]

var stan::math::fma ( double  a,
const var b,
double  c 
)
inline

The fused multiply-add function for a value, variable, and value (C99).

This function returns the product of the first two arguments plus the third argument.

The derivative is

$\frac{d}{d y} (c * y) + d = c$, and

Parameters
aFirst multiplicand.
bSecond multiplicand.
cSummand.
Returns
Product of the multiplicands plus the summand, ($a * $b) + $c.

Definition at line 199 of file fma.hpp.

§ fma() [14/15]

var stan::math::fma ( double  a,
double  b,
const var c 
)
inline

The fused multiply-add function for two values and a variable, and value (C99).

This function returns the product of the first two arguments plus the third argument.

The derivative is

$\frac{\partial}{\partial z} (c * d) + z = 1$.

Parameters
aFirst multiplicand.
bSecond multiplicand.
cSummand.
Returns
Product of the multiplicands plus the summand, ($a * $b) + $c.

Definition at line 217 of file fma.hpp.

§ fma() [15/15]

var stan::math::fma ( double  a,
const var b,
const var c 
)
inline

The fused multiply-add function for a value and two variables (C99).

This function returns the product of the first two arguments plus the third argument.

The partial derivaties are

$\frac{\partial}{\partial y} (c * y) + z = c$, and

$\frac{\partial}{\partial z} (c * y) + z = 1$.

Parameters
aFirst multiplicand.
bSecond multiplicand.
cSummand.
Returns
Product of the multiplicands plus the summand, ($a * $b) + $c.

Definition at line 237 of file fma.hpp.

§ fmax() [1/7]

template<typename T1 , typename T2 >
boost::math::tools::promote_args<T1, T2>::type stan::math::fmax ( const T1 &  x,
const T2 &  y 
)
inline

Return the greater of the two specified arguments.

If one is greater than the other, return not-a-number.

Parameters
xFirst argument.
ySecond argument.
Returns
maximum of x or y and if one is NaN return the other

Definition at line 20 of file fmax.hpp.

§ fmax() [2/7]

template<typename T >
fvar<T> stan::math::fmax ( const fvar< T > &  x1,
const fvar< T > &  x2 
)
inline

Return the greater of the two specified arguments.

If one is greater than the other, return not-a-number.

Parameters
x1First argument.
x2Second argument.
Returns
maximum of arguments, and if one is NaN return the other

Definition at line 23 of file fmax.hpp.

§ fmax() [3/7]

template<typename T >
fvar<T> stan::math::fmax ( double  x1,
const fvar< T > &  x2 
)
inline

Return the greater of the two specified arguments.

If one is greater than the other, return not-a-number.

Parameters
x1First argument.
x2Second argument.
Returns
maximum of arguments, and if one is NaN return the other

Definition at line 49 of file fmax.hpp.

§ fmax() [4/7]

var stan::math::fmax ( const var a,
const var b 
)
inline

Returns the maximum of the two variable arguments (C99).

No new variable implementations are created, with this function defined as if by

fmax(a, b) = a if a's value is greater than b's, and .

fmax(a, b) = b if b's value is greater than or equal to a's.

\[ \mbox{fmax}(x, y) = \begin{cases} x & \mbox{if } x \geq y \\ y & \mbox{if } x < y \\[6pt] x & \mbox{if } -\infty\leq x\leq \infty, y = \textrm{NaN}\\ y & \mbox{if } -\infty\leq y\leq \infty, x = \textrm{NaN}\\ \textrm{NaN} & \mbox{if } x, y = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{fmax}(x, y)}{\partial x} = \begin{cases} 1 & \mbox{if } x \geq y \\ 0 & \mbox{if } x < y \\[6pt] 1 & \mbox{if } -\infty\leq x\leq \infty, y = \textrm{NaN}\\ 0 & \mbox{if } -\infty\leq y\leq \infty, x = \textrm{NaN}\\ \textrm{NaN} & \mbox{if } x, y = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{fmax}(x, y)}{\partial y} = \begin{cases} 0 & \mbox{if } x \geq y \\ 1 & \mbox{if } x < y \\[6pt] 0 & \mbox{if } -\infty\leq x\leq \infty, y = \textrm{NaN}\\ 1 & \mbox{if } -\infty\leq y\leq \infty, x = \textrm{NaN}\\ \textrm{NaN} & \mbox{if } x, y = \textrm{NaN} \end{cases} \]

Parameters
aFirst variable.
bSecond variable.
Returns
If the first variable's value is larger than the second's, the first variable, otherwise the second variable.

Definition at line 61 of file fmax.hpp.

§ fmax() [5/7]

template<typename T >
fvar<T> stan::math::fmax ( const fvar< T > &  x1,
double  x2 
)
inline

Return the greater of the two specified arguments.

If one is greater than the other, return not-a-number.

Parameters
x1First argument.
x2Second argument.
Returns
maximum of arguments, and if one is NaN return the other

Definition at line 75 of file fmax.hpp.

§ fmax() [6/7]

var stan::math::fmax ( const var a,
double  b 
)
inline

Returns the maximum of the variable and scalar, promoting the scalar to a variable if it is larger (C99).

For fmax(a, b), if a's value is greater than b, then a is returned, otherwise a fesh variable implementation wrapping the value b is returned.

Parameters
aFirst variable.
bSecond value
Returns
If the first variable's value is larger than or equal to the second value, the first variable, otherwise the second value promoted to a fresh variable.

Definition at line 89 of file fmax.hpp.

§ fmax() [7/7]

var stan::math::fmax ( double  a,
const var b 
)
inline

Returns the maximum of a scalar and variable, promoting the scalar to a variable if it is larger (C99).

For fmax(a, b), if a is greater than b's value, then a fresh variable implementation wrapping a is returned, otherwise b is returned.

Parameters
aFirst value.
bSecond variable.
Returns
If the first value is larger than the second variable's value, return the first value promoted to a variable, otherwise return the second variable.

Definition at line 117 of file fmax.hpp.

§ fmin() [1/7]

template<typename T >
fvar<T> stan::math::fmin ( const fvar< T > &  x1,
const fvar< T > &  x2 
)
inline

Definition at line 14 of file fmin.hpp.

§ fmin() [2/7]

template<typename T1 , typename T2 >
boost::math::tools::promote_args<T1, T2>::type stan::math::fmin ( const T1 &  x,
const T2 &  y 
)
inline

Return the lesser of the two specified arguments.

If one is greater than the other, return not-a-number.

Parameters
xFirst argument.
ySecond argument.
Returns
Minimum of x or y and if one is NaN return the other

Definition at line 20 of file fmin.hpp.

§ fmin() [3/7]

template<typename T >
fvar<T> stan::math::fmin ( double  x1,
const fvar< T > &  x2 
)
inline

Definition at line 32 of file fmin.hpp.

§ fmin() [4/7]

template<typename T >
fvar<T> stan::math::fmin ( const fvar< T > &  x1,
double  x2 
)
inline

Definition at line 50 of file fmin.hpp.

§ fmin() [5/7]

var stan::math::fmin ( const var a,
const var b 
)
inline

Returns the minimum of the two variable arguments (C99).

For fmin(a, b), if a's value is less than b's, then a is returned, otherwise b is returned.

\[ \mbox{fmin}(x, y) = \begin{cases} x & \mbox{if } x \leq y \\ y & \mbox{if } x > y \\[6pt] x & \mbox{if } -\infty\leq x\leq \infty, y = \textrm{NaN}\\ y & \mbox{if } -\infty\leq y\leq \infty, x = \textrm{NaN}\\ \textrm{NaN} & \mbox{if } x, y = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{fmin}(x, y)}{\partial x} = \begin{cases} 1 & \mbox{if } x \leq y \\ 0 & \mbox{if } x > y \\[6pt] 1 & \mbox{if } -\infty\leq x\leq \infty, y = \textrm{NaN}\\ 0 & \mbox{if } -\infty\leq y\leq \infty, x = \textrm{NaN}\\ \textrm{NaN} & \mbox{if } x, y = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{fmin}(x, y)}{\partial y} = \begin{cases} 0 & \mbox{if } x \leq y \\ 1 & \mbox{if } x > y \\[6pt] 0 & \mbox{if } -\infty\leq x\leq \infty, y = \textrm{NaN}\\ 1 & \mbox{if } -\infty\leq y\leq \infty, x = \textrm{NaN}\\ \textrm{NaN} & \mbox{if } x, y = \textrm{NaN} \end{cases} \]

Parameters
aFirst variable.
bSecond variable.
Returns
If the first variable's value is smaller than the second's, the first variable, otherwise the second variable.

Definition at line 57 of file fmin.hpp.

§ fmin() [6/7]

var stan::math::fmin ( const var a,
double  b 
)
inline

Returns the minimum of the variable and scalar, promoting the scalar to a variable if it is larger (C99).

For fmin(a, b), if a's value is less than or equal to b, then a is returned, otherwise a fresh variable wrapping b is returned.

Parameters
aFirst variable.
bSecond value
Returns
If the first variable's value is less than or equal to the second value, the first variable, otherwise the second value promoted to a fresh variable.

Definition at line 84 of file fmin.hpp.

§ fmin() [7/7]

var stan::math::fmin ( double  a,
const var b 
)
inline

Returns the minimum of a scalar and variable, promoting the scalar to a variable if it is larger (C99).

For fmin(a, b), if a is less than b's value, then a fresh variable implementation wrapping a is returned, otherwise b is returned.

Parameters
aFirst value.
bSecond variable.
Returns
If the first value is smaller than the second variable's value, return the first value promoted to a variable, otherwise return the second variable.

Definition at line 112 of file fmin.hpp.

§ fmod() [1/6]

template<typename T >
fvar<T> stan::math::fmod ( const fvar< T > &  x1,
const fvar< T > &  x2 
)
inline

Definition at line 15 of file fmod.hpp.

§ fmod() [2/6]

template<typename T >
fvar<T> stan::math::fmod ( const fvar< T > &  x1,
double  x2 
)
inline

Definition at line 25 of file fmod.hpp.

§ fmod() [3/6]

template<typename T >
fvar<T> stan::math::fmod ( double  x1,
const fvar< T > &  x2 
)
inline

Definition at line 37 of file fmod.hpp.

§ fmod() [4/6]

var stan::math::fmod ( const var a,
const var b 
)
inline

Return the floating point remainder after dividing the first variable by the second (cmath).

The partial derivatives with respect to the variables are defined everywhere but where $x = y$, but we set these to match other values, with

$\frac{\partial}{\partial x} \mbox{fmod}(x, y) = 1$, and

$\frac{\partial}{\partial y} \mbox{fmod}(x, y) = -\lfloor \frac{x}{y} \rfloor$.

\[ \mbox{fmod}(x, y) = \begin{cases} x - \lfloor \frac{x}{y}\rfloor y & \mbox{if } -\infty\leq x, y \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN or } y = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{fmod}(x, y)}{\partial x} = \begin{cases} 1 & \mbox{if } -\infty\leq x, y\leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN or } y = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{fmod}(x, y)}{\partial y} = \begin{cases} -\lfloor \frac{x}{y}\rfloor & \mbox{if } -\infty\leq x, y\leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN or } y = \textrm{NaN} \end{cases} \]

Parameters
aFirst variable.
bSecond variable.
Returns
Floating pointer remainder of dividing the first variable by the second.

Definition at line 103 of file fmod.hpp.

§ fmod() [5/6]

var stan::math::fmod ( const var a,
double  b 
)
inline

Return the floating point remainder after dividing the the first variable by the second scalar (cmath).

The derivative with respect to the variable is

$\frac{d}{d x} \mbox{fmod}(x, c) = \frac{1}{c}$.

Parameters
aFirst variable.
bSecond scalar.
Returns
Floating pointer remainder of dividing the first variable by the second scalar.

Definition at line 120 of file fmod.hpp.

§ fmod() [6/6]

var stan::math::fmod ( double  a,
const var b 
)
inline

Return the floating point remainder after dividing the first scalar by the second variable (cmath).

The derivative with respect to the variable is

$\frac{d}{d y} \mbox{fmod}(c, y) = -\lfloor \frac{c}{y} \rfloor$.

Parameters
aFirst scalar.
bSecond variable.
Returns
Floating pointer remainder of dividing first scalar by the second variable.

Definition at line 137 of file fmod.hpp.

§ frechet_ccdf_log()

template<typename T_y , typename T_shape , typename T_scale >
return_type<T_y, T_shape, T_scale>::type stan::math::frechet_ccdf_log ( const T_y &  y,
const T_shape &  alpha,
const T_scale &  sigma 
)

Definition at line 30 of file frechet_ccdf_log.hpp.

§ frechet_cdf()

template<typename T_y , typename T_shape , typename T_scale >
return_type<T_y, T_shape, T_scale>::type stan::math::frechet_cdf ( const T_y &  y,
const T_shape &  alpha,
const T_scale &  sigma 
)

Definition at line 30 of file frechet_cdf.hpp.

§ frechet_cdf_log()

template<typename T_y , typename T_shape , typename T_scale >
return_type<T_y, T_shape, T_scale>::type stan::math::frechet_cdf_log ( const T_y &  y,
const T_shape &  alpha,
const T_scale &  sigma 
)

Definition at line 30 of file frechet_cdf_log.hpp.

§ frechet_lccdf()

template<typename T_y , typename T_shape , typename T_scale >
return_type<T_y, T_shape, T_scale>::type stan::math::frechet_lccdf ( const T_y &  y,
const T_shape &  alpha,
const T_scale &  sigma 
)

Definition at line 30 of file frechet_lccdf.hpp.

§ frechet_lcdf()

template<typename T_y , typename T_shape , typename T_scale >
return_type<T_y, T_shape, T_scale>::type stan::math::frechet_lcdf ( const T_y &  y,
const T_shape &  alpha,
const T_scale &  sigma 
)

Definition at line 30 of file frechet_lcdf.hpp.

§ frechet_log() [1/2]

template<bool propto, typename T_y , typename T_shape , typename T_scale >
return_type<T_y, T_shape, T_scale>::type stan::math::frechet_log ( const T_y &  y,
const T_shape &  alpha,
const T_scale &  sigma 
)

Definition at line 33 of file frechet_log.hpp.

§ frechet_log() [2/2]

template<typename T_y , typename T_shape , typename T_scale >
return_type<T_y, T_shape, T_scale>::type stan::math::frechet_log ( const T_y &  y,
const T_shape &  alpha,
const T_scale &  sigma 
)
inline

Definition at line 130 of file frechet_log.hpp.

§ frechet_lpdf() [1/2]

template<bool propto, typename T_y , typename T_shape , typename T_scale >
return_type<T_y, T_shape, T_scale>::type stan::math::frechet_lpdf ( const T_y &  y,
const T_shape &  alpha,
const T_scale &  sigma 
)

Definition at line 33 of file frechet_lpdf.hpp.

§ frechet_lpdf() [2/2]

template<typename T_y , typename T_shape , typename T_scale >
return_type<T_y, T_shape, T_scale>::type stan::math::frechet_lpdf ( const T_y &  y,
const T_shape &  alpha,
const T_scale &  sigma 
)
inline

Definition at line 130 of file frechet_lpdf.hpp.

§ frechet_rng()

template<class RNG >
double stan::math::frechet_rng ( double  alpha,
double  sigma,
RNG &  rng 
)
inline

Definition at line 26 of file frechet_rng.hpp.

§ free_cvodes_memory()

void stan::math::free_cvodes_memory ( N_Vector &  cvodes_state,
N_Vector *  cvodes_state_sens,
void *  cvodes_mem,
size_t  S 
)
inline

Free memory allocated for CVODES state, sensitivity, and general memory.

Parameters
[in]cvodes_stateState vector.
[in]cvodes_state_sensSensivity vector.
[in]cvodes_memMemory held for CVODES.
[in]SNumber of sensitivities being calculated.

Definition at line 34 of file integrate_ode_bdf.hpp.

§ gamma_ccdf_log()

template<typename T_y , typename T_shape , typename T_inv_scale >
return_type<T_y, T_shape, T_inv_scale>::type stan::math::gamma_ccdf_log ( const T_y &  y,
const T_shape &  alpha,
const T_inv_scale &  beta 
)

Definition at line 34 of file gamma_ccdf_log.hpp.

§ gamma_cdf()

template<typename T_y , typename T_shape , typename T_inv_scale >
return_type<T_y, T_shape, T_inv_scale>::type stan::math::gamma_cdf ( const T_y &  y,
const T_shape &  alpha,
const T_inv_scale &  beta 
)

The cumulative density function for a gamma distribution for y with the specified shape and inverse scale parameters.

Parameters
yA scalar variable.
alphaShape parameter.
betaInverse scale parameter.
Exceptions
std::domain_errorif alpha is not greater than 0.
std::domain_errorif beta is not greater than 0.
std::domain_errorif y is not greater than or equal to 0.
Template Parameters
T_yType of scalar.
T_shapeType of shape.
T_inv_scaleType of inverse scale.

Definition at line 48 of file gamma_cdf.hpp.

§ gamma_cdf_log()

template<typename T_y , typename T_shape , typename T_inv_scale >
return_type<T_y, T_shape, T_inv_scale>::type stan::math::gamma_cdf_log ( const T_y &  y,
const T_shape &  alpha,
const T_inv_scale &  beta 
)

Definition at line 34 of file gamma_cdf_log.hpp.

§ gamma_lccdf()

template<typename T_y , typename T_shape , typename T_inv_scale >
return_type<T_y, T_shape, T_inv_scale>::type stan::math::gamma_lccdf ( const T_y &  y,
const T_shape &  alpha,
const T_inv_scale &  beta 
)

Definition at line 34 of file gamma_lccdf.hpp.

§ gamma_lcdf()

template<typename T_y , typename T_shape , typename T_inv_scale >
return_type<T_y, T_shape, T_inv_scale>::type stan::math::gamma_lcdf ( const T_y &  y,
const T_shape &  alpha,
const T_inv_scale &  beta 
)

Definition at line 34 of file gamma_lcdf.hpp.

§ gamma_log() [1/2]

template<bool propto, typename T_y , typename T_shape , typename T_inv_scale >
return_type<T_y, T_shape, T_inv_scale>::type stan::math::gamma_log ( const T_y &  y,
const T_shape &  alpha,
const T_inv_scale &  beta 
)

The log of a gamma density for y with the specified shape and inverse scale parameters.

Shape and inverse scale parameters must be greater than 0. y must be greater than or equal to 0.

\begin{eqnarray*} y &\sim& \mbox{\sf{Gamma}}(\alpha, \beta) \\ \log (p (y \, |\, \alpha, \beta) ) &=& \log \left( \frac{\beta^\alpha}{\Gamma(\alpha)} y^{\alpha - 1} \exp^{- \beta y} \right) \\ &=& \alpha \log(\beta) - \log(\Gamma(\alpha)) + (\alpha - 1) \log(y) - \beta y\\ & & \mathrm{where} \; y > 0 \end{eqnarray*}

Parameters
yA scalar variable.
alphaShape parameter.
betaInverse scale parameter.
Exceptions
std::domain_errorif alpha is not greater than 0.
std::domain_errorif beta is not greater than 0.
std::domain_errorif y is not greater than or equal to 0.
Template Parameters
T_yType of scalar.
T_shapeType of shape.
T_inv_scaleType of inverse scale.

Definition at line 53 of file gamma_log.hpp.

§ gamma_log() [2/2]

template<typename T_y , typename T_shape , typename T_inv_scale >
return_type<T_y, T_shape, T_inv_scale>::type stan::math::gamma_log ( const T_y &  y,
const T_shape &  alpha,
const T_inv_scale &  beta 
)
inline

Definition at line 152 of file gamma_log.hpp.

§ gamma_lpdf() [1/2]

template<bool propto, typename T_y , typename T_shape , typename T_inv_scale >
return_type<T_y, T_shape, T_inv_scale>::type stan::math::gamma_lpdf ( const T_y &  y,
const T_shape &  alpha,
const T_inv_scale &  beta 
)

The log of a gamma density for y with the specified shape and inverse scale parameters.

Shape and inverse scale parameters must be greater than 0. y must be greater than or equal to 0.

\begin{eqnarray*} y &\sim& \mbox{\sf{Gamma}}(\alpha, \beta) \\ \log (p (y \, |\, \alpha, \beta) ) &=& \log \left( \frac{\beta^\alpha}{\Gamma(\alpha)} y^{\alpha - 1} \exp^{- \beta y} \right) \\ &=& \alpha \log(\beta) - \log(\Gamma(\alpha)) + (\alpha - 1) \log(y) - \beta y\\ & & \mathrm{where} \; y > 0 \end{eqnarray*}

Parameters
yA scalar variable.
alphaShape parameter.
betaInverse scale parameter.
Exceptions
std::domain_errorif alpha is not greater than 0.
std::domain_errorif beta is not greater than 0.
std::domain_errorif y is not greater than or equal to 0.
Template Parameters
T_yType of scalar.
T_shapeType of shape.
T_inv_scaleType of inverse scale.

Definition at line 53 of file gamma_lpdf.hpp.

§ gamma_lpdf() [2/2]

template<typename T_y , typename T_shape , typename T_inv_scale >
return_type<T_y, T_shape, T_inv_scale>::type stan::math::gamma_lpdf ( const T_y &  y,
const T_shape &  alpha,
const T_inv_scale &  beta 
)
inline

Definition at line 152 of file gamma_lpdf.hpp.

§ gamma_p() [1/7]

template<typename T >
fvar<T> stan::math::gamma_p ( const fvar< T > &  x1,
const fvar< T > &  x2 
)
inline

Definition at line 14 of file gamma_p.hpp.

§ gamma_p() [2/7]

template<typename T >
fvar<T> stan::math::gamma_p ( const fvar< T > &  x1,
double  x2 
)
inline

Definition at line 49 of file gamma_p.hpp.

§ gamma_p() [3/7]

double stan::math::gamma_p ( double  x,
double  a 
)
inline

\[ \mbox{gamma\_p}(a, z) = \begin{cases} \textrm{error} & \mbox{if } a\leq 0 \textrm{ or } z < 0\\ P(a, z) & \mbox{if } a > 0, z \geq 0 \\[6pt] \textrm{NaN} & \mbox{if } a = \textrm{NaN or } z = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{gamma\_p}(a, z)}{\partial a} = \begin{cases} \textrm{error} & \mbox{if } a\leq 0 \textrm{ or } z < 0\\ \frac{\partial\, P(a, z)}{\partial a} & \mbox{if } a > 0, z \geq 0 \\[6pt] \textrm{NaN} & \mbox{if } a = \textrm{NaN or } z = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{gamma\_p}(a, z)}{\partial z} = \begin{cases} \textrm{error} & \mbox{if } a\leq 0 \textrm{ or } z < 0\\ \frac{\partial\, P(a, z)}{\partial z} & \mbox{if } a > 0, z \geq 0 \\[6pt] \textrm{NaN} & \mbox{if } a = \textrm{NaN or } z = \textrm{NaN} \end{cases} \]

\[ P(a, z)=\frac{1}{\Gamma(a)}\int_0^zt^{a-1}e^{-t}dt \]

\[ \frac{\partial \, P(a, z)}{\partial a} = -\frac{\Psi(a)}{\Gamma^2(a)}\int_0^zt^{a-1}e^{-t}dt + \frac{1}{\Gamma(a)}\int_0^z (a-1)t^{a-2}e^{-t}dt \]

\[ \frac{\partial \, P(a, z)}{\partial z} = \frac{z^{a-1}e^{-z}}{\Gamma(a)} \]

Exceptions
domain_errorif x is at pole

Definition at line 54 of file gamma_p.hpp.

§ gamma_p() [4/7]

template<typename T >
fvar<T> stan::math::gamma_p ( double  x1,
const fvar< T > &  x2 
)
inline

Definition at line 83 of file gamma_p.hpp.

§ gamma_p() [5/7]

var stan::math::gamma_p ( const var a,
const var b 
)
inline

Definition at line 103 of file gamma_p.hpp.

§ gamma_p() [6/7]

var stan::math::gamma_p ( const var a,
double  b 
)
inline

Definition at line 108 of file gamma_p.hpp.

§ gamma_p() [7/7]

var stan::math::gamma_p ( double  a,
const var b 
)
inline

Definition at line 113 of file gamma_p.hpp.

§ gamma_q() [1/7]

template<typename T >
fvar<T> stan::math::gamma_q ( const fvar< T > &  x1,
const fvar< T > &  x2 
)
inline

Definition at line 14 of file gamma_q.hpp.

§ gamma_q() [2/7]

template<typename T >
fvar<T> stan::math::gamma_q ( const fvar< T > &  x1,
double  x2 
)
inline

Definition at line 49 of file gamma_q.hpp.

§ gamma_q() [3/7]

double stan::math::gamma_q ( double  x,
double  a 
)
inline

\[ \mbox{gamma\_q}(a, z) = \begin{cases} \textrm{error} & \mbox{if } a\leq 0 \textrm{ or } z < 0\\ Q(a, z) & \mbox{if } a > 0, z \geq 0 \\[6pt] \textrm{NaN} & \mbox{if } a = \textrm{NaN or } z = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{gamma\_q}(a, z)}{\partial a} = \begin{cases} \textrm{error} & \mbox{if } a\leq 0 \textrm{ or } z < 0\\ \frac{\partial\, Q(a, z)}{\partial a} & \mbox{if } a > 0, z \geq 0 \\[6pt] \textrm{NaN} & \mbox{if } a = \textrm{NaN or } z = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{gamma\_q}(a, z)}{\partial z} = \begin{cases} \textrm{error} & \mbox{if } a\leq 0 \textrm{ or } z < 0\\ \frac{\partial\, Q(a, z)}{\partial z} & \mbox{if } a > 0, z \geq 0 \\[6pt] \textrm{NaN} & \mbox{if } a = \textrm{NaN or } z = \textrm{NaN} \end{cases} \]

\[ Q(a, z)=\frac{1}{\Gamma(a)}\int_z^\infty t^{a-1}e^{-t}dt \]

\[ \frac{\partial \, Q(a, z)}{\partial a} = -\frac{\Psi(a)}{\Gamma^2(a)}\int_z^\infty t^{a-1}e^{-t}dt + \frac{1}{\Gamma(a)}\int_z^\infty (a-1)t^{a-2}e^{-t}dt \]

\[ \frac{\partial \, Q(a, z)}{\partial z} = -\frac{z^{a-1}e^{-z}}{\Gamma(a)} \]

Exceptions
domain_errorif x is at pole

Definition at line 52 of file gamma_q.hpp.

§ gamma_q() [4/7]

var stan::math::gamma_q ( const var a,
const var b 
)
inline

Definition at line 59 of file gamma_q.hpp.

§ gamma_q() [5/7]

var stan::math::gamma_q ( const var a,
double  b 
)
inline

Definition at line 64 of file gamma_q.hpp.

§ gamma_q() [6/7]

var stan::math::gamma_q ( double  a,
const var b 
)
inline

Definition at line 69 of file gamma_q.hpp.

§ gamma_q() [7/7]

template<typename T >
fvar<T> stan::math::gamma_q ( double  x1,
const fvar< T > &  x2 
)
inline

Definition at line 83 of file gamma_q.hpp.

§ gamma_rng()

template<class RNG >
double stan::math::gamma_rng ( double  alpha,
double  beta,
RNG &  rng 
)
inline

Definition at line 29 of file gamma_rng.hpp.

§ gaussian_dlm_obs_log() [1/4]

template<bool propto, typename T_y , typename T_F , typename T_G , typename T_V , typename T_W , typename T_m0 , typename T_C0 >
return_type< T_y, typename return_type<T_F, T_G, T_V, T_W, T_m0, T_C0>::type >::type stan::math::gaussian_dlm_obs_log ( const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &  y,
const Eigen::Matrix< T_F, Eigen::Dynamic, Eigen::Dynamic > &  F,
const Eigen::Matrix< T_G, Eigen::Dynamic, Eigen::Dynamic > &  G,
const Eigen::Matrix< T_V, Eigen::Dynamic, Eigen::Dynamic > &  V,
const Eigen::Matrix< T_W, Eigen::Dynamic, Eigen::Dynamic > &  W,
const Eigen::Matrix< T_m0, Eigen::Dynamic, 1 > &  m0,
const Eigen::Matrix< T_C0, Eigen::Dynamic, Eigen::Dynamic > &  C0 
)

The log of a Gaussian dynamic linear model (GDLM).

This distribution is equivalent to, for $t = 1:T$,

\begin{eqnarray*} y_t & \sim N(F' \theta_t, V) \\ \theta_t & \sim N(G \theta_{t-1}, W) \\ \theta_0 & \sim N(m_0, C_0) \end{eqnarray*}

If V is a vector, then the Kalman filter is applied sequentially.

Parameters
yA r x T matrix of observations. Rows are variables, columns are observations.
FA n x r matrix. The design matrix.
GA n x n matrix. The transition matrix.
VA r x r matrix. The observation covariance matrix.
WA n x n matrix. The state covariance matrix.
m0A n x 1 matrix. The mean vector of the distribution of the initial state.
C0A n x n matrix. The covariance matrix of the distribution of the initial state.
Returns
The log of the joint density of the GDLM.
Exceptions
std::domain_errorif a matrix in the Kalman filter is not positive semi-definite.
Template Parameters
T_yType of scalar.
T_FType of design matrix.
T_GType of transition matrix.
T_VType of observation covariance matrix.
T_WType of state covariance matrix.
T_m0Type of initial state mean vector.
T_C0Type of initial state covariance matrix.

Definition at line 78 of file gaussian_dlm_obs_log.hpp.

§ gaussian_dlm_obs_log() [2/4]

template<typename T_y , typename T_F , typename T_G , typename T_V , typename T_W , typename T_m0 , typename T_C0 >
return_type< T_y, typename return_type<T_F, T_G, T_V, T_W, T_m0, T_C0>::type >::type stan::math::gaussian_dlm_obs_log ( const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &  y,
const Eigen::Matrix< T_F, Eigen::Dynamic, Eigen::Dynamic > &  F,
const Eigen::Matrix< T_G, Eigen::Dynamic, Eigen::Dynamic > &  G,
const Eigen::Matrix< T_V, Eigen::Dynamic, Eigen::Dynamic > &  V,
const Eigen::Matrix< T_W, Eigen::Dynamic, Eigen::Dynamic > &  W,
const Eigen::Matrix< T_m0, Eigen::Dynamic, 1 > &  m0,
const Eigen::Matrix< T_C0, Eigen::Dynamic, Eigen::Dynamic > &  C0 
)
inline

Definition at line 202 of file gaussian_dlm_obs_log.hpp.

§ gaussian_dlm_obs_log() [3/4]

template<bool propto, typename T_y , typename T_F , typename T_G , typename T_V , typename T_W , typename T_m0 , typename T_C0 >
return_type< T_y, typename return_type<T_F, T_G, T_V, T_W, T_m0, T_C0>::type >::type stan::math::gaussian_dlm_obs_log ( const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &  y,
const Eigen::Matrix< T_F, Eigen::Dynamic, Eigen::Dynamic > &  F,
const Eigen::Matrix< T_G, Eigen::Dynamic, Eigen::Dynamic > &  G,
const Eigen::Matrix< T_V, Eigen::Dynamic, 1 > &  V,
const Eigen::Matrix< T_W, Eigen::Dynamic, Eigen::Dynamic > &  W,
const Eigen::Matrix< T_m0, Eigen::Dynamic, 1 > &  m0,
const Eigen::Matrix< T_C0, Eigen::Dynamic, Eigen::Dynamic > &  C0 
)

The log of a Gaussian dynamic linear model (GDLM) with uncorrelated observation disturbances.

This distribution is equivalent to, for $t = 1:T$,

\begin{eqnarray*} y_t & \sim N(F' \theta_t, diag(V)) \\ \theta_t & \sim N(G \theta_{t-1}, W) \\ \theta_0 & \sim N(m_0, C_0) \end{eqnarray*}

If V is a vector, then the Kalman filter is applied sequentially.

Parameters
yA r x T matrix of observations. Rows are variables, columns are observations.
FA n x r matrix. The design matrix.
GA n x n matrix. The transition matrix.
VA size r vector. The diagonal of the observation covariance matrix.
WA n x n matrix. The state covariance matrix.
m0A n x 1 matrix. The mean vector of the distribution of the initial state.
C0A n x n matrix. The covariance matrix of the distribution of the initial state.
Returns
The log of the joint density of the GDLM.
Exceptions
std::domain_errorif a matrix in the Kalman filter is not semi-positive definite.
Template Parameters
T_yType of scalar.
T_FType of design matrix.
T_GType of transition matrix.
T_VType of observation variances
T_WType of state covariance matrix.
T_m0Type of initial state mean vector.
T_C0Type of initial state covariance matrix.

Definition at line 262 of file gaussian_dlm_obs_log.hpp.

§ gaussian_dlm_obs_log() [4/4]

template<typename T_y , typename T_F , typename T_G , typename T_V , typename T_W , typename T_m0 , typename T_C0 >
return_type<T_y, typename return_type<T_F, T_G, T_V, T_W, T_m0, T_C0>::type>::type stan::math::gaussian_dlm_obs_log ( const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &  y,
const Eigen::Matrix< T_F, Eigen::Dynamic, Eigen::Dynamic > &  F,
const Eigen::Matrix< T_G, Eigen::Dynamic, Eigen::Dynamic > &  G,
const Eigen::Matrix< T_V, Eigen::Dynamic, 1 > &  V,
const Eigen::Matrix< T_W, Eigen::Dynamic, Eigen::Dynamic > &  W,
const Eigen::Matrix< T_m0, Eigen::Dynamic, 1 > &  m0,
const Eigen::Matrix< T_C0, Eigen::Dynamic, Eigen::Dynamic > &  C0 
)
inline

Definition at line 398 of file gaussian_dlm_obs_log.hpp.

§ gaussian_dlm_obs_lpdf() [1/4]

template<bool propto, typename T_y , typename T_F , typename T_G , typename T_V , typename T_W , typename T_m0 , typename T_C0 >
return_type< T_y, typename return_type<T_F, T_G, T_V, T_W, T_m0, T_C0>::type >::type stan::math::gaussian_dlm_obs_lpdf ( const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &  y,
const Eigen::Matrix< T_F, Eigen::Dynamic, Eigen::Dynamic > &  F,
const Eigen::Matrix< T_G, Eigen::Dynamic, Eigen::Dynamic > &  G,
const Eigen::Matrix< T_V, Eigen::Dynamic, Eigen::Dynamic > &  V,
const Eigen::Matrix< T_W, Eigen::Dynamic, Eigen::Dynamic > &  W,
const Eigen::Matrix< T_m0, Eigen::Dynamic, 1 > &  m0,
const Eigen::Matrix< T_C0, Eigen::Dynamic, Eigen::Dynamic > &  C0 
)

The log of a Gaussian dynamic linear model (GDLM).

This distribution is equivalent to, for $t = 1:T$,

\begin{eqnarray*} y_t & \sim N(F' \theta_t, V) \\ \theta_t & \sim N(G \theta_{t-1}, W) \\ \theta_0 & \sim N(m_0, C_0) \end{eqnarray*}

If V is a vector, then the Kalman filter is applied sequentially.

Parameters
yA r x T matrix of observations. Rows are variables, columns are observations.
FA n x r matrix. The design matrix.
GA n x n matrix. The transition matrix.
VA r x r matrix. The observation covariance matrix.
WA n x n matrix. The state covariance matrix.
m0A n x 1 matrix. The mean vector of the distribution of the initial state.
C0A n x n matrix. The covariance matrix of the distribution of the initial state.
Returns
The log of the joint density of the GDLM.
Exceptions
std::domain_errorif a matrix in the Kalman filter is not positive semi-definite.
Template Parameters
T_yType of scalar.
T_FType of design matrix.
T_GType of transition matrix.
T_VType of observation covariance matrix.
T_WType of state covariance matrix.
T_m0Type of initial state mean vector.
T_C0Type of initial state covariance matrix.

Definition at line 78 of file gaussian_dlm_obs_lpdf.hpp.

§ gaussian_dlm_obs_lpdf() [2/4]

template<typename T_y , typename T_F , typename T_G , typename T_V , typename T_W , typename T_m0 , typename T_C0 >
return_type< T_y, typename return_type<T_F, T_G, T_V, T_W, T_m0, T_C0>::type >::type stan::math::gaussian_dlm_obs_lpdf ( const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &  y,
const Eigen::Matrix< T_F, Eigen::Dynamic, Eigen::Dynamic > &  F,
const Eigen::Matrix< T_G, Eigen::Dynamic, Eigen::Dynamic > &  G,
const Eigen::Matrix< T_V, Eigen::Dynamic, Eigen::Dynamic > &  V,
const Eigen::Matrix< T_W, Eigen::Dynamic, Eigen::Dynamic > &  W,
const Eigen::Matrix< T_m0, Eigen::Dynamic, 1 > &  m0,
const Eigen::Matrix< T_C0, Eigen::Dynamic, Eigen::Dynamic > &  C0 
)
inline

Definition at line 202 of file gaussian_dlm_obs_lpdf.hpp.

§ gaussian_dlm_obs_lpdf() [3/4]

template<bool propto, typename T_y , typename T_F , typename T_G , typename T_V , typename T_W , typename T_m0 , typename T_C0 >
return_type< T_y, typename return_type<T_F, T_G, T_V, T_W, T_m0, T_C0>::type >::type stan::math::gaussian_dlm_obs_lpdf ( const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &  y,
const Eigen::Matrix< T_F, Eigen::Dynamic, Eigen::Dynamic > &  F,
const Eigen::Matrix< T_G, Eigen::Dynamic, Eigen::Dynamic > &  G,
const Eigen::Matrix< T_V, Eigen::Dynamic, 1 > &  V,
const Eigen::Matrix< T_W, Eigen::Dynamic, Eigen::Dynamic > &  W,
const Eigen::Matrix< T_m0, Eigen::Dynamic, 1 > &  m0,
const Eigen::Matrix< T_C0, Eigen::Dynamic, Eigen::Dynamic > &  C0 
)

The log of a Gaussian dynamic linear model (GDLM) with uncorrelated observation disturbances.

This distribution is equivalent to, for $t = 1:T$,

\begin{eqnarray*} y_t & \sim N(F' \theta_t, diag(V)) \\ \theta_t & \sim N(G \theta_{t-1}, W) \\ \theta_0 & \sim N(m_0, C_0) \end{eqnarray*}

If V is a vector, then the Kalman filter is applied sequentially.

Parameters
yA r x T matrix of observations. Rows are variables, columns are observations.
FA n x r matrix. The design matrix.
GA n x n matrix. The transition matrix.
VA size r vector. The diagonal of the observation covariance matrix.
WA n x n matrix. The state covariance matrix.
m0A n x 1 matrix. The mean vector of the distribution of the initial state.
C0A n x n matrix. The covariance matrix of the distribution of the initial state.
Returns
The log of the joint density of the GDLM.
Exceptions
std::domain_errorif a matrix in the Kalman filter is not semi-positive definite.
Template Parameters
T_yType of scalar.
T_FType of design matrix.
T_GType of transition matrix.
T_VType of observation variances
T_WType of state covariance matrix.
T_m0Type of initial state mean vector.
T_C0Type of initial state covariance matrix.

Definition at line 262 of file gaussian_dlm_obs_lpdf.hpp.

§ gaussian_dlm_obs_lpdf() [4/4]

template<typename T_y , typename T_F , typename T_G , typename T_V , typename T_W , typename T_m0 , typename T_C0 >
return_type<T_y, typename return_type<T_F, T_G, T_V, T_W, T_m0, T_C0>::type>::type stan::math::gaussian_dlm_obs_lpdf ( const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &  y,
const Eigen::Matrix< T_F, Eigen::Dynamic, Eigen::Dynamic > &  F,
const Eigen::Matrix< T_G, Eigen::Dynamic, Eigen::Dynamic > &  G,
const Eigen::Matrix< T_V, Eigen::Dynamic, 1 > &  V,
const Eigen::Matrix< T_W, Eigen::Dynamic, Eigen::Dynamic > &  W,
const Eigen::Matrix< T_m0, Eigen::Dynamic, 1 > &  m0,
const Eigen::Matrix< T_C0, Eigen::Dynamic, Eigen::Dynamic > &  C0 
)
inline

Definition at line 398 of file gaussian_dlm_obs_lpdf.hpp.

§ get_base1() [1/12]

template<typename T >
const T& stan::math::get_base1 ( const std::vector< T > &  x,
size_t  i,
const char *  error_msg,
size_t  idx 
)
inline

Return a reference to the value of the specified vector at the specified base-one index.

If the index is out of range, throw a std::out_of_range exception with the specified error message and index indicated.

Parameters
xVector from which to get a value.
iIndex into vector plus 1.
error_msgError message if the index is out of range.
idxNested index level to report in error message if the index is out of range.
Returns
Value of vector at i - 1
Template Parameters
Ttype of value.
Exceptions
std::out_of_rangeif idx is out of range.

Definition at line 28 of file get_base1.hpp.

§ get_base1() [2/12]

template<typename T >
const T& stan::math::get_base1 ( const std::vector< std::vector< T > > &  x,
size_t  i1,
size_t  i2,
const char *  error_msg,
size_t  idx 
)
inline

Return a reference to the value of the specified vector at the specified base-one indexes.

If an index is out of range, throw a std::out_of_range exception with the specified error message and index indicated.

Parameters
xVector from which to get a value.
i1First index plus 1.
i2Second index plus 1.
error_msgError message if an index is out of range.
idxNested index level to report in error message if the index is out of range.
Returns
Value of vector at indexes.
Template Parameters
Ttype of value.
Exceptions
std::out_of_rangeif idx is out of range.

Definition at line 54 of file get_base1.hpp.

§ get_base1() [3/12]

template<typename T >
const T& stan::math::get_base1 ( const std::vector< std::vector< std::vector< T > > > &  x,
size_t  i1,
size_t  i2,
size_t  i3,
const char *  error_msg,
size_t  idx 
)
inline

Return a reference to the value of the specified vector at the specified base-one indexes.

If an index is out of range, throw a std::out_of_range exception with the specified error message and index indicated.

Parameters
xVector from which to get a value.
i1First index plus 1.
i2Second index plus 1.
i3Third index plus 1.
error_msgError message if an index is out of range.
idxNested index level to report in error message if the index is out of range.
Returns
Value of vector at indexes.
Template Parameters
Ttype of value.
Exceptions
std::out_of_rangeif idx is out of range.

Definition at line 82 of file get_base1.hpp.

§ get_base1() [4/12]

template<typename T >
const T& stan::math::get_base1 ( const std::vector< std::vector< std::vector< std::vector< T > > > > &  x,
size_t  i1,
size_t  i2,
size_t  i3,
size_t  i4,
const char *  error_msg,
size_t  idx 
)
inline

Return a reference to the value of the specified vector at the specified base-one indexes.

If an index is out of range, throw a std::out_of_range exception with the specified error message and index indicated.

Parameters
xVector from which to get a value.
i1First index plus 1.
i2Second index plus 1.
i3Third index plus 1.
i4Fourth index plus 1.
error_msgError message if an index is out of range.
idxNested index level to report in error message if the index is out of range.
Returns
Value of vector at indexes.
Template Parameters
Ttype of value.
Exceptions
std::out_of_rangeif idx is out of range.

Definition at line 112 of file get_base1.hpp.

§ get_base1() [5/12]

template<typename T >
const T& stan::math::get_base1 ( const std::vector< std::vector< std::vector< std::vector< std::vector< T > > > > > &  x,
size_t  i1,
size_t  i2,
size_t  i3,
size_t  i4,
size_t  i5,
const char *  error_msg,
size_t  idx 
)
inline

Return a reference to the value of the specified vector at the specified base-one indexes.

If an index is out of range, throw a std::out_of_range exception with the specified error message and index indicated.

Parameters
xVector from which to get a value.
i1First index plus 1.
i2Second index plus 1.
i3Third index plus 1.
i4Fourth index plus 1.
i5Fifth index plus 1.
error_msgError message if an index is out of range.
idxNested index level to report in error message if the index is out of range.
Returns
Value of vector at indexes.
Template Parameters
Ttype of value.
Exceptions
std::out_of_rangeif idx is out of range.

Definition at line 144 of file get_base1.hpp.

§ get_base1() [6/12]

template<typename T >
const T& stan::math::get_base1 ( const std::vector< std::vector< std::vector< std::vector< std::vector< std::vector< T > > > > > > &  x,
size_t  i1,
size_t  i2,
size_t  i3,
size_t  i4,
size_t  i5,
size_t  i6,
const char *  error_msg,
size_t  idx 
)
inline

Return a reference to the value of the specified vector at the specified base-one indexes.

If an index is out of range, throw a std::out_of_range exception with the specified error message and index indicated.

Parameters
xVector from which to get a value.
i1First index plus 1.
i2Second index plus 1.
i3Third index plus 1.
i4Fourth index plus 1.
i5Fifth index plus 1.
i6Sixth index plus 1.
error_msgError message if an index is out of range.
idxNested index level to report in error message if the index is out of range.
Returns
Value of vector at indexes.
Template Parameters
Ttype of value.
Exceptions
std::out_of_rangeif idx is out of range.

Definition at line 179 of file get_base1.hpp.

§ get_base1() [7/12]

template<typename T >
const T& stan::math::get_base1 ( const std::vector< std::vector< std::vector< std::vector< std::vector< std::vector< std::vector< T > > > > > > > &  x,
size_t  i1,
size_t  i2,
size_t  i3,
size_t  i4,
size_t  i5,
size_t  i6,
size_t  i7,
const char *  error_msg,
size_t  idx 
)
inline

Return a reference to the value of the specified vector at the specified base-one indexes.

If an index is out of range, throw a std::out_of_range exception with the specified error message and index indicated.

Parameters
xVector from which to get a value.
i1First index plus 1.
i2Second index plus 1.
i3Third index plus 1.
i4Fourth index plus 1.
i5Fifth index plus 1.
i6Sixth index plus 1.
i7Seventh index plus 1.
error_msgError message if an index is out of range.
idxNested index level to report in error message if the index is out of range.
Returns
Value of vector at indexes.
Template Parameters
Ttype of value.
Exceptions
std::out_of_rangeif idx is out of range.

Definition at line 216 of file get_base1.hpp.

§ get_base1() [8/12]

template<typename T >
const T& stan::math::get_base1 ( const std::vector< std::vector< std::vector< std::vector< std::vector< std::vector< std::vector< std::vector< T > > > > > > > > &  x,
size_t  i1,
size_t  i2,
size_t  i3,
size_t  i4,
size_t  i5,
size_t  i6,
size_t  i7,
size_t  i8,
const char *  error_msg,
size_t  idx 
)
inline

Return a reference to the value of the specified vector at the specified base-one indexes.

If an index is out of range, throw a std::out_of_range exception with the specified error message and index indicated.

Parameters
xVector from which to get a value.
i1First index plus 1.
i2Second index plus 1.
i3Third index plus 1.
i4Fourth index plus 1.
i5Fifth index plus 1.
i6Sixth index plus 1.
i7Seventh index plus 1.
i8Eigth index plus 1.
error_msgError message if an index is out of range.
idxNested index level to report in error message if the index is out of range.
Returns
Value of vector at indexes.
Template Parameters
Ttype of value.
Exceptions
std::out_of_rangeif idx is out of range.

Definition at line 255 of file get_base1.hpp.

§ get_base1() [9/12]

template<typename T >
Eigen::Matrix<T, 1, Eigen::Dynamic> stan::math::get_base1 ( const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &  x,
size_t  m,
const char *  error_msg,
size_t  idx 
)
inline

Return a copy of the row of the specified vector at the specified base-one row index.

If the index is out of range, throw a std::out_of_range exception with the specified error message and index indicated.

Warning: Because a copy is involved, it is inefficient to access element of matrices by first using this method to get a row then using a second call to get the value at a specified column.

Parameters
xMatrix from which to get a row
mIndex into matrix plus 1.
error_msgError message if the index is out of range.
idxNested index level to report in error message if the index is out of range.
Returns
Row of matrix at i - 1.
Template Parameters
Ttype of value.
Exceptions
std::out_of_rangeif idx is out of range.

Definition at line 294 of file get_base1.hpp.

§ get_base1() [10/12]

template<typename T >
const T& stan::math::get_base1 ( const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &  x,
size_t  m,
size_t  n,
const char *  error_msg,
size_t  idx 
)
inline

Return a reference to the value of the specified matrix at the specified base-one row and column indexes.

If either index is out of range, throw a std::out_of_range exception with the specified error message and index indicated.

Parameters
xMatrix from which to get a row
mRow index plus 1.
nColumn index plus 1.
error_msgError message if either index is out of range.
idxNested index level to report in error message if either index is out of range.
Returns
Value of matrix at row m - 1 and column n - 1.
Template Parameters
Ttype of value.
Exceptions
std::out_of_rangeif idx is out of range.

Definition at line 321 of file get_base1.hpp.

§ get_base1() [11/12]

template<typename T >
const T& stan::math::get_base1 ( const Eigen::Matrix< T, Eigen::Dynamic, 1 > &  x,
size_t  m,
const char *  error_msg,
size_t  idx 
)
inline

Return a reference to the value of the specified column vector at the specified base-one index.

If the index is out of range, throw a std::out_of_range exception with the specified error message and index indicated.

Parameters
xColumn vector from which to get a value.
mRow index plus 1.
error_msgError message if the index is out of range.
idxNested index level to report in error message if the index is out of range.
Returns
Value of column vector at row m - 1.
Template Parameters
Ttype of value.
Exceptions
std::out_of_rangeif idx is out of range.

Definition at line 348 of file get_base1.hpp.

§ get_base1() [12/12]

template<typename T >
const T& stan::math::get_base1 ( const Eigen::Matrix< T, 1, Eigen::Dynamic > &  x,
size_t  n,
const char *  error_msg,
size_t  idx 
)
inline

Return a reference to the value of the specified row vector at the specified base-one index.

If the index is out of range, throw a std::out_of_range exception with the specified error message and index indicated.

Parameters
xRow vector from which to get a value.
nColumn index plus 1.
error_msgError message if the index is out of range.
idxNested index level to report in error message if the index is out of range.
Returns
Value of row vector at column n - 1.
Template Parameters
Ttype of value.
Exceptions
std::out_of_rangeif idx is out of range.

Definition at line 373 of file get_base1.hpp.

§ get_base1_lhs() [1/12]

template<typename T >
T& stan::math::get_base1_lhs ( std::vector< T > &  x,
size_t  i,
const char *  error_msg,
size_t  idx 
)
inline

Return a reference to the value of the specified vector at the specified base-one index.

If the index is out of range, throw a std::out_of_range exception with the specified error message and index indicated.

Parameters
xVector from which to get a value.
iIndex into vector plus 1.
error_msgError message if the index is out of range.
idxNested index level to report in error message if the index is out of range.
Returns
Value of vector at i - 1
Template Parameters
Ttype of value.
Exceptions
std::out_of_rangeif idx is out of range.

Definition at line 28 of file get_base1_lhs.hpp.

§ get_base1_lhs() [2/12]

template<typename T >
T& stan::math::get_base1_lhs ( std::vector< std::vector< T > > &  x,
size_t  i1,
size_t  i2,
const char *  error_msg,
size_t  idx 
)
inline

Return a reference to the value of the specified vector at the specified base-one indexes.

If an index is out of range, throw a std::out_of_range exception with the specified error message and index indicated.

Parameters
xVector from which to get a value.
i1First index plus 1.
i2Second index plus 1.
error_msgError message if an index is out of range.
idxNested index level to report in error message if the index is out of range.
Returns
Value of vector at indexes.
Template Parameters
Ttype of value.
Exceptions
std::out_of_rangeif idx is out of range.

Definition at line 54 of file get_base1_lhs.hpp.

§ get_base1_lhs() [3/12]

template<typename T >
T& stan::math::get_base1_lhs ( std::vector< std::vector< std::vector< T > > > &  x,
size_t  i1,
size_t  i2,
size_t  i3,
const char *  error_msg,
size_t  idx 
)
inline

Return a reference to the value of the specified vector at the specified base-one indexes.

If an index is out of range, throw a std::out_of_range exception with the specified error message and index indicated.

Parameters
xVector from which to get a value.
i1First index plus 1.
i2Second index plus 1.
i3Third index plus 1.
error_msgError message if an index is out of range.
idxNested index level to report in error message if the index is out of range.
Returns
Value of vector at indexes.
Template Parameters
Ttype of value.
Exceptions
std::out_of_rangeif idx is out of range.

Definition at line 82 of file get_base1_lhs.hpp.

§ get_base1_lhs() [4/12]

template<typename T >
T& stan::math::get_base1_lhs ( std::vector< std::vector< std::vector< std::vector< T > > > > &  x,
size_t  i1,
size_t  i2,
size_t  i3,
size_t  i4,
const char *  error_msg,
size_t  idx 
)
inline

Return a reference to the value of the specified vector at the specified base-one indexes.

If an index is out of range, throw a std::out_of_range exception with the specified error message and index indicated.

Parameters
xVector from which to get a value.
i1First index plus 1.
i2Second index plus 1.
i3Third index plus 1.
i4Fourth index plus 1.
error_msgError message if an index is out of range.
idxNested index level to report in error message if the index is out of range.
Returns
Value of vector at indexes.
Template Parameters
Ttype of value.
Exceptions
std::out_of_rangeif idx is out of range.

Definition at line 112 of file get_base1_lhs.hpp.

§ get_base1_lhs() [5/12]

template<typename T >
T& stan::math::get_base1_lhs ( std::vector< std::vector< std::vector< std::vector< std::vector< T > > > > > &  x,
size_t  i1,
size_t  i2,
size_t  i3,
size_t  i4,
size_t  i5,
const char *  error_msg,
size_t  idx 
)
inline

Return a reference to the value of the specified vector at the specified base-one indexes.

If an index is out of range, throw a std::out_of_range exception with the specified error message and index indicated.

Parameters
xVector from which to get a value.
i1First index plus 1.
i2Second index plus 1.
i3Third index plus 1.
i4Fourth index plus 1.
i5Fifth index plus 1.
error_msgError message if an index is out of range.
idxNested index level to report in error message if the index is out of range.
Returns
Value of vector at indexes.
Template Parameters
Ttype of value.
Exceptions
std::out_of_rangeif idx is out of range.

Definition at line 145 of file get_base1_lhs.hpp.

§ get_base1_lhs() [6/12]

template<typename T >
T& stan::math::get_base1_lhs ( std::vector< std::vector< std::vector< std::vector< std::vector< std::vector< T > > > > > > &  x,
size_t  i1,
size_t  i2,
size_t  i3,
size_t  i4,
size_t  i5,
size_t  i6,
const char *  error_msg,
size_t  idx 
)
inline

Return a reference to the value of the specified vector at the specified base-one indexes.

If an index is out of range, throw a std::out_of_range exception with the specified error message and index indicated.

Parameters
xVector from which to get a value.
i1First index plus 1.
i2Second index plus 1.
i3Third index plus 1.
i4Fourth index plus 1.
i5Fifth index plus 1.
i6Sixth index plus 1.
error_msgError message if an index is out of range.
idxNested index level to report in error message if the index is out of range.
Returns
Value of vector at indexes.
Template Parameters
Ttype of value.
Exceptions
std::out_of_rangeif idx is out of range.

Definition at line 180 of file get_base1_lhs.hpp.

§ get_base1_lhs() [7/12]

template<typename T >
T& stan::math::get_base1_lhs ( std::vector< std::vector< std::vector< std::vector< std::vector< std::vector< std::vector< T > > > > > > > &  x,
size_t  i1,
size_t  i2,
size_t  i3,
size_t  i4,
size_t  i5,
size_t  i6,
size_t  i7,
const char *  error_msg,
size_t  idx 
)
inline

Return a reference to the value of the specified vector at the specified base-one indexes.

If an index is out of range, throw a std::out_of_range exception with the specified error message and index indicated.

Parameters
xVector from which to get a value.
i1First index plus 1.
i2Second index plus 1.
i3Third index plus 1.
i4Fourth index plus 1.
i5Fifth index plus 1.
i6Sixth index plus 1.
i7Seventh index plus 1.
error_msgError message if an index is out of range.
idxNested index level to report in error message if the index is out of range.
Returns
Value of vector at indexes.
Template Parameters
Ttype of value.
Exceptions
std::out_of_rangeif idx is out of range.

Definition at line 217 of file get_base1_lhs.hpp.

§ get_base1_lhs() [8/12]

template<typename T >
T& stan::math::get_base1_lhs ( std::vector< std::vector< std::vector< std::vector< std::vector< std::vector< std::vector< std::vector< T > > > > > > > > &  x,
size_t  i1,
size_t  i2,
size_t  i3,
size_t  i4,
size_t  i5,
size_t  i6,
size_t  i7,
size_t  i8,
const char *  error_msg,
size_t  idx 
)
inline

Return a reference to the value of the specified vector at the specified base-one indexes.

If an index is out of range, throw a std::out_of_range exception with the specified error message and index indicated.

Parameters
xVector from which to get a value.
i1First index plus 1.
i2Second index plus 1.
i3Third index plus 1.
i4Fourth index plus 1.
i5Fifth index plus 1.
i6Sixth index plus 1.
i7Seventh index plus 1.
i8Eigth index plus 1.
error_msgError message if an index is out of range.
idxNested index level to report in error message if the index is out of range.
Returns
Value of vector at indexes.
Template Parameters
Ttype of value.
Exceptions
std::out_of_rangeif idx is out of range.

Definition at line 257 of file get_base1_lhs.hpp.

§ get_base1_lhs() [9/12]

template<typename T >
Eigen::Block<Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> > stan::math::get_base1_lhs ( Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &  x,
size_t  m,
const char *  error_msg,
size_t  idx 
)
inline

Return a copy of the row of the specified vector at the specified base-one row index.

If the index is out of range, throw a std::out_of_range exception with the specified error message and index indicated.

Warning: Because a copy is involved, it is inefficient to access element of matrices by first using this method to get a row then using a second call to get the value at a specified column.

Parameters
xMatrix from which to get a row
mIndex into matrix plus 1.
error_msgError message if the index is out of range.
idxNested index level to report in error message if the index is out of range.
Returns
Row of matrix at i - 1.
Template Parameters
Ttype of value.
Exceptions
std::out_of_rangeif idx is out of range.

Definition at line 298 of file get_base1_lhs.hpp.

§ get_base1_lhs() [10/12]

template<typename T >
T& stan::math::get_base1_lhs ( Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &  x,
size_t  m,
size_t  n,
const char *  error_msg,
size_t  idx 
)
inline

Return a reference to the value of the specified matrix at the specified base-one row and column indexes.

If either index is out of range, throw a std::out_of_range exception with the specified error message and index indicated.

Parameters
xMatrix from which to get a row
mRow index plus 1.
nColumn index plus 1.
error_msgError message if either index is out of range.
idxNested index level to report in error message if either index is out of range.
Returns
Value of matrix at row m - 1 and column n - 1.
Template Parameters
Ttype of value.
Exceptions
std::out_of_rangeif idx is out of range.

Definition at line 325 of file get_base1_lhs.hpp.

§ get_base1_lhs() [11/12]

template<typename T >
T& stan::math::get_base1_lhs ( Eigen::Matrix< T, Eigen::Dynamic, 1 > &  x,
size_t  m,
const char *  error_msg,
size_t  idx 
)
inline

Return a reference to the value of the specified column vector at the specified base-one index.

If the index is out of range, throw a std::out_of_range exception with the specified error message and index indicated.

Parameters
xColumn vector from which to get a value.
mRow index plus 1.
error_msgError message if the index is out of range.
idxNested index level to report in error message if the index is out of range.
Returns
Value of column vector at row m - 1.
Template Parameters
Ttype of value.
Exceptions
std::out_of_rangeif idx is out of range.

Definition at line 352 of file get_base1_lhs.hpp.

§ get_base1_lhs() [12/12]

template<typename T >
T& stan::math::get_base1_lhs ( Eigen::Matrix< T, 1, Eigen::Dynamic > &  x,
size_t  n,
const char *  error_msg,
size_t  idx 
)
inline

Return a reference to the value of the specified row vector at the specified base-one index.

If the index is out of range, throw a std::out_of_range exception with the specified error message and index indicated.

Parameters
xRow vector from which to get a value.
nColumn index plus 1.
error_msgError message if the index is out of range.
idxNested index level to report in error message if the index is out of range.
Returns
Value of row vector at column n - 1.
Template Parameters
Ttype of value.
Exceptions
std::out_of_rangeif idx is out of range.

Definition at line 377 of file get_base1_lhs.hpp.

§ get_lp()

template<typename T_lp , typename T_lp_accum >
boost::math::tools::promote_args<T_lp, T_lp_accum>::type stan::math::get_lp ( const T_lp &  lp,
const accumulator< T_lp_accum > &  lp_accum 
)
inline

Definition at line 13 of file get_lp.hpp.

§ grad() [1/3]

static void stan::math::grad ( vari vi)
static

§ grad() [2/3]

void stan::math::grad ( var v,
Eigen::Matrix< var, Eigen::Dynamic, 1 > &  x,
Eigen::VectorXd &  g 
)
inline

Propagate chain rule to calculate gradients starting from the specified variable.

Resizes the input vector to be the correct size.

The grad() function does not itself recover any memory. use recover_memory() or recover_memory_nested() to recover memory.

Parameters
[in]vValue of function being differentiated
[in]xVariables being differentiated with respect to
[out]gGradient, d/dx v, evaluated at x.

Definition at line 24 of file grad.hpp.

§ grad() [3/3]

static void stan::math::grad ( vari vi)
static

Compute the gradient for all variables starting from the specified root variable implementation.

Does not recover memory. This chainable variable's adjoint is initialized using the method init_dependent() and then the chain rule is applied working down the stack from this vari and calling each vari's chain() method in turn.

This function computes a nested gradient only going back as far as the last nesting.

This function does not recover any memory from the computation.

Parameters
viVariable implementation for root of partial derivative propagation.

Definition at line 30 of file grad.hpp.

§ grad_2F1()

template<typename T >
void stan::math::grad_2F1 ( T &  gradA,
T &  gradC,
a,
b,
c,
z,
precision = 1e-6 
)

Definition at line 12 of file grad_2F1.hpp.

§ grad_F32()

template<typename T >
void stan::math::grad_F32 ( T *  g,
a,
b,
c,
d,
e,
z,
precision = 1e-6 
)

Definition at line 10 of file grad_F32.hpp.

§ grad_hessian()

template<typename F >
void stan::math::grad_hessian ( const F &  f,
const Eigen::Matrix< double, Eigen::Dynamic, 1 > &  x,
double &  fx,
Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > &  H,
std::vector< Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > > &  grad_H 
)

Calculate the value, the Hessian, and the gradient of the Hessian of the specified function at the specified argument.

The functor must implement

fvar<fvar<var> > operator()(const Eigen::Matrix<fvar<fvar<var> >, Eigen::Dynamic, 1>&)

using only operations that are defined for fvar and var.

This latter constraint usually requires the functions to be defined in terms of the libraries defined in Stan or in terms of functions with appropriately general namespace imports that eventually depend on functions defined in Stan.

Template Parameters
FType of function
Parameters
[in]fFunction
[in]xArgument to function
[out]fxFunction applied to argument
[out]HHessian of function at argument
[out]grad_HGradient of the Hessian of function at argument

Definition at line 43 of file grad_hessian.hpp.

§ grad_inc_beta() [1/3]

void stan::math::grad_inc_beta ( double &  g1,
double &  g2,
double  a,
double  b,
double  z 
)
inline

Definition at line 17 of file grad_inc_beta.hpp.

§ grad_inc_beta() [2/3]

void stan::math::grad_inc_beta ( var g1,
var g2,
const var a,
const var b,
const var z 
)
inline

Gradient of the incomplete beta function beta(a, b, z) with respect to the first two arguments.

Uses the equivalence to a hypergeometric function. See http://dlmf.nist.gov/8.17#ii

Parameters
[out]g1d/da
[out]g2d/db
[in]aa
[in]bb
[in]zz

Definition at line 33 of file grad_inc_beta.hpp.

§ grad_inc_beta() [3/3]

template<typename T >
void stan::math::grad_inc_beta ( fvar< T > &  g1,
fvar< T > &  g2,
fvar< T >  a,
fvar< T >  b,
fvar< T >  z 
)

Gradient of the incomplete beta function beta(a, b, z) with respect to the first two arguments.

Uses the equivalence to a hypergeometric function. See http://dlmf.nist.gov/8.17#ii

Template Parameters
Ttype of fvar
Parameters
[out]g1d/da
[out]g2d/db
[in]aa
[in]bb
[in]zz

Definition at line 34 of file grad_inc_beta.hpp.

§ grad_reg_inc_beta()

template<typename T >
void stan::math::grad_reg_inc_beta ( T &  g1,
T &  g2,
const T &  a,
const T &  b,
const T &  z,
const T &  digammaA,
const T &  digammaB,
const T &  digammaSum,
const T &  betaAB 
)

Computes the gradients of the regularized incomplete beta function.

Specifically, this function computes gradients of ibeta(a, b, z), with respect to the arguments a and b.

Template Parameters
Ttype of arguments
Parameters
[out]g1partial derivative of ibeta(a, b, z) with respect to a
[out]g2partial derivative of ibeta(a, b, z) with respect to b
[in]aa
[in]bb
[in]zz
[in]digammaAthe value of digamma(a)
[in]digammaBthe value of digamma(b)
[in]digammaSumthe value of digamma(a + b)
[in]betaABthe value of beta(a, b)

Definition at line 32 of file grad_reg_inc_beta.hpp.

§ grad_reg_inc_gamma()

template<typename T >
T stan::math::grad_reg_inc_gamma ( a,
z,
g,
dig,
double  precision = 1e-6 
)

Gradient of the regularized incomplete gamma functions igamma(a, z)

For small z, the gradient is computed via the series expansion; for large z, the series is numerically inaccurate due to cancellation and the asymptotic expansion is used.

Parameters
ashape parameter, a > 0
zlocation z >= 0
gboost::math::tgamma(a) (precomputed value)
digboost::math::digamma(a) (precomputed value)
precisionrequired precision; applies to series expansion only

For the asymptotic expansion, the gradient is given by:

\[ \begin{array}{rcl} \Gamma(a, z) & = & z^{a-1}e^{-z} \sum_{k=0}^N \frac{(a-1)_k}{z^k} \qquad , z \gg a\\ Q(a, z) & = & \frac{z^{a-1}e^{-z}}{\Gamma(a)} \sum_{k=0}^N \frac{(a-1)_k}{z^k}\\ (a)_k & = & (a)_{k-1}(a-k)\\ \frac{d}{da} (a)_k & = & (a)_{k-1} + (a-k)\frac{d}{da} (a)_{k-1}\\ \frac{d}{da}Q(a, z) & = & (log(z) - \psi(a)) Q(a, z)\\ && + \frac{z^{a-1}e^{-z}}{\Gamma(a)} \sum_{k=0}^N \left(\frac{d}{da} (a-1)_k\right) \frac{1}{z^k} \end{array} \]

Definition at line 40 of file grad_reg_inc_gamma.hpp.

§ grad_tr_mat_times_hessian()

template<typename F >
void stan::math::grad_tr_mat_times_hessian ( const F &  f,
const Eigen::Matrix< double, Eigen::Dynamic, 1 > &  x,
const Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > &  M,
Eigen::Matrix< double, Eigen::Dynamic, 1 > &  grad_tr_MH 
)

Definition at line 16 of file grad_tr_mat_times_hessian.hpp.

§ gradient() [1/2]

template<typename T , typename F >
void stan::math::gradient ( const F &  f,
const Eigen::Matrix< T, Eigen::Dynamic, 1 > &  x,
T &  fx,
Eigen::Matrix< T, Eigen::Dynamic, 1 > &  grad_fx 
)

Calculate the value and the gradient of the specified function at the specified argument.

The functor must implement

fvar<T> operator()(const Eigen::Matrix<T, Eigen::Dynamic, 1>&)

using only operations that are defined for fvar. This latter constraint usually requires the functions to be defined in terms of the libraries defined in Stan or in terms of functions with appropriately general namespace imports that eventually depend on functions defined in Stan.

Time and memory usage is on the order of the size of the fully unfolded expression for the function applied to the argument, independently of dimension.

Template Parameters
FType of function
Parameters
[in]fFunction
[in]xArgument to function
[out]fxFunction applied to argument
[out]grad_fxGradient of function at argument

Definition at line 40 of file gradient.hpp.

§ gradient() [2/2]

template<typename F >
void stan::math::gradient ( const F &  f,
const Eigen::Matrix< double, Eigen::Dynamic, 1 > &  x,
double &  fx,
Eigen::Matrix< double, Eigen::Dynamic, 1 > &  grad_fx 
)

Calculate the value and the gradient of the specified function at the specified argument.

The functor must implement

var operator()(const Eigen::Matrix<var, Eigen::Dynamic, 1>&)

using only operations that are defined for var. This latter constraint usually requires the functions to be defined in terms of the libraries defined in Stan or in terms of functions with appropriately general namespace imports that eventually depend on functions defined in Stan.

Time and memory usage is on the order of the size of the fully unfolded expression for the function applied to the argument, independently of dimension.

Template Parameters
FType of function
Parameters
[in]fFunction
[in]xArgument to function
[out]fxFunction applied to argument
[out]grad_fxGradient of function at argument

Definition at line 42 of file gradient.hpp.

§ gradient_dot_vector()

template<typename T1 , typename T2 , typename F >
void stan::math::gradient_dot_vector ( const F &  f,
const Eigen::Matrix< T1, Eigen::Dynamic, 1 > &  x,
const Eigen::Matrix< T2, Eigen::Dynamic, 1 > &  v,
T1 &  fx,
T1 &  grad_fx_dot_v 
)

Definition at line 14 of file gradient_dot_vector.hpp.

§ gumbel_ccdf_log()

template<typename T_y , typename T_loc , typename T_scale >
return_type<T_y, T_loc, T_scale>::type stan::math::gumbel_ccdf_log ( const T_y &  y,
const T_loc &  mu,
const T_scale &  beta 
)

Definition at line 27 of file gumbel_ccdf_log.hpp.

§ gumbel_cdf()

template<typename T_y , typename T_loc , typename T_scale >
return_type<T_y, T_loc, T_scale>::type stan::math::gumbel_cdf ( const T_y &  y,
const T_loc &  mu,
const T_scale &  beta 
)

Definition at line 27 of file gumbel_cdf.hpp.

§ gumbel_cdf_log()

template<typename T_y , typename T_loc , typename T_scale >
return_type<T_y, T_loc, T_scale>::type stan::math::gumbel_cdf_log ( const T_y &  y,
const T_loc &  mu,
const T_scale &  beta 
)

Definition at line 27 of file gumbel_cdf_log.hpp.

§ gumbel_lccdf()

template<typename T_y , typename T_loc , typename T_scale >
return_type<T_y, T_loc, T_scale>::type stan::math::gumbel_lccdf ( const T_y &  y,
const T_loc &  mu,
const T_scale &  beta 
)

Definition at line 27 of file gumbel_lccdf.hpp.

§ gumbel_lcdf()

template<typename T_y , typename T_loc , typename T_scale >
return_type<T_y, T_loc, T_scale>::type stan::math::gumbel_lcdf ( const T_y &  y,
const T_loc &  mu,
const T_scale &  beta 
)

Definition at line 27 of file gumbel_lcdf.hpp.

§ gumbel_log() [1/2]

template<bool propto, typename T_y , typename T_loc , typename T_scale >
return_type<T_y, T_loc, T_scale>::type stan::math::gumbel_log ( const T_y &  y,
const T_loc &  mu,
const T_scale &  beta 
)

Definition at line 27 of file gumbel_log.hpp.

§ gumbel_log() [2/2]

template<typename T_y , typename T_loc , typename T_scale >
return_type<T_y, T_loc, T_scale>::type stan::math::gumbel_log ( const T_y &  y,
const T_loc &  mu,
const T_scale &  beta 
)
inline

Definition at line 100 of file gumbel_log.hpp.

§ gumbel_lpdf() [1/2]

template<bool propto, typename T_y , typename T_loc , typename T_scale >
return_type<T_y, T_loc, T_scale>::type stan::math::gumbel_lpdf ( const T_y &  y,
const T_loc &  mu,
const T_scale &  beta 
)

Definition at line 27 of file gumbel_lpdf.hpp.

§ gumbel_lpdf() [2/2]

template<typename T_y , typename T_loc , typename T_scale >
return_type<T_y, T_loc, T_scale>::type stan::math::gumbel_lpdf ( const T_y &  y,
const T_loc &  mu,
const T_scale &  beta 
)
inline

Definition at line 100 of file gumbel_lpdf.hpp.

§ gumbel_rng()

template<class RNG >
double stan::math::gumbel_rng ( double  mu,
double  beta,
RNG &  rng 
)
inline

Definition at line 23 of file gumbel_rng.hpp.

§ head() [1/3]

template<typename T >
Eigen::Matrix<T, Eigen::Dynamic, 1> stan::math::head ( const Eigen::Matrix< T, Eigen::Dynamic, 1 > &  v,
size_t  n 
)
inline

Return the specified number of elements as a vector from the front of the specified vector.

Template Parameters
TType of value in vector.
Parameters
vVector input.
nSize of return.
Returns
The first n elements of v.
Exceptions
std::out_of_rangeif n is out of range.

Definition at line 26 of file head.hpp.

§ head() [2/3]

template<typename T >
Eigen::Matrix<T, 1, Eigen::Dynamic> stan::math::head ( const Eigen::Matrix< T, 1, Eigen::Dynamic > &  rv,
size_t  n 
)
inline

Return the specified number of elements as a row vector from the front of the specified row vector.

Template Parameters
TType of value in vector.
Parameters
rvRow vector.
nSize of return row vector.
Returns
The first n elements of rv.
Exceptions
std::out_of_rangeif n is out of range.

Definition at line 46 of file head.hpp.

§ head() [3/3]

template<typename T >
std::vector<T> stan::math::head ( const std::vector< T > &  sv,
size_t  n 
)

Return the specified number of elements as a standard vector from the front of the specified standard vector.

Template Parameters
TType of value in vector.
Parameters
svStandard vector.
nSize of return.
Returns
The first n elements of sv.
Exceptions
std::out_of_rangeif n is out of range.

Definition at line 64 of file head.hpp.

§ hessian() [1/2]

template<typename F >
void stan::math::hessian ( const F &  f,
const Eigen::Matrix< double, Eigen::Dynamic, 1 > &  x,
double &  fx,
Eigen::Matrix< double, Eigen::Dynamic, 1 > &  grad,
Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > &  H 
)

Calculate the value, the gradient, and the Hessian, of the specified function at the specified argument in O(N^2) time and O(N^2) space.

The functor must implement

fvar<var> operator()(const Eigen::Matrix<fvar<var>, Eigen::Dynamic, 1>&)

using only operations that are defined for fvar and var.

This latter constraint usually requires the functions to be defined in terms of the libraries defined in Stan or in terms of functions with appropriately general namespace imports that eventually depend on functions defined in Stan.

Template Parameters
FType of function
Parameters
[in]fFunction
[in]xArgument to function
[out]fxFunction applied to argument
[out]gradgradient of function at argument
[out]HHessian of function at argument

Definition at line 44 of file hessian.hpp.

§ hessian() [2/2]

template<typename T , typename F >
void stan::math::hessian ( const F &  f,
const Eigen::Matrix< T, Eigen::Dynamic, 1 > &  x,
T &  fx,
Eigen::Matrix< T, Eigen::Dynamic, 1 > &  grad,
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &  H 
)

Definition at line 73 of file hessian.hpp.

§ hessian_times_vector() [1/2]

template<typename F >
void stan::math::hessian_times_vector ( const F &  f,
const Eigen::Matrix< double, Eigen::Dynamic, 1 > &  x,
const Eigen::Matrix< double, Eigen::Dynamic, 1 > &  v,
double &  fx,
Eigen::Matrix< double, Eigen::Dynamic, 1 > &  Hv 
)

Definition at line 15 of file hessian_times_vector.hpp.

§ hessian_times_vector() [2/2]

template<typename T , typename F >
void stan::math::hessian_times_vector ( const F &  f,
const Eigen::Matrix< T, Eigen::Dynamic, 1 > &  x,
const Eigen::Matrix< T, Eigen::Dynamic, 1 > &  v,
T &  fx,
Eigen::Matrix< T, Eigen::Dynamic, 1 > &  Hv 
)

Definition at line 42 of file hessian_times_vector.hpp.

§ hypergeometric_log() [1/2]

template<bool propto, typename T_n , typename T_N , typename T_a , typename T_b >
double stan::math::hypergeometric_log ( const T_n &  n,
const T_N &  N,
const T_a &  a,
const T_b &  b 
)

Definition at line 28 of file hypergeometric_log.hpp.

§ hypergeometric_log() [2/2]

template<typename T_n , typename T_N , typename T_a , typename T_b >
double stan::math::hypergeometric_log ( const T_n &  n,
const T_N &  N,
const T_a &  a,
const T_b &  b 
)
inline

Definition at line 75 of file hypergeometric_log.hpp.

§ hypergeometric_lpmf() [1/2]

template<bool propto, typename T_n , typename T_N , typename T_a , typename T_b >
double stan::math::hypergeometric_lpmf ( const T_n &  n,
const T_N &  N,
const T_a &  a,
const T_b &  b 
)

Definition at line 28 of file hypergeometric_lpmf.hpp.

§ hypergeometric_lpmf() [2/2]

template<typename T_n , typename T_N , typename T_a , typename T_b >
double stan::math::hypergeometric_lpmf ( const T_n &  n,
const T_N &  N,
const T_a &  a,
const T_b &  b 
)
inline

Definition at line 75 of file hypergeometric_lpmf.hpp.

§ hypergeometric_rng()

template<class RNG >
int stan::math::hypergeometric_rng ( int  N,
int  a,
int  b,
RNG &  rng 
)
inline

Definition at line 15 of file hypergeometric_rng.hpp.

§ hypot() [1/7]

template<typename T >
fvar<T> stan::math::hypot ( const fvar< T > &  x1,
const fvar< T > &  x2 
)
inline

Return the length of the hypoteneuse of a right triangle with opposite and adjacent side lengths given by the specified arguments (C++11).

In symbols, if the arguments are 1 and x2, the result is sqrt(x1 * x1 + x2 * x2).

Template Parameters
TScalar type of autodiff variables.
Parameters
x1First argument.
x2Second argument.
Returns
Length of hypoteneuse of right triangle with opposite and adjacent side lengths x1 and x2.

Definition at line 25 of file hypot.hpp.

§ hypot() [2/7]

template<typename T1 , typename T2 >
boost::math::tools::promote_args<T1, T2>::type stan::math::hypot ( const T1 &  x,
const T2 &  y 
)
inline

Return the length of the hypoteneuse of a right triangle with opposite and adjacent side lengths given by the specified arguments (C++11).

In symbols, if the arguments are x and y, the result is sqrt(x * x + y * y).

Parameters
xFirst argument.
ySecond argument.
Returns
Length of hypoteneuse of right triangle with opposite and adjacent side lengths x and y.

Definition at line 25 of file hypot.hpp.

§ hypot() [3/7]

template<typename T >
fvar<T> stan::math::hypot ( const fvar< T > &  x1,
double  x2 
)
inline

Return the length of the hypoteneuse of a right triangle with opposite and adjacent side lengths given by the specified arguments (C++11).

In symbols, if the arguments are 1 and x2, the result is sqrt(x1 * x1 + x2 * x2).

Template Parameters
TScalar type of autodiff variable.
Parameters
x1First argument.
x2Second argument.
Returns
Length of hypoteneuse of right triangle with opposite and adjacent side lengths x1 and x2.

Definition at line 45 of file hypot.hpp.

§ hypot() [4/7]

var stan::math::hypot ( const var a,
const var b 
)
inline

Returns the length of the hypoteneuse of a right triangle with sides of the specified lengths (C99).

The partial derivatives are given by

$\frac{\partial}{\partial x} \sqrt{x^2 + y^2} = \frac{x}{\sqrt{x^2 + y^2}}$, and

$\frac{\partial}{\partial y} \sqrt{x^2 + y^2} = \frac{y}{\sqrt{x^2 + y^2}}$.

Parameters
[in]aLength of first side.
[in]bLength of second side.
Returns
Length of hypoteneuse.

Definition at line 47 of file hypot.hpp.

§ hypot() [5/7]

var stan::math::hypot ( const var a,
double  b 
)
inline

Returns the length of the hypoteneuse of a right triangle with sides of the specified lengths (C99).

The derivative is

$\frac{d}{d x} \sqrt{x^2 + c^2} = \frac{x}{\sqrt{x^2 + c^2}}$.

Parameters
[in]aLength of first side.
[in]bLength of second side.
Returns
Length of hypoteneuse.

Definition at line 63 of file hypot.hpp.

§ hypot() [6/7]

template<typename T >
fvar<T> stan::math::hypot ( double  x1,
const fvar< T > &  x2 
)
inline

Return the length of the hypoteneuse of a right triangle with opposite and adjacent side lengths given by the specified arguments (C++11).

In symbols, if the arguments are 1 and x2, the result is sqrt(x1 * x1 + x2 * x2).

Template Parameters
TScalar type of autodiff variable.
Parameters
x1First argument.
x2Second argument.
Returns
Length of hypoteneuse of right triangle with opposite and adjacent side lengths x1 and x2.

Definition at line 65 of file hypot.hpp.

§ hypot() [7/7]

var stan::math::hypot ( double  a,
const var b 
)
inline

Returns the length of the hypoteneuse of a right triangle with sides of the specified lengths (C99).

The derivative is

$\frac{d}{d y} \sqrt{c^2 + y^2} = \frac{y}{\sqrt{c^2 + y^2}}$.

\[ \mbox{hypot}(x, y) = \begin{cases} \textrm{NaN} & \mbox{if } x < 0 \text{ or } y < 0 \\ \sqrt{x^2+y^2} & \mbox{if } x, y\geq 0 \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN or } y = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{hypot}(x, y)}{\partial x} = \begin{cases} \textrm{NaN} & \mbox{if } x < 0 \text{ or } y < 0 \\ \frac{x}{\sqrt{x^2+y^2}} & \mbox{if } x, y\geq 0 \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN or } y = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{hypot}(x, y)}{\partial y} = \begin{cases} \textrm{NaN} & \mbox{if } x < 0 \text{ or } y < 0 \\ \frac{y}{\sqrt{x^2+y^2}} & \mbox{if } x, y\geq 0 \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN or } y = \textrm{NaN} \end{cases} \]

Parameters
[in]aLength of first side.
[in]bLength of second side.
Returns
Length of hypoteneuse.

Definition at line 106 of file hypot.hpp.

§ ibeta() [1/2]

double stan::math::ibeta ( double  a,
double  b,
double  x 
)
inline

The normalized incomplete beta function of a, b, and x.

Used to compute the cumulative density function for the beta distribution.

Parameters
aShape parameter a <= 0; a and b can't both be 0
bShape parameter b <= 0
xRandom variate. 0 <= x <= 1
Exceptions
ifconstraints are violated or if any argument is NaN
Returns
The normalized incomplete beta function.

Definition at line 23 of file ibeta.hpp.

§ ibeta() [2/2]

var stan::math::ibeta ( const var a,
const var b,
const var x 
)
inline

The normalized incomplete beta function of a, b, and x.

Used to compute the cumulative density function for the beta distribution.

Partial derivatives are those specified by wolfram alpha. The values were checked using both finite differences and by independent code for calculating the derivatives found in JSS (paper by Boik and Robison-Cox).

Parameters
aShape parameter.
bShape parameter.
xRandom variate.
Returns
The normalized incomplete beta function.
Exceptions
ifany argument is NaN.

Definition at line 224 of file ibeta.hpp.

§ identity_constrain() [1/2]

template<typename T >
T stan::math::identity_constrain ( x)
inline

Returns the result of applying the identity constraint transform to the input.

This method is effectively a no-op and is mainly useful as a placeholder in auto-generated code.

Parameters
xFree scalar.
Returns
Transformed input.
Template Parameters
TType of scalar.

Definition at line 21 of file identity_constrain.hpp.

§ identity_constrain() [2/2]

template<typename T >
T stan::math::identity_constrain ( const T  x,
T &   
)
inline

Returns the result of applying the identity constraint transform to the input and increments the log probability reference with the log absolute Jacobian determinant.

This method is effectively a no-op and mainly useful as a placeholder in auto-generated code.

Parameters
xFree scalar. lp Reference to log probability.
Returns
Transformed input.
Template Parameters
TType of scalar.

Definition at line 40 of file identity_constrain.hpp.

§ identity_free()

template<typename T >
T stan::math::identity_free ( const T  y)
inline

Returns the result of applying the inverse of the identity constraint transform to the input.

This method is effectively a no-op and mainly useful as a placeholder in auto-generated code.

Parameters
yConstrained scalar.
Returns
The input.
Template Parameters
TType of scalar.

Definition at line 20 of file identity_free.hpp.

§ if_else() [1/4]

var stan::math::if_else ( bool  c,
const var y_true,
const var y_false 
)
inline

If the specified condition is true, return the first variable, otherwise return the second variable.

Parameters
cBoolean condition.
y_trueVariable to return if condition is true.
y_falseVariable to return if condition is false.

Definition at line 17 of file if_else.hpp.

§ if_else() [2/4]

template<typename T_true , typename T_false >
boost::math::tools::promote_args<T_true, T_false>::type stan::math::if_else ( const bool  c,
const T_true  y_true,
const T_false  y_false 
)
inline

Return the second argument if the first argument is true and otherwise return the second argument.

This is just a convenience method to provide a function with the same behavior as the built-in ternary operator. In general, this function behaves as if defined by

if_else(c, y1, y0) = c ? y1 : y0.

Parameters
cBoolean condition value.
y_trueValue to return if condition is true.
y_falseValue to return if condition is false.

Definition at line 25 of file if_else.hpp.

§ if_else() [3/4]

var stan::math::if_else ( bool  c,
double  y_true,
const var y_false 
)
inline

If the specified condition is true, return a new variable constructed from the first scalar, otherwise return the second variable.

Parameters
cBoolean condition.
y_trueValue to promote to variable and return if condition is true.
y_falseVariable to return if condition is false.

Definition at line 29 of file if_else.hpp.

§ if_else() [4/4]

var stan::math::if_else ( bool  c,
const var y_true,
double  y_false 
)
inline

If the specified condition is true, return the first variable, otherwise return a new variable constructed from the second scalar.

Parameters
cBoolean condition.
y_trueVariable to return if condition is true.
y_falseValue to promote to variable and return if condition is false.

Definition at line 44 of file if_else.hpp.

§ inc_beta() [1/3]

double stan::math::inc_beta ( double  a,
double  b,
double  x 
)
inline

Definition at line 9 of file inc_beta.hpp.

§ inc_beta() [2/3]

template<typename T >
fvar<T> stan::math::inc_beta ( const fvar< T > &  a,
const fvar< T > &  b,
const fvar< T > &  x 
)
inline

Definition at line 19 of file inc_beta.hpp.

§ inc_beta() [3/3]

var stan::math::inc_beta ( const var a,
const var b,
const var c 
)
inline

Definition at line 42 of file inc_beta.hpp.

§ inc_beta_dda()

template<typename T >
T stan::math::inc_beta_dda ( a,
b,
z,
digamma_a,
digamma_ab 
)

Returns the partial derivative of the regularized incomplete beta function, I_{z}(a, b) with respect to a.

The power series used to compute the deriative tends to converge slowly when a and b are large, especially if z approaches 1. The implementation will throw an exception if the series have not converged within 100,000 iterations. The current implementation has been tested for values of a and b up to 12500 and z = 0.999.

Template Parameters
Tscalar types of arguments
Parameters
aa
bb
zupper bound of the integral
digamma_avalue of digamma(a)
digamma_abvalue of digamma(b)
Returns
partial derivative of the incomplete beta with respect to a
Precondition
a >= 0
b >= 0
0 <= z <= 1

Definition at line 39 of file inc_beta_dda.hpp.

§ inc_beta_ddb()

template<typename T >
T stan::math::inc_beta_ddb ( a,
b,
z,
digamma_b,
digamma_ab 
)

Returns the partial derivative of the regularized incomplete beta function, I_{z}(a, b) with respect to b.

The power series used to compute the deriative tends to converge slowly when a and b are large, especailly if z approaches 1. The implementation will throw an exception if the series have not converged within 100,000 iterations. The current implementation has been tested for values of a and b up to 12500 and z = 0.999.

Template Parameters
Tscalar types of arguments
Parameters
aa
bb
zupper bound of the integral
digamma_bvalue of digamma(b)
digamma_abvalue of digamma(b)
Returns
partial derivative of the incomplete beta with respect to b
Precondition
a >= 0
b >= 0
0 <= z <= 1

Definition at line 39 of file inc_beta_ddb.hpp.

§ inc_beta_ddz() [1/2]

template<typename T >
T stan::math::inc_beta_ddz ( a,
b,
z 
)

Returns the partial derivative of the regularized incomplete beta function, I_{z}(a, b) with respect to z.

Template Parameters
Tscalar types of arguments
Parameters
aa
bb
zupper bound of the integral
Returns
partial derivative of the incomplete beta with respect to z
Precondition
a > 0
b > 0
0 < z <= 1

Definition at line 27 of file inc_beta_ddz.hpp.

§ inc_beta_ddz() [2/2]

template<>
double stan::math::inc_beta_ddz ( double  a,
double  b,
double  z 
)
inline

Definition at line 35 of file inc_beta_ddz.hpp.

§ initialize() [1/4]

template<typename T >
void stan::math::initialize ( T &  x,
const T &  v 
)
inline

Definition at line 16 of file initialize.hpp.

§ initialize() [2/4]

template<typename T , typename V >
boost::enable_if_c<boost::is_arithmetic<V>::value, void>::type stan::math::initialize ( T &  x,
v 
)
inline

Definition at line 22 of file initialize.hpp.

§ initialize() [3/4]

template<typename T , int R, int C, typename V >
void stan::math::initialize ( Eigen::Matrix< T, R, C > &  x,
const V &  v 
)
inline

Definition at line 26 of file initialize.hpp.

§ initialize() [4/4]

template<typename T , typename V >
void stan::math::initialize ( std::vector< T > &  x,
const V &  v 
)
inline

Definition at line 31 of file initialize.hpp.

§ initialize_variable() [1/3]

void stan::math::initialize_variable ( var variable,
const var value 
)
inline

Initialize variable to value.

(Function may look pointless, but its needed to bottom out recursion.)

Definition at line 15 of file initialize_variable.hpp.

§ initialize_variable() [2/3]

template<int R, int C>
void stan::math::initialize_variable ( Eigen::Matrix< var, R, C > &  matrix,
const var value 
)
inline

Initialize every cell in the matrix to the specified value.

Definition at line 24 of file initialize_variable.hpp.

§ initialize_variable() [3/3]

template<typename T >
void stan::math::initialize_variable ( std::vector< T > &  variables,
const var value 
)
inline

Initialize the variables in the standard vector recursively.

Definition at line 34 of file initialize_variable.hpp.

§ int_step()

template<typename T >
unsigned int stan::math::int_step ( const T  y)

The integer step, or Heaviside, function.

For double NaN input, int_step(NaN) returns 0.

\[ \mbox{int\_step}(x) = \begin{cases} 0 & \mbox{if } x \leq 0 \\ 1 & \mbox{if } x > 0 \\[6pt] 0 & \mbox{if } x = \textrm{NaN} \end{cases} \]

Parameters
yValue to test.
Returns
1 if value is greater than 0 and 0 otherwise
Template Parameters
TScalar argument type.

Definition at line 25 of file int_step.hpp.

§ integrate_ode_bdf()

template<typename F , typename T_initial , typename T_param >
std::vector<std::vector<typename stan::return_type<T_initial, T_param>::type> > stan::math::integrate_ode_bdf ( const F &  f,
const std::vector< T_initial > &  y0,
double  t0,
const std::vector< double > &  ts,
const std::vector< T_param > &  theta,
const std::vector< double > &  x,
const std::vector< int > &  x_int,
std::ostream *  msgs = 0,
double  relative_tolerance = 1e-10,
double  absolute_tolerance = 1e-10,
long int  max_num_steps = 1e8 
)

Return the solutions for the specified system of ordinary differential equations given the specified initial state, initial times, times of desired solution, and parameters and data, writing error and warning messages to the specified stream.

This function is templated to allow the initial times to be either data or autodiff variables and the parameters to be data or autodiff variables. The autodiff-based implementation for reverse-mode are defined in namespace stan::math and may be invoked via argument-dependent lookup by including their headers.

The solver used is based on the backward differentiation formula which is an implicit numerical integration scheme appropiate for stiff ODE systems.

Template Parameters
Ftype of ODE system function.
T_initialtype of scalars for initial values.
T_paramtype of scalars for parameters.
Parameters
[in]ffunctor for the base ordinary differential equation.
[in]y0initial state.
[in]t0initial time.
[in]tstimes of the desired solutions, in strictly increasing order, all greater than the initial time.
[in]thetaparameter vector for the ODE.
[in]xcontinuous data vector for the ODE.
[in]x_intinteger data vector for the ODE.
[in,out]msgsthe print stream for warning messages.
[in]relative_tolerancerelative tolerance passed to CVODE.
[in]absolute_toleranceabsolute tolerance passed to CVODE.
[in]max_num_stepsmaximal number of admissable steps between time-points
Returns
a vector of states, each state being a vector of the same size as the state variable, corresponding to a time in ts.

Definition at line 83 of file integrate_ode_bdf.hpp.

§ integrate_ode_rk45()

template<typename F , typename T1 , typename T2 >
std::vector<std::vector<typename stan::return_type<T1, T2>::type> > stan::math::integrate_ode_rk45 ( const F &  f,
const std::vector< T1 >  y0,
double  t0,
const std::vector< double > &  ts,
const std::vector< T2 > &  theta,
const std::vector< double > &  x,
const std::vector< int > &  x_int,
std::ostream *  msgs = 0,
double  relative_tolerance = 1e-6,
double  absolute_tolerance = 1e-6,
int  max_num_steps = 1E6 
)

Return the solutions for the specified system of ordinary differential equations given the specified initial state, initial times, times of desired solution, and parameters and data, writing error and warning messages to the specified stream.

Warning: If the system of equations is stiff, roughly defined by having varying time scales across dimensions, then this solver is likely to be slow.

This function is templated to allow the initial times to be either data or autodiff variables and the parameters to be data or autodiff variables. The autodiff-based implementation for reverse-mode are defined in namespace stan::math and may be invoked via argument-dependent lookup by including their headers.

This function uses the Dormand-Prince method as implemented in Boost's boost::numeric::odeint::runge_kutta_dopri5 integrator.

Template Parameters
Ftype of ODE system function.
T1type of scalars for initial values.
T2type of scalars for parameters.
Parameters
[in]ffunctor for the base ordinary differential equation.
[in]y0initial state.
[in]t0initial time.
[in]tstimes of the desired solutions, in strictly increasing order, all greater than the initial time.
[in]thetaparameter vector for the ODE.
[in]xcontinuous data vector for the ODE.
[in]x_intinteger data vector for the ODE.
[out]msgsthe print stream for warning messages.
[in]relative_tolerancerelative tolerance parameter for Boost's ode solver. Defaults to 1e-6.
[in]absolute_toleranceabsolute tolerance parameter for Boost's ode solver. Defaults to 1e-6.
[in]max_num_stepsmaximum number of steps to take within the Boost ode solver.
Returns
a vector of states, each state being a vector of the same size as the state variable, corresponding to a time in ts.

Definition at line 66 of file integrate_ode_rk45.hpp.

§ inv() [1/4]

double stan::math::inv ( double  x)
inline

Definition at line 7 of file inv.hpp.

§ inv() [2/4]

template<typename T >
fvar<T> stan::math::inv ( const fvar< T > &  x)
inline

Definition at line 14 of file inv.hpp.

§ inv() [3/4]

template<typename T >
apply_scalar_unary<inv_fun, T>::return_t stan::math::inv ( const T &  x)
inline

Vectorized version of inv().

Parameters
xContainer.
Template Parameters
TContainer type.
Returns
1 divided by each value in x.

Definition at line 31 of file inv.hpp.

§ inv() [4/4]

var stan::math::inv ( const var a)
inline

\[ \mbox{inv}(x) = \begin{cases} \frac{1}{x} & \mbox{if } -\infty\leq x \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{inv}(x)}{\partial x} = \begin{cases} -\frac{1}{x^2} & \mbox{if } -\infty\leq x\leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

Definition at line 42 of file inv.hpp.

§ inv_chi_square_ccdf_log()

template<typename T_y , typename T_dof >
return_type<T_y, T_dof>::type stan::math::inv_chi_square_ccdf_log ( const T_y &  y,
const T_dof &  nu 
)

Definition at line 32 of file inv_chi_square_ccdf_log.hpp.

§ inv_chi_square_cdf()

template<typename T_y , typename T_dof >
return_type<T_y, T_dof>::type stan::math::inv_chi_square_cdf ( const T_y &  y,
const T_dof &  nu 
)

Definition at line 32 of file inv_chi_square_cdf.hpp.

§ inv_chi_square_cdf_log()

template<typename T_y , typename T_dof >
return_type<T_y, T_dof>::type stan::math::inv_chi_square_cdf_log ( const T_y &  y,
const T_dof &  nu 
)

Definition at line 32 of file inv_chi_square_cdf_log.hpp.

§ inv_chi_square_lccdf()

template<typename T_y , typename T_dof >
return_type<T_y, T_dof>::type stan::math::inv_chi_square_lccdf ( const T_y &  y,
const T_dof &  nu 
)

Definition at line 32 of file inv_chi_square_lccdf.hpp.

§ inv_chi_square_lcdf()

template<typename T_y , typename T_dof >
return_type<T_y, T_dof>::type stan::math::inv_chi_square_lcdf ( const T_y &  y,
const T_dof &  nu 
)

Definition at line 32 of file inv_chi_square_lcdf.hpp.

§ inv_chi_square_log() [1/2]

template<bool propto, typename T_y , typename T_dof >
return_type<T_y, T_dof>::type stan::math::inv_chi_square_log ( const T_y &  y,
const T_dof &  nu 
)

The log of an inverse chi-squared density for y with the specified degrees of freedom parameter.

The degrees of freedom prarameter must be greater than 0. y must be greater than 0.

\begin{eqnarray*} y &\sim& \mbox{\sf{Inv-}}\chi^2_\nu \\ \log (p (y \, |\, \nu)) &=& \log \left( \frac{2^{-\nu / 2}}{\Gamma (\nu / 2)} y^{- (\nu / 2 + 1)} \exp^{-1 / (2y)} \right) \\ &=& - \frac{\nu}{2} \log(2) - \log (\Gamma (\nu / 2)) - (\frac{\nu}{2} + 1) \log(y) - \frac{1}{2y} \\ & & \mathrm{ where } \; y > 0 \end{eqnarray*}

Parameters
yA scalar variable.
nuDegrees of freedom.
Exceptions
std::domain_errorif nu is not greater than or equal to 0
std::domain_errorif y is not greater than or equal to 0.
Template Parameters
T_yType of scalar.
T_dofType of degrees of freedom.

Definition at line 51 of file inv_chi_square_log.hpp.

§ inv_chi_square_log() [2/2]

template<typename T_y , typename T_dof >
return_type<T_y, T_dof>::type stan::math::inv_chi_square_log ( const T_y &  y,
const T_dof &  nu 
)
inline

Definition at line 132 of file inv_chi_square_log.hpp.

§ inv_chi_square_lpdf() [1/2]

template<bool propto, typename T_y , typename T_dof >
return_type<T_y, T_dof>::type stan::math::inv_chi_square_lpdf ( const T_y &  y,
const T_dof &  nu 
)

The log of an inverse chi-squared density for y with the specified degrees of freedom parameter.

The degrees of freedom prarameter must be greater than 0. y must be greater than 0.

\begin{eqnarray*} y &\sim& \mbox{\sf{Inv-}}\chi^2_\nu \\ \log (p (y \, |\, \nu)) &=& \log \left( \frac{2^{-\nu / 2}}{\Gamma (\nu / 2)} y^{- (\nu / 2 + 1)} \exp^{-1 / (2y)} \right) \\ &=& - \frac{\nu}{2} \log(2) - \log (\Gamma (\nu / 2)) - (\frac{\nu}{2} + 1) \log(y) - \frac{1}{2y} \\ & & \mathrm{ where } \; y > 0 \end{eqnarray*}

Parameters
yA scalar variable.
nuDegrees of freedom.
Exceptions
std::domain_errorif nu is not greater than or equal to 0
std::domain_errorif y is not greater than or equal to 0.
Template Parameters
T_yType of scalar.
T_dofType of degrees of freedom.

Definition at line 51 of file inv_chi_square_lpdf.hpp.

§ inv_chi_square_lpdf() [2/2]

template<typename T_y , typename T_dof >
return_type<T_y, T_dof>::type stan::math::inv_chi_square_lpdf ( const T_y &  y,
const T_dof &  nu 
)
inline

Definition at line 132 of file inv_chi_square_lpdf.hpp.

§ inv_chi_square_rng()

template<class RNG >
double stan::math::inv_chi_square_rng ( double  nu,
RNG &  rng 
)
inline

Definition at line 27 of file inv_chi_square_rng.hpp.

§ inv_cloglog() [1/4]

template<typename T >
fvar<T> stan::math::inv_cloglog ( const fvar< T > &  x)
inline

Definition at line 14 of file inv_cloglog.hpp.

§ inv_cloglog() [2/4]

template<typename T >
apply_scalar_unary<inv_cloglog_fun, T>::return_t stan::math::inv_cloglog ( const T &  x)
inline

Vectorized version of inv_cloglog().

Parameters
xContainer.
Template Parameters
TContainer type.
Returns
1 - exp(-exp()) applied to each value in x.

Definition at line 31 of file inv_cloglog.hpp.

§ inv_cloglog() [3/4]

var stan::math::inv_cloglog ( const var a)
inline

Return the inverse complementary log-log function applied specified variable (stan).

See inv_cloglog() for the double-based version.

The derivative is given by

$\frac{d}{dx} \mbox{cloglog}^{-1}(x) = \exp (x - \exp (x))$.

Parameters
aVariable argument.
Returns
The inverse complementary log-log of the specified argument.

Definition at line 36 of file inv_cloglog.hpp.

§ inv_cloglog() [4/4]

double stan::math::inv_cloglog ( double  x)
inline

The inverse complementary log-log function.

The function is defined by

inv_cloglog(x) = 1 - exp(-exp(x)).

This function can be used to implement the inverse link function for complementary-log-log regression.

\[ \mbox{inv\_cloglog}(y) = \begin{cases} \mbox{cloglog}^{-1}(y) & \mbox{if } -\infty\leq y \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } y = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{inv\_cloglog}(y)}{\partial y} = \begin{cases} \frac{\partial\, \mbox{cloglog}^{-1}(y)}{\partial y} & \mbox{if } -\infty\leq y\leq \infty \\[6pt] \textrm{NaN} & \mbox{if } y = \textrm{NaN} \end{cases} \]

\[ \mbox{cloglog}^{-1}(y) = 1 - \exp \left( - \exp(y) \right) \]

\[ \frac{\partial \, \mbox{cloglog}^{-1}(y)}{\partial y} = \exp(y-\exp(y)) \]

Parameters
xArgument.
Returns
Inverse complementary log-log of the argument.

Definition at line 47 of file inv_cloglog.hpp.

§ inv_gamma_ccdf_log()

template<typename T_y , typename T_shape , typename T_scale >
return_type<T_y, T_shape, T_scale>::type stan::math::inv_gamma_ccdf_log ( const T_y &  y,
const T_shape &  alpha,
const T_scale &  beta 
)

Definition at line 34 of file inv_gamma_ccdf_log.hpp.

§ inv_gamma_cdf()

template<typename T_y , typename T_shape , typename T_scale >
return_type<T_y, T_shape, T_scale>::type stan::math::inv_gamma_cdf ( const T_y &  y,
const T_shape &  alpha,
const T_scale &  beta 
)

The CDF of an inverse gamma density for y with the specified shape and scale parameters.

y, shape, and scale parameters must be greater than 0.

Parameters
yA scalar variable.
alphaShape parameter.
betaScale parameter.
Exceptions
std::domain_errorif alpha is not greater than 0.
std::domain_errorif beta is not greater than 0.
std::domain_errorif y is not greater than 0.
Template Parameters
T_yType of scalar.
T_shapeType of shape.
T_scaleType of scale.

Definition at line 51 of file inv_gamma_cdf.hpp.

§ inv_gamma_cdf_log()

template<typename T_y , typename T_shape , typename T_scale >
return_type<T_y, T_shape, T_scale>::type stan::math::inv_gamma_cdf_log ( const T_y &  y,
const T_shape &  alpha,
const T_scale &  beta 
)

Definition at line 35 of file inv_gamma_cdf_log.hpp.

§ inv_gamma_lccdf()

template<typename T_y , typename T_shape , typename T_scale >
return_type<T_y, T_shape, T_scale>::type stan::math::inv_gamma_lccdf ( const T_y &  y,
const T_shape &  alpha,
const T_scale &  beta 
)

Definition at line 34 of file inv_gamma_lccdf.hpp.

§ inv_gamma_lcdf()

template<typename T_y , typename T_shape , typename T_scale >
return_type<T_y, T_shape, T_scale>::type stan::math::inv_gamma_lcdf ( const T_y &  y,
const T_shape &  alpha,
const T_scale &  beta 
)

Definition at line 35 of file inv_gamma_lcdf.hpp.

§ inv_gamma_log() [1/2]

template<bool propto, typename T_y , typename T_shape , typename T_scale >
return_type<T_y, T_shape, T_scale>::type stan::math::inv_gamma_log ( const T_y &  y,
const T_shape &  alpha,
const T_scale &  beta 
)

The log of an inverse gamma density for y with the specified shape and scale parameters.

Shape and scale parameters must be greater than 0. y must be greater than 0.

Parameters
yA scalar variable.
alphaShape parameter.
betaScale parameter.
Exceptions
std::domain_errorif alpha is not greater than 0.
std::domain_errorif beta is not greater than 0.
std::domain_errorif y is not greater than 0.
Template Parameters
T_yType of scalar.
T_shapeType of shape.
T_scaleType of scale.

Definition at line 50 of file inv_gamma_log.hpp.

§ inv_gamma_log() [2/2]

template<typename T_y , typename T_shape , typename T_scale >
return_type<T_y, T_shape, T_scale>::type stan::math::inv_gamma_log ( const T_y &  y,
const T_shape &  alpha,
const T_scale &  beta 
)
inline

Definition at line 150 of file inv_gamma_log.hpp.

§ inv_gamma_lpdf() [1/2]

template<bool propto, typename T_y , typename T_shape , typename T_scale >
return_type<T_y, T_shape, T_scale>::type stan::math::inv_gamma_lpdf ( const T_y &  y,
const T_shape &  alpha,
const T_scale &  beta 
)

The log of an inverse gamma density for y with the specified shape and scale parameters.

Shape and scale parameters must be greater than 0. y must be greater than 0.

Parameters
yA scalar variable.
alphaShape parameter.
betaScale parameter.
Exceptions
std::domain_errorif alpha is not greater than 0.
std::domain_errorif beta is not greater than 0.
std::domain_errorif y is not greater than 0.
Template Parameters
T_yType of scalar.
T_shapeType of shape.
T_scaleType of scale.

Definition at line 50 of file inv_gamma_lpdf.hpp.

§ inv_gamma_lpdf() [2/2]

template<typename T_y , typename T_shape , typename T_scale >
return_type<T_y, T_shape, T_scale>::type stan::math::inv_gamma_lpdf ( const T_y &  y,
const T_shape &  alpha,
const T_scale &  beta 
)
inline

Definition at line 150 of file inv_gamma_lpdf.hpp.

§ inv_gamma_rng()

template<class RNG >
double stan::math::inv_gamma_rng ( double  alpha,
double  beta,
RNG &  rng 
)
inline

Definition at line 29 of file inv_gamma_rng.hpp.

§ inv_logit() [1/4]

template<typename T >
fvar<T> stan::math::inv_logit ( const fvar< T > &  x)
inline

Returns the inverse logit function applied to the argument.

Template Parameters
Tscalar type of forward-mode autodiff variable argument.
Parameters
xargument
Returns
inverse logit of argument

Definition at line 20 of file inv_logit.hpp.

§ inv_logit() [2/4]

template<typename T >
apply_scalar_unary<inv_logit_fun, T>::return_t stan::math::inv_logit ( const T &  x)
inline

Vectorized version of inv_logit().

Parameters
xContainer.
Template Parameters
TContainer type.
Returns
Inverse logit applied to each value in x.

Definition at line 31 of file inv_logit.hpp.

§ inv_logit() [3/4]

var stan::math::inv_logit ( const var a)
inline

The inverse logit function for variables (stan).

See inv_logit() for the double-based version.

The derivative of inverse logit is

$\frac{d}{dx} \mbox{logit}^{-1}(x) = \mbox{logit}^{-1}(x) (1 - \mbox{logit}^{-1}(x))$.

Parameters
aArgument variable.
Returns
Inverse logit of argument.

Definition at line 34 of file inv_logit.hpp.

§ inv_logit() [4/4]

double stan::math::inv_logit ( double  a)
inline

Returns the inverse logit function applied to the argument.

The inverse logit function is defined by

$\mbox{logit}^{-1}(x) = \frac{1}{1 + \exp(-x)}$.

This function can be used to implement the inverse link function for logistic regression.

The inverse to this function is logit.

\[ \mbox{inv\_logit}(y) = \begin{cases} \mbox{logit}^{-1}(y) & \mbox{if } -\infty\leq y \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } y = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{inv\_logit}(y)}{\partial y} = \begin{cases} \frac{\partial\, \mbox{logit}^{-1}(y)}{\partial y} & \mbox{if } -\infty\leq y\leq \infty \\[6pt] \textrm{NaN} & \mbox{if } y = \textrm{NaN} \end{cases} \]

\[ \mbox{logit}^{-1}(y) = \frac{1}{1 + \exp(-y)} \]

\[ \frac{\partial \, \mbox{logit}^{-1}(y)}{\partial y} = \frac{\exp(y)}{(\exp(y)+1)^2} \]

Parameters
aArgument.
Returns
Inverse logit of argument.

Definition at line 49 of file inv_logit.hpp.

§ inv_Phi() [1/4]

template<typename T >
fvar<T> stan::math::inv_Phi ( const fvar< T > &  p)
inline

Definition at line 14 of file inv_Phi.hpp.

§ inv_Phi() [2/4]

double stan::math::inv_Phi ( double  p)
inline

The inverse of the unit normal cumulative distribution function.

The return value for a specified input probability, $p$, is the unit normal variate, $x$, such that

$\Phi(x) = \int_{-\infty}^x \mbox{\sf Norm}(x|0, 1) \ dx = p$

Algorithm first derived in 2003 by Peter Jon Aklam at http://home.online.no/~pjacklam/notes/invnorm/

Parameters
pArgument between 0 and 1.
Returns
Real number

Definition at line 26 of file inv_Phi.hpp.

§ inv_Phi() [3/4]

template<typename T >
apply_scalar_unary<inv_Phi_fun, T>::return_t stan::math::inv_Phi ( const T &  x)
inline

Vectorized version of inv_Phi().

Parameters
xContainer of variables in range [0, 1].
Template Parameters
TContainer type.
Returns
Inverse unit normal CDF of each value in x.
Exceptions
std::domain_errorif any value is not between 0 and 1.

Definition at line 33 of file inv_Phi.hpp.

§ inv_Phi() [4/4]

var stan::math::inv_Phi ( const var p)
inline

The inverse of unit normal cumulative density function.

See inv_Phi() for the double-based version.

The derivative is the reciprocal of unit normal density function,

Parameters
pProbability
Returns
The unit normal inverse cdf evaluated at p

Definition at line 37 of file inv_Phi.hpp.

§ inv_sqrt() [1/4]

double stan::math::inv_sqrt ( double  x)
inline

Definition at line 9 of file inv_sqrt.hpp.

§ inv_sqrt() [2/4]

template<typename T >
fvar<T> stan::math::inv_sqrt ( const fvar< T > &  x)
inline

Definition at line 14 of file inv_sqrt.hpp.

§ inv_sqrt() [3/4]

template<typename T >
apply_scalar_unary<inv_sqrt_fun, T>::return_t stan::math::inv_sqrt ( const T &  x)
inline

Vectorized version of inv_sqrt().

Parameters
xContainer.
Template Parameters
TContainer type.
Returns
1 / sqrt of each value in x.

Definition at line 31 of file inv_sqrt.hpp.

§ inv_sqrt() [4/4]

var stan::math::inv_sqrt ( const var a)
inline

\[ \mbox{inv\_sqrt}(x) = \begin{cases} \frac{1}{\sqrt{x}} & \mbox{if } -\infty\leq x \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{inv\_sqrt}(x)}{\partial x} = \begin{cases} -\frac{1}{2\sqrt{x^3}} & \mbox{if } -\infty\leq x\leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

Definition at line 42 of file inv_sqrt.hpp.

§ inv_square() [1/4]

double stan::math::inv_square ( double  x)
inline

Definition at line 7 of file inv_square.hpp.

§ inv_square() [2/4]

template<typename T >
fvar<T> stan::math::inv_square ( const fvar< T > &  x)
inline

Definition at line 14 of file inv_square.hpp.

§ inv_square() [3/4]

template<typename T >
apply_scalar_unary<inv_square_fun, T>::return_t stan::math::inv_square ( const T &  x)
inline

Vectorized version of inv_square().

Parameters
xContainer.
Template Parameters
TContainer type.
Returns
1 / the square of each value in x.

Definition at line 31 of file inv_square.hpp.

§ inv_square() [4/4]

var stan::math::inv_square ( const var a)
inline

\[ \mbox{inv\_square}(x) = \begin{cases} \frac{1}{x^2} & \mbox{if } -\infty\leq x \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{inv\_square}(x)}{\partial x} = \begin{cases} -\frac{2}{x^3} & \mbox{if } -\infty\leq x\leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

Definition at line 42 of file inv_square.hpp.

§ inv_wishart_log() [1/2]

template<bool propto, typename T_y , typename T_dof , typename T_scale >
boost::math::tools::promote_args<T_y, T_dof, T_scale>::type stan::math::inv_wishart_log ( const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &  W,
const T_dof &  nu,
const Eigen::Matrix< T_scale, Eigen::Dynamic, Eigen::Dynamic > &  S 
)

The log of the Inverse-Wishart density for the given W, degrees of freedom, and scale matrix.

The scale matrix, S, must be k x k, symmetric, and semi-positive definite.

\begin{eqnarray*} W &\sim& \mbox{\sf{Inv-Wishart}}_{\nu} (S) \\ \log (p (W \, |\, \nu, S) ) &=& \log \left( \left(2^{\nu k/2} \pi^{k (k-1) /4} \prod_{i=1}^k{\Gamma (\frac{\nu + 1 - i}{2})} \right)^{-1} \times \left| S \right|^{\nu/2} \left| W \right|^{-(\nu + k + 1) / 2} \times \exp (-\frac{1}{2} \mbox{tr} (S W^{-1})) \right) \\ &=& -\frac{\nu k}{2}\log(2) - \frac{k (k-1)}{4} \log(\pi) - \sum_{i=1}^{k}{\log (\Gamma (\frac{\nu+1-i}{2}))} +\frac{\nu}{2} \log(\det(S)) - \frac{\nu+k+1}{2}\log (\det(W)) - \frac{1}{2} \mbox{tr}(S W^{-1}) \end{eqnarray*}

Parameters
WA scalar matrix
nuDegrees of freedom
SThe scale matrix
Returns
The log of the Inverse-Wishart density at W given nu and S.
Exceptions
std::domain_errorif nu is not greater than k-1
std::domain_errorif S is not square, not symmetric, or not semi-positive definite.
Template Parameters
T_yType of scalar.
T_dofType of degrees of freedom.
T_scaleType of scale.

Definition at line 48 of file inv_wishart_log.hpp.

§ inv_wishart_log() [2/2]

template<typename T_y , typename T_dof , typename T_scale >
boost::math::tools::promote_args<T_y, T_dof, T_scale>::type stan::math::inv_wishart_log ( const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &  W,
const T_dof &  nu,
const Eigen::Matrix< T_scale, Eigen::Dynamic, Eigen::Dynamic > &  S 
)
inline

Definition at line 108 of file inv_wishart_log.hpp.

§ inv_wishart_lpdf() [1/2]

template<bool propto, typename T_y , typename T_dof , typename T_scale >
boost::math::tools::promote_args<T_y, T_dof, T_scale>::type stan::math::inv_wishart_lpdf ( const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &  W,
const T_dof &  nu,
const Eigen::Matrix< T_scale, Eigen::Dynamic, Eigen::Dynamic > &  S 
)

The log of the Inverse-Wishart density for the given W, degrees of freedom, and scale matrix.

The scale matrix, S, must be k x k, symmetric, and semi-positive definite.

\begin{eqnarray*} W &\sim& \mbox{\sf{Inv-Wishart}}_{\nu} (S) \\ \log (p (W \, |\, \nu, S) ) &=& \log \left( \left(2^{\nu k/2} \pi^{k (k-1) /4} \prod_{i=1}^k{\Gamma (\frac{\nu + 1 - i}{2})} \right)^{-1} \times \left| S \right|^{\nu/2} \left| W \right|^{-(\nu + k + 1) / 2} \times \exp (-\frac{1}{2} \mbox{tr} (S W^{-1})) \right) \\ &=& -\frac{\nu k}{2}\log(2) - \frac{k (k-1)}{4} \log(\pi) - \sum_{i=1}^{k}{\log (\Gamma (\frac{\nu+1-i}{2}))} +\frac{\nu}{2} \log(\det(S)) - \frac{\nu+k+1}{2}\log (\det(W)) - \frac{1}{2} \mbox{tr}(S W^{-1}) \end{eqnarray*}

Parameters
WA scalar matrix
nuDegrees of freedom
SThe scale matrix
Returns
The log of the Inverse-Wishart density at W given nu and S.
Exceptions
std::domain_errorif nu is not greater than k-1
std::domain_errorif S is not square, not symmetric, or not semi-positive definite.
Template Parameters
T_yType of scalar.
T_dofType of degrees of freedom.
T_scaleType of scale.

Definition at line 48 of file inv_wishart_lpdf.hpp.

§ inv_wishart_lpdf() [2/2]

template<typename T_y , typename T_dof , typename T_scale >
boost::math::tools::promote_args<T_y, T_dof, T_scale>::type stan::math::inv_wishart_lpdf ( const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &  W,
const T_dof &  nu,
const Eigen::Matrix< T_scale, Eigen::Dynamic, Eigen::Dynamic > &  S 
)
inline

Definition at line 109 of file inv_wishart_lpdf.hpp.

§ inv_wishart_rng()

template<class RNG >
Eigen::MatrixXd stan::math::inv_wishart_rng ( double  nu,
const Eigen::MatrixXd &  S,
RNG &  rng 
)
inline

Definition at line 15 of file inv_wishart_rng.hpp.

§ invalid_argument() [1/2]

template<typename T >
void stan::math::invalid_argument ( const char *  function,
const char *  name,
const T &  y,
const char *  msg1,
const char *  msg2 
)
inline

Throw an invalid_argument exception with a consistently formatted message.

This is an abstraction for all Stan functions to use when throwing invalid argument. This will allow us to change the behavior for all functions at once.

The message is: "<function>: <name> <msg1><y><msg2>"

Template Parameters
TType of variable
Parameters
functionName of the function
nameName of the variable
yVariable
msg1Message to print before the variable
msg2Message to print after the variable
Exceptions
std::invalid_argument

Definition at line 31 of file invalid_argument.hpp.

§ invalid_argument() [2/2]

template<typename T >
void stan::math::invalid_argument ( const char *  function,
const char *  name,
const T &  y,
const char *  msg1 
)
inline

Throw an invalid_argument exception with a consistently formatted message.

This is an abstraction for all Stan functions to use when throwing invalid argument. This will allow us to change the behavior for all functions at once. (We've already changed behavior mulitple times up to Stan v2.5.0.)

The message is: "<function>: <name> <msg1><y>"

Template Parameters
TType of variable
Parameters
functionName of the function
nameName of the variable
yVariable
msg1Message to print before the variable
Exceptions
std::invalid_argument

Definition at line 66 of file invalid_argument.hpp.

§ invalid_argument_vec() [1/2]

template<typename T >
void stan::math::invalid_argument_vec ( const char *  function,
const char *  name,
const T &  y,
size_t  i,
const char *  msg1,
const char *  msg2 
)
inline

Throw an invalid argument exception with a consistently formatted message.

This is an abstraction for all Stan functions to use when throwing invalid arguments. This will allow us to change the behavior for all functions at once. (We've already changed behavior mulitple times up to Stan v2.5.0.)

The message is: "<function>: <name>[<i+error_index>] <msg1><y>" where error_index is the value of stan::error_index::value which indicates whether the message should be 0 or 1 indexed.

Template Parameters
TType of variable
Parameters
functionName of the function
nameName of the variable
yVariable
iIndex
msg1Message to print before the variable
msg2Message to print after the variable
Exceptions
std::invalid_argument

Definition at line 37 of file invalid_argument_vec.hpp.

§ invalid_argument_vec() [2/2]

template<typename T >
void stan::math::invalid_argument_vec ( const char *  function,
const char *  name,
const T &  y,
size_t  i,
const char *  msg 
)
inline

Throw an invalid argument exception with a consistently formatted message.

This is an abstraction for all Stan functions to use when throwing invalid arguments. This will allow us to change the behavior for all functions at once. (We've already changed behavior mulitple times up to Stan v2.5.0.)

The message is: "<function>: <name>[<i+error_index>] <msg1><y>" where error_index is the value of stan::error_index::value which indicates whether the message should be 0 or 1 indexed.

Template Parameters
TType of variable
Parameters
functionName of the function
nameName of the variable
yVariable
iIndex
msgMessage to print before the variable
Exceptions
std::invalid_argument

Definition at line 73 of file invalid_argument_vec.hpp.

§ inverse() [1/2]

template<typename T , int R, int C>
Eigen::Matrix<T, R, C> stan::math::inverse ( const Eigen::Matrix< T, R, C > &  m)
inline

Returns the inverse of the specified matrix.

Parameters
mSpecified matrix.
Returns
Inverse of the matrix.

Definition at line 18 of file inverse.hpp.

§ inverse() [2/2]

template<typename T , int R, int C>
Eigen::Matrix<fvar<T>, R, C> stan::math::inverse ( const Eigen::Matrix< fvar< T >, R, C > &  m)
inline

Definition at line 20 of file inverse.hpp.

§ inverse_softmax()

template<typename Vector >
void stan::math::inverse_softmax ( const Vector &  simplex,
Vector &  y 
)

Writes the inverse softmax of the simplex argument into the second argument.

See softmax for the inverse function and a definition of the relation.

The inverse softmax function is defined by

$\mbox{inverse\_softmax}(x)[i] = \log x[i]$.

This function defines the inverse of softmax up to a scaling factor.

Because of the definition, values of 0.0 in the simplex are converted to negative infinity, and values of 1.0 are converted to 0.0.

There is no check that the input vector is a valid simplex vector.

Parameters
simplexSimplex vector input.
yVector into which the inverse softmax is written.
Exceptions
std::invalid_argumentif size of the input and output vectors differ.

Definition at line 34 of file inverse_softmax.hpp.

§ inverse_spd()

template<typename T >
Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> stan::math::inverse_spd ( const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &  m)
inline

Returns the inverse of the specified symmetric, pos/neg-definite matrix.

Parameters
mSpecified matrix.
Returns
Inverse of the matrix.

Definition at line 20 of file inverse_spd.hpp.

§ is_aligned()

template<typename T >
bool stan::math::is_aligned ( T *  ptr,
unsigned int  bytes_aligned 
)

Return true if the specified pointer is aligned on the number of bytes.

This doesn't really make sense other than for powers of 2.

Parameters
ptrPointer to test.
bytes_alignedNumber of bytes of alignment required.
Returns
true if pointer is aligned.
Template Parameters
Typeof object to which pointer points.

Definition at line 29 of file stack_alloc.hpp.

§ is_inf() [1/3]

int stan::math::is_inf ( double  x)
inline

Returns 1 if the input is infinite and 0 otherwise.

Delegates to boost::math::isinf.

Parameters
xValue to test.
Returns
1 if the value is infinite.

Definition at line 18 of file is_inf.hpp.

§ is_inf() [2/3]

int stan::math::is_inf ( const var v)
inline

Returns 1 if the input's value is infinite and 0 otherwise.

Delegates to is_inf.

Parameters
vValue to test.
Returns
1 if the value is infinite and 0 otherwise.

Definition at line 20 of file is_inf.hpp.

§ is_inf() [3/3]

template<typename T >
int stan::math::is_inf ( const fvar< T > &  x)
inline

Returns 1 if the input's value is infinite and 0 otherwise.

Delegates to is_inf.

Parameters
xValue to test.
Returns
1 if the value is infinite and 0 otherwise.

Definition at line 21 of file is_inf.hpp.

§ is_nan() [1/3]

bool stan::math::is_nan ( double  x)
inline

Returns 1 if the input is NaN and 0 otherwise.

Delegates to boost::math::isnan.

Parameters
xValue to test.
Returns
1 if the value is NaN.

Definition at line 17 of file is_nan.hpp.

§ is_nan() [2/3]

bool stan::math::is_nan ( const var v)
inline

Returns 1 if the input's value is NaN and 0 otherwise.

Delegates to is_nan(double).

Parameters
vValue to test.
Returns
1 if the value is NaN and 0 otherwise.

Definition at line 20 of file is_nan.hpp.

§ is_nan() [3/3]

template<typename T >
int stan::math::is_nan ( const fvar< T > &  x)
inline

Returns 1 if the input's value is NaN and 0 otherwise.

Delegates to is_nan.

Parameters
xValue to test.
Returns
1 if the value is NaN and 0 otherwise.

Definition at line 21 of file is_nan.hpp.

§ is_uninitialized() [1/2]

template<typename T >
bool stan::math::is_uninitialized ( x)
inline

Returns true if the specified variable is uninitialized.

Arithmetic types are always initialized by definition (the value is not specified).

Template Parameters
TType of object to test.
Parameters
xObject to test.
Returns
true if the specified object is uninitialized.
false if input is NaN.

Definition at line 18 of file is_uninitialized.hpp.

§ is_uninitialized() [2/2]

bool stan::math::is_uninitialized ( var  x)
inline

Returns true if the specified variable is uninitialized.

This overload of the is_uninitialized() function delegates the return to the is_uninitialized() method on the specified variable.

Parameters
xObject to test.
Returns
true if the specified object is uninitialized.

Definition at line 22 of file is_uninitialized.hpp.

§ jacobian() [1/2]

template<typename T , typename F >
void stan::math::jacobian ( const F &  f,
const Eigen::Matrix< T, Eigen::Dynamic, 1 > &  x,
Eigen::Matrix< T, Eigen::Dynamic, 1 > &  fx,
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &  J 
)

Definition at line 13 of file jacobian.hpp.

§ jacobian() [2/2]

template<typename F >
void stan::math::jacobian ( const F &  f,
const Eigen::Matrix< double, Eigen::Dynamic, 1 > &  x,
Eigen::Matrix< double, Eigen::Dynamic, 1 > &  fx,
Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > &  J 
)

Definition at line 14 of file jacobian.hpp.

§ lb_constrain() [1/2]

template<typename T , typename TL >
T stan::math::lb_constrain ( const T  x,
const TL  lb 
)
inline

Return the lower-bounded value for the specified unconstrained input and specified lower bound.

The transform applied is

$f(x) = \exp(x) + L$

where $L$ is the constant lower bound.

If the lower bound is negative infinity, this function reduces to identity_constrain(x).

Parameters
xUnconstrained scalar input.
lbLower-bound on constrained ouptut.
Returns
Lower-bound constrained value correspdonding to inputs.
Template Parameters
TType of scalar.
TLType of lower bound.

Definition at line 33 of file lb_constrain.hpp.

§ lb_constrain() [2/2]

template<typename T , typename TL >
boost::math::tools::promote_args<T, TL>::type stan::math::lb_constrain ( const T  x,
const TL  lb,
T &  lp 
)
inline

Return the lower-bounded value for the speicifed unconstrained input and specified lower bound, incrementing the specified reference with the log absolute Jacobian determinant of the transform.

If the lower bound is negative infinity, this function reduces to identity_constraint(x, lp).

Parameters
xUnconstrained scalar input.
lbLower-bound on output.
lpReference to log probability to increment.
Returns
Loer-bound constrained value corresponding to inputs.
Template Parameters
TType of scalar.
TLType of lower bound.

Definition at line 59 of file lb_constrain.hpp.

§ lb_free()

template<typename T , typename TL >
boost::math::tools::promote_args<T, TL>::type stan::math::lb_free ( const T  y,
const TL  lb 
)
inline

Return the unconstrained value that produces the specified lower-bound constrained value.

If the lower bound is negative infinity, it is ignored and the function reduces to identity_free(y).

Parameters
yInput scalar.
lbLower bound.
Returns
Unconstrained value that produces the input when constrained.
Template Parameters
TType of scalar.
TLType of lower bound.
Exceptions
std::domain_errorif y is lower than the lower bound.

Definition at line 31 of file lb_free.hpp.

§ lbeta() [1/4]

template<typename T >
fvar<T> stan::math::lbeta ( const fvar< T > &  x1,
const fvar< T > &  x2 
)
inline

Definition at line 15 of file lbeta.hpp.

§ lbeta() [2/4]

template<typename T >
fvar<T> stan::math::lbeta ( double  x1,
const fvar< T > &  x2 
)
inline

Definition at line 26 of file lbeta.hpp.

§ lbeta() [3/4]

template<typename T >
fvar<T> stan::math::lbeta ( const fvar< T > &  x1,
double  x2 
)
inline

Definition at line 35 of file lbeta.hpp.

§ lbeta() [4/4]

template<typename T1 , typename T2 >
boost::math::tools::promote_args<T1, T2>::type stan::math::lbeta ( const T1  a,
const T2  b 
)
inline

Return the log of the beta function applied to the specified arguments.

The beta function is defined for $a > 0$ and $b > 0$ by

$\mbox{B}(a, b) = \frac{\Gamma(a) \Gamma(b)}{\Gamma(a+b)}$.

This function returns its log,

$\log \mbox{B}(a, b) = \log \Gamma(a) + \log \Gamma(b) - \log \Gamma(a+b)$.

See boost::math::lgamma() for the double-based and stan::math for the variable-based log Gamma function.

\[ \mbox{lbeta}(\alpha, \beta) = \begin{cases} \ln\int_0^1 u^{\alpha - 1} (1 - u)^{\beta - 1} \, du & \mbox{if } \alpha, \beta>0 \\[6pt] \textrm{NaN} & \mbox{if } \alpha = \textrm{NaN or } \beta = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{lbeta}(\alpha, \beta)}{\partial \alpha} = \begin{cases} \Psi(\alpha)-\Psi(\alpha+\beta) & \mbox{if } \alpha, \beta>0 \\[6pt] \textrm{NaN} & \mbox{if } \alpha = \textrm{NaN or } \beta = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{lbeta}(\alpha, \beta)}{\partial \beta} = \begin{cases} \Psi(\beta)-\Psi(\alpha+\beta) & \mbox{if } \alpha, \beta>0 \\[6pt] \textrm{NaN} & \mbox{if } \alpha = \textrm{NaN or } \beta = \textrm{NaN} \end{cases} \]

Parameters
aFirst value
bSecond value
Returns
Log of the beta function applied to the two values.
Template Parameters
T1Type of first value.
T2Type of second value.

Definition at line 59 of file lbeta.hpp.

§ ldexp()

template<typename T >
T stan::math::ldexp ( const T &  a,
int  b 
)
inline

Returns the product of a (the significand) and 2 to power b (the exponent).

Template Parameters
TScalar type of significand
Parameters
[in]athe significand
[in]ban integer that is the exponent
Returns
product of a times 2 to the power b

Definition at line 19 of file ldexp.hpp.

§ lgamma() [1/5]

template<typename T >
fvar<T> stan::math::lgamma ( const fvar< T > &  x)
inline

Return the natural logarithm of the gamma function applied to the specified argument.

Template Parameters
TScalar type of autodiff variable.
Parameters
xArgument.
Returns
natural logarithm of the gamma function of argument.

Definition at line 20 of file lgamma.hpp.

§ lgamma() [2/5]

var stan::math::lgamma ( const var a)
inline

The log gamma function for variables (C99).

The derivatie is the digamma function,

$\frac{d}{dx} \Gamma(x) = \psi^{(0)}(x)$.

Parameters
aThe variable.
Returns
Log gamma of the variable.

Definition at line 34 of file lgamma.hpp.

§ lgamma() [3/5]

template<typename T >
apply_scalar_unary<lgamma_fun, T>::return_t stan::math::lgamma ( const T &  x)
inline

Vectorized version of lgamma().

Parameters
xContainer.
Template Parameters
TContainer type.
Returns
Natural log of the gamma function applied to each value in x.
Exceptions
std::domain_errorif any value is a negative integer or 0.

Definition at line 34 of file lgamma.hpp.

§ lgamma() [4/5]

double stan::math::lgamma ( double  x)
inline

Return the natural logarithm of the gamma function applied to the specified argument.

\[ \mbox{lgamma}(x) = \begin{cases} \textrm{error} & \mbox{if } x\in \{\dots, -3, -2, -1, 0\}\\ \ln\Gamma(x) & \mbox{if } x\not\in \{\dots, -3, -2, -1, 0\}\\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{lgamma}(x)}{\partial x} = \begin{cases} \textrm{error} & \mbox{if } x\in \{\dots, -3, -2, -1, 0\}\\ \Psi(x) & \mbox{if } x\not\in \{\dots, -3, -2, -1, 0\}\\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

Parameters
xargument
Returns
natural logarithm of the gamma function applied to argument

Definition at line 36 of file lgamma.hpp.

§ lgamma() [5/5]

double stan::math::lgamma ( int  x)
inline

Return the natural logarithm of the gamma function applied to the specified argument.

Parameters
xargument
Returns
natural logarithm of the gamma function applied to argument

Definition at line 48 of file lgamma.hpp.

§ lkj_corr_cholesky_log() [1/2]

template<bool propto, typename T_covar , typename T_shape >
boost::math::tools::promote_args<T_covar, T_shape>::type stan::math::lkj_corr_cholesky_log ( const Eigen::Matrix< T_covar, Eigen::Dynamic, Eigen::Dynamic > &  L,
const T_shape &  eta 
)

Definition at line 56 of file lkj_corr_cholesky_log.hpp.

§ lkj_corr_cholesky_log() [2/2]

template<typename T_covar , typename T_shape >
boost::math::tools::promote_args<T_covar, T_shape>::type stan::math::lkj_corr_cholesky_log ( const Eigen::Matrix< T_covar, Eigen::Dynamic, Eigen::Dynamic > &  L,
const T_shape &  eta 
)
inline

Definition at line 96 of file lkj_corr_cholesky_log.hpp.

§ lkj_corr_cholesky_lpdf() [1/2]

template<bool propto, typename T_covar , typename T_shape >
boost::math::tools::promote_args<T_covar, T_shape>::type stan::math::lkj_corr_cholesky_lpdf ( const Eigen::Matrix< T_covar, Eigen::Dynamic, Eigen::Dynamic > &  L,
const T_shape &  eta 
)

Definition at line 56 of file lkj_corr_cholesky_lpdf.hpp.

§ lkj_corr_cholesky_lpdf() [2/2]

template<typename T_covar , typename T_shape >
boost::math::tools::promote_args<T_covar, T_shape>::type stan::math::lkj_corr_cholesky_lpdf ( const Eigen::Matrix< T_covar, Eigen::Dynamic, Eigen::Dynamic > &  L,
const T_shape &  eta 
)
inline

Definition at line 96 of file lkj_corr_cholesky_lpdf.hpp.

§ lkj_corr_cholesky_rng()

template<class RNG >
Eigen::MatrixXd stan::math::lkj_corr_cholesky_rng ( size_t  K,
double  eta,
RNG &  rng 
)
inline

Definition at line 52 of file lkj_corr_cholesky_rng.hpp.

§ lkj_corr_log() [1/2]

template<bool propto, typename T_y , typename T_shape >
boost::math::tools::promote_args<T_y, T_shape>::type stan::math::lkj_corr_log ( const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &  y,
const T_shape &  eta 
)

Definition at line 58 of file lkj_corr_log.hpp.

§ lkj_corr_log() [2/2]

template<typename T_y , typename T_shape >
boost::math::tools::promote_args<T_y, T_shape>::type stan::math::lkj_corr_log ( const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &  y,
const T_shape &  eta 
)
inline

Definition at line 91 of file lkj_corr_log.hpp.

§ lkj_corr_lpdf() [1/2]

template<bool propto, typename T_y , typename T_shape >
boost::math::tools::promote_args<T_y, T_shape>::type stan::math::lkj_corr_lpdf ( const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &  y,
const T_shape &  eta 
)

Definition at line 83 of file lkj_corr_lpdf.hpp.

§ lkj_corr_lpdf() [2/2]

template<typename T_y , typename T_shape >
boost::math::tools::promote_args<T_y, T_shape>::type stan::math::lkj_corr_lpdf ( const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &  y,
const T_shape &  eta 
)
inline

Definition at line 116 of file lkj_corr_lpdf.hpp.

§ lkj_corr_rng()

template<class RNG >
Eigen::MatrixXd stan::math::lkj_corr_rng ( size_t  K,
double  eta,
RNG &  rng 
)
inline

Return a random correlation matrix (symmetric, positive definite, unit diagonal) of the specified dimensionality drawn from the LKJ distribution with the specified degrees of freedom using the specified random number generator.

Template Parameters
RNGRandom number generator type.
Parameters
[in]KNumber of rows and columns of generated matrix.
[in]etaDegrees of freedom for LKJ distribution.
[in,out]rngRandom-number generator to use.
Returns
Random variate with specified distribution.
Exceptions
std::domain_errorIf the shape parameter is not positive.

Definition at line 26 of file lkj_corr_rng.hpp.

§ lkj_cov_log() [1/4]

template<bool propto, typename T_y , typename T_loc , typename T_scale , typename T_shape >
boost::math::tools::promote_args<T_y, T_loc, T_scale, T_shape>::type stan::math::lkj_cov_log ( const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &  y,
const Eigen::Matrix< T_loc, Eigen::Dynamic, 1 > &  mu,
const Eigen::Matrix< T_scale, Eigen::Dynamic, 1 > &  sigma,
const T_shape &  eta 
)

Definition at line 22 of file lkj_cov_log.hpp.

§ lkj_cov_log() [2/4]

template<typename T_y , typename T_loc , typename T_scale , typename T_shape >
boost::math::tools::promote_args<T_y, T_loc, T_scale, T_shape>::type stan::math::lkj_cov_log ( const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &  y,
const Eigen::Matrix< T_loc, Eigen::Dynamic, 1 > &  mu,
const Eigen::Matrix< T_scale, Eigen::Dynamic, 1 > &  sigma,
const T_shape &  eta 
)
inline

Definition at line 67 of file lkj_cov_log.hpp.

§ lkj_cov_log() [3/4]

template<bool propto, typename T_y , typename T_loc , typename T_scale , typename T_shape >
boost::math::tools::promote_args<T_y, T_loc, T_scale, T_shape>::type stan::math::lkj_cov_log ( const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &  y,
const T_loc &  mu,
const T_scale &  sigma,
const T_shape &  eta 
)

Definition at line 80 of file lkj_cov_log.hpp.

§ lkj_cov_log() [4/4]

template<typename T_y , typename T_loc , typename T_scale , typename T_shape >
boost::math::tools::promote_args<T_y, T_loc, T_scale, T_shape>::type stan::math::lkj_cov_log ( const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &  y,
const T_loc &  mu,
const T_scale &  sigma,
const T_shape &  eta 
)
inline

Definition at line 115 of file lkj_cov_log.hpp.

§ lkj_cov_lpdf() [1/4]

template<bool propto, typename T_y , typename T_loc , typename T_scale , typename T_shape >
boost::math::tools::promote_args<T_y, T_loc, T_scale, T_shape>::type stan::math::lkj_cov_lpdf ( const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &  y,
const Eigen::Matrix< T_loc, Eigen::Dynamic, 1 > &  mu,
const Eigen::Matrix< T_scale, Eigen::Dynamic, 1 > &  sigma,
const T_shape &  eta 
)

Definition at line 22 of file lkj_cov_lpdf.hpp.

§ lkj_cov_lpdf() [2/4]

template<typename T_y , typename T_loc , typename T_scale , typename T_shape >
boost::math::tools::promote_args<T_y, T_loc, T_scale, T_shape>::type stan::math::lkj_cov_lpdf ( const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &  y,
const Eigen::Matrix< T_loc, Eigen::Dynamic, 1 > &  mu,
const Eigen::Matrix< T_scale, Eigen::Dynamic, 1 > &  sigma,
const T_shape &  eta 
)
inline

Definition at line 67 of file lkj_cov_lpdf.hpp.

§ lkj_cov_lpdf() [3/4]

template<bool propto, typename T_y , typename T_loc , typename T_scale , typename T_shape >
boost::math::tools::promote_args<T_y, T_loc, T_scale, T_shape>::type stan::math::lkj_cov_lpdf ( const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &  y,
const T_loc &  mu,
const T_scale &  sigma,
const T_shape &  eta 
)

Definition at line 80 of file lkj_cov_lpdf.hpp.

§ lkj_cov_lpdf() [4/4]

template<typename T_y , typename T_loc , typename T_scale , typename T_shape >
boost::math::tools::promote_args<T_y, T_loc, T_scale, T_shape>::type stan::math::lkj_cov_lpdf ( const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &  y,
const T_loc &  mu,
const T_scale &  sigma,
const T_shape &  eta 
)
inline

Definition at line 115 of file lkj_cov_lpdf.hpp.

§ lmgamma() [1/3]

template<typename T >
fvar<typename stan::return_type<T, int>::type> stan::math::lmgamma ( int  x1,
const fvar< T > &  x2 
)
inline

Definition at line 15 of file lmgamma.hpp.

§ lmgamma() [2/3]

var stan::math::lmgamma ( int  a,
const var b 
)
inline

Definition at line 28 of file lmgamma.hpp.

§ lmgamma() [3/3]

template<typename T >
boost::math::tools::promote_args<T>::type stan::math::lmgamma ( int  k,
x 
)
inline

Return the natural logarithm of the multivariate gamma function with the speciifed dimensions and argument.

The multivariate gamma function $\Gamma_k(x)$ for dimensionality $k$ and argument $x$ is defined by

$\Gamma_k(x) = \pi^{k(k-1)/4} \, \prod_{j=1}^k \Gamma(x + (1 - j)/2)$,

where $\Gamma()$ is the gamma function.

\[ \mbox{lmgamma}(n, x) = \begin{cases} \textrm{error} & \mbox{if } x\in \{\dots, -3, -2, -1, 0\}\\ \ln\Gamma_n(x) & \mbox{if } x\not\in \{\dots, -3, -2, -1, 0\}\\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{lmgamma}(n, x)}{\partial x} = \begin{cases} \textrm{error} & \mbox{if } x\in \{\dots, -3, -2, -1, 0\}\\ \frac{\partial\, \ln\Gamma_n(x)}{\partial x} & \mbox{if } x\not\in \{\dots, -3, -2, -1, 0\}\\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \ln\Gamma_n(x) = \pi^{n(n-1)/4} \, \prod_{j=1}^n \Gamma(x + (1 - j)/2) \]

\[ \frac{\partial \, \ln\Gamma_n(x)}{\partial x} = \sum_{j=1}^n \Psi(x + (1 - j) / 2) \]

Parameters
kNumber of dimensions.
xFunction argument.
Returns
Natural log of the multivariate gamma function.
Template Parameters
TType of scalar.

Definition at line 56 of file lmgamma.hpp.

§ log() [1/4]

template<typename T >
fvar<T> stan::math::log ( const fvar< T > &  x)
inline

Definition at line 14 of file log.hpp.

§ log() [2/4]

double stan::math::log ( int  x)
inline

Return the natural log of the specified argument.

This version is required to disambiguate log(int).

Parameters
[in]xArgument.
Returns
Natural log of argument.

Definition at line 16 of file log.hpp.

§ log() [3/4]

template<typename T >
apply_scalar_unary<log_fun, T>::return_t stan::math::log ( const T &  x)
inline

Return the elementwise natural log of the specified argument, which may be a scalar or any Stan container of numeric scalars.

The return type is the same as the argument type.

Template Parameters
TArgument type.
Parameters
[in]xArgument.
Returns
Elementwise application of natural log to the argument.

Definition at line 40 of file log.hpp.

§ log() [4/4]

var stan::math::log ( const var a)
inline

Return the natural log of the specified variable (cmath).

The derivative is defined by

$\frac{d}{dx} \log x = \frac{1}{x}$.

\[ \mbox{log}(x) = \begin{cases} \textrm{NaN} & \mbox{if } x < 0\\ \ln(x) & \mbox{if } x \geq 0 \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{log}(x)}{\partial x} = \begin{cases} \textrm{NaN} & \mbox{if } x < 0\\ \frac{1}{x} & \mbox{if } x\geq 0 \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

Parameters
aVariable whose log is taken.
Returns
Natural log of variable.

Definition at line 50 of file log.hpp.

§ log10() [1/4]

template<typename T >
fvar<T> stan::math::log10 ( const fvar< T > &  x)
inline

Definition at line 13 of file log10.hpp.

§ log10() [2/4]

template<typename T >
apply_scalar_unary<log10_fun, T>::return_t stan::math::log10 ( const T &  x)
inline

Vectorized version of log10().

Parameters
xContainer.
Template Parameters
TContainer type.
Returns
Log base-10 applied to each value in x.

Definition at line 32 of file log10.hpp.

§ log10() [3/4]

var stan::math::log10 ( const var a)
inline

Return the base 10 log of the specified variable (cmath).

The derivative is defined by

$\frac{d}{dx} \log_{10} x = \frac{1}{x \log 10}$.

\[ \mbox{log10}(x) = \begin{cases} \textrm{NaN} & \mbox{if } x < 0\\ \log_{10}(x) & \mbox{if } x \geq 0 \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{log10}(x)}{\partial x} = \begin{cases} \textrm{NaN} & \mbox{if } x < 0\\ \frac{1}{x \ln10} & \mbox{if } x\geq 0 \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

Parameters
aVariable whose log is taken.
Returns
Base 10 log of variable.

Definition at line 54 of file log10.hpp.

§ log10() [4/4]

double stan::math::log10 ( )
inline

Return natural logarithm of ten.

Returns
Natural logarithm of ten.

Definition at line 112 of file constants.hpp.

§ log1m() [1/4]

template<typename T >
fvar<T> stan::math::log1m ( const fvar< T > &  x)
inline

Definition at line 13 of file log1m.hpp.

§ log1m() [2/4]

template<typename T >
apply_scalar_unary<log1m_fun, T>::return_t stan::math::log1m ( const T &  x)
inline

Vectorized version of log1m().

Parameters
xContainer.
Template Parameters
TContainer type.
Returns
Natural log of 1 minus each value in x.

Definition at line 31 of file log1m.hpp.

§ log1m() [3/4]

var stan::math::log1m ( const var a)
inline

The log (1 - x) function for variables.

The derivative is given by

$\frac{d}{dx} \log (1 - x) = -\frac{1}{1 - x}$.

Parameters
aThe variable.
Returns
The variable representing log of 1 minus the variable.

Definition at line 32 of file log1m.hpp.

§ log1m() [4/4]

double stan::math::log1m ( double  x)
inline

Return the natural logarithm of one minus the specified value.

The main use of this function is to cut down on intermediate values during algorithmic differentiation.

\[ \mbox{log1m}(x) = \begin{cases} \ln(1-x) & \mbox{if } x \leq 1 \\ \textrm{NaN} & \mbox{if } x > 1\\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{log1m}(x)}{\partial x} = \begin{cases} -\frac{1}{1-x} & \mbox{if } x \leq 1 \\ \textrm{NaN} & \mbox{if } x > 1\\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

Parameters
[in]xArgument.
Returns
Natural log of one minus the argument.
Exceptions
std::domain_errorIf the argument is greater than 1.
std::overflow_errorIf the computation overflows.

Definition at line 39 of file log1m.hpp.

§ log1m_exp() [1/4]

template<typename T >
fvar<T> stan::math::log1m_exp ( const fvar< T > &  x)
inline

Return the natural logarithm of one minus the exponentiation of the specified argument.

Template Parameters
TScalar type of autodiff variable.
Parameters
xArgument.
Returns
log of one minus the exponentiation of the argument.

Definition at line 23 of file log1m_exp.hpp.

§ log1m_exp() [2/4]

template<typename T >
apply_scalar_unary<log1m_exp_fun, T>::return_t stan::math::log1m_exp ( const T &  x)
inline

Vectorized version of log1m_exp().

Parameters
xContainer.
Template Parameters
TContainer type.
Returns
Natural log of (1 - exp()) applied to each value in x.

Definition at line 31 of file log1m_exp.hpp.

§ log1m_exp() [3/4]

var stan::math::log1m_exp ( const var x)
inline

Return the log of 1 minus the exponential of the specified variable.

The deriative of log(1 - exp(x)) with respect to x is -1 / expm1(-x).

Parameters
[in]xArgument.
Returns
Natural logarithm of one minus the exponential of the argument.

Definition at line 34 of file log1m_exp.hpp.

§ log1m_exp() [4/4]

double stan::math::log1m_exp ( double  a)
inline

Calculates the natural logarithm of one minus the exponential of the specified value without overflow,.

log1m_exp(x) = log(1-exp(x))

This function is only defined for x < 0

\[ \mbox{log1m\_exp}(x) = \begin{cases} \ln(1-\exp(x)) & \mbox{if } x < 0 \\ \textrm{NaN} & \mbox{if } x \geq 0\\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{asinh}(x)}{\partial x} = \begin{cases} -\frac{\exp(x)}{1-\exp(x)} & \mbox{if } x < 0 \\ \textrm{NaN} & \mbox{if } x \geq 0\\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

Parameters
[in]aArgument.
Returns
natural logarithm of one minus the exponential of the argument.

Definition at line 44 of file log1m_exp.hpp.

§ log1m_inv_logit() [1/5]

var stan::math::log1m_inv_logit ( const var u)
inline

Return the natural logarithm of one minus the inverse logit of the specified argument.

Parameters
uargument
Returns
log of one minus the inverse logit of the argument

Definition at line 19 of file log1m_inv_logit.hpp.

§ log1m_inv_logit() [2/5]

template<typename T >
fvar<T> stan::math::log1m_inv_logit ( const fvar< T > &  x)
inline

Return the natural logarithm of one minus the inverse logit of the specified argument.

Template Parameters
Tscalar type of forward-mode autodiff variable argument.
Parameters
xargument
Returns
log of one minus the inverse logit of the argument

Definition at line 21 of file log1m_inv_logit.hpp.

§ log1m_inv_logit() [3/5]

double stan::math::log1m_inv_logit ( double  u)
inline

Returns the natural logarithm of 1 minus the inverse logit of the specified argument.

\[ \mbox{log1m\_inv\_logit}(x) = \begin{cases} -\ln(\exp(x)+1) & \mbox{if } -\infty\leq x \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{log1m\_inv\_logit}(x)}{\partial x} = \begin{cases} -\frac{\exp(x)}{\exp(x)+1} & \mbox{if } -\infty\leq x\leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

Parameters
uargument
Returns
log of one minus the inverse logit of the argument

Definition at line 34 of file log1m_inv_logit.hpp.

§ log1m_inv_logit() [4/5]

template<typename T >
apply_scalar_unary<log1m_inv_logit_fun, T>::return_t stan::math::log1m_inv_logit ( const T &  x)
inline

Return the elementwise application of log1m_inv_logit() to specified argument container.

The return type promotes the underlying scalar argument type to double if it is an integer, and otherwise is the argument type.

Template Parameters
TContainer type.
Parameters
xContainer.
Returns
Elementwise log1m_inv_logit of members of container.

Definition at line 40 of file log1m_inv_logit.hpp.

§ log1m_inv_logit() [5/5]

double stan::math::log1m_inv_logit ( int  u)
inline

Return the natural logarithm of one minus the inverse logit of the specified argument.

Parameters
uargument
Returns
log of one minus the inverse logit of the argument

Definition at line 48 of file log1m_inv_logit.hpp.

§ log1p() [1/5]

template<typename T >
fvar<T> stan::math::log1p ( const fvar< T > &  x)
inline

Definition at line 11 of file log1p.hpp.

§ log1p() [2/5]

double stan::math::log1p ( double  x)
inline

Return the natural logarithm of one plus the specified value.

\[ \mbox{log1p}(x) = \log(1 + x) \]

This version is more stable for arguments near zero than the direct definition. If log1p(x) is defined to be negative infinity.

Parameters
[in]xArgument.
Returns
Natural log of one plus the argument.
Exceptions
std::domain_errorIf argument is less than -1.

Definition at line 25 of file log1p.hpp.

§ log1p() [3/5]

var stan::math::log1p ( const var a)
inline

The log (1 + x) function for variables (C99).

The derivative is given by

$\frac{d}{dx} \log (1 + x) = \frac{1}{1 + x}$.

Parameters
aThe variable.
Returns
The log of 1 plus the variable.

Definition at line 32 of file log1p.hpp.

§ log1p() [4/5]

double stan::math::log1p ( int  x)
inline

Return the natural logarithm of one plus the specified argument.

This version is required to disambiguate log1p(int).

Parameters
[in]xArgument.
Returns
Natural logarithm of one plus the argument.
Exceptions
std::domain_errorIf argument is less than -1.

Definition at line 38 of file log1p.hpp.

§ log1p() [5/5]

template<typename T >
apply_scalar_unary<log1p_fun, T>::return_t stan::math::log1p ( const T &  x)
inline

Return the elementwise application of log1p() to specified argument container.

The return type promotes the underlying scalar argument type to double if it is an integer, and otherwise is the argument type.

Template Parameters
TContainer type.
Parameters
xContainer.
Returns
Elementwise log1p of members of container.

Definition at line 39 of file log1p.hpp.

§ log1p_exp() [1/4]

template<typename T >
fvar<T> stan::math::log1p_exp ( const fvar< T > &  x)
inline

Definition at line 13 of file log1p_exp.hpp.

§ log1p_exp() [2/4]

var stan::math::log1p_exp ( const var a)
inline

Return the log of 1 plus the exponential of the specified variable.

Definition at line 28 of file log1p_exp.hpp.

§ log1p_exp() [3/4]

template<typename T >
apply_scalar_unary<log1p_exp_fun, T>::return_t stan::math::log1p_exp ( const T &  x)
inline

Vectorized version of log1m_exp().

Parameters
xContainer.
Template Parameters
TContainer type.
Returns
Natural log of (1 + exp()) applied to each value in x.

Definition at line 31 of file log1p_exp.hpp.

§ log1p_exp() [4/4]

double stan::math::log1p_exp ( double  a)
inline

Calculates the log of 1 plus the exponential of the specified value without overflow.

This function is related to other special functions by:

log1p_exp(x)

= log1p(exp(a))

= log(1 + exp(x))

= log_sum_exp(0, x).

\[ \mbox{log1p\_exp}(x) = \begin{cases} \ln(1+\exp(x)) & \mbox{if } -\infty\leq x \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{log1p\_exp}(x)}{\partial x} = \begin{cases} \frac{\exp(x)}{1+\exp(x)} & \mbox{if } -\infty\leq x\leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

Definition at line 42 of file log1p_exp.hpp.

§ log2() [1/6]

template<typename T >
fvar<T> stan::math::log2 ( const fvar< T > &  x)
inline

Return the base two logarithm of the specified argument.

Template Parameters
Tscalar type
Parameters
xargument
Returns
base two logarithm of argument

Definition at line 19 of file log2.hpp.

§ log2() [2/6]

double stan::math::log2 ( double  u)
inline

Returns the base two logarithm of the argument (C99, C++11).

The function is defined by:

log2(a) = log(a) / std::log(2.0).

Parameters
[in]uargument
Returns
base two logarithm of argument

Definition at line 20 of file log2.hpp.

§ log2() [3/6]

double stan::math::log2 ( int  u)
inline

Return the base two logarithm of the specified argument.

This version is required to disambiguate log2(int).

Parameters
[in]uargument
Returns
base two logarithm of argument

Definition at line 32 of file log2.hpp.

§ log2() [4/6]

template<typename T >
apply_scalar_unary<log2_fun, T>::return_t stan::math::log2 ( const T &  x)
inline

Return the elementwise application of log2() to specified argument container.

The return type promotes the underlying scalar argument type to double if it is an integer, and otherwise is the argument type.

Template Parameters
Tcontainer type
Parameters
xcontainer
Returns
elementwise log2 of container elements

Definition at line 39 of file log2.hpp.

§ log2() [5/6]

double stan::math::log2 ( )
inline

Return natural logarithm of two.

Returns
Natural logarithm of two.

Definition at line 41 of file log2.hpp.

§ log2() [6/6]

var stan::math::log2 ( const var a)
inline

Returns the base 2 logarithm of the specified variable (C99).

See log2() for the double-based version.

The derivative is

$\frac{d}{dx} \log_2 x = \frac{1}{x \log 2}$.

\[ \mbox{log2}(x) = \begin{cases} \textrm{NaN} & \mbox{if } x < 0 \\ \log_2(x) & \mbox{if } x\geq 0 \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{log2}(x)}{\partial x} = \begin{cases} \textrm{NaN} & \mbox{if } x < 0 \\ \frac{1}{x\ln2} & \mbox{if } x\geq 0 \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

Parameters
aSpecified variable.
Returns
Base 2 logarithm of the variable.

Definition at line 53 of file log2.hpp.

§ log_determinant() [1/3]

template<int R, int C>
var stan::math::log_determinant ( const Eigen::Matrix< var, R, C > &  m)
inline

Definition at line 12 of file log_determinant.hpp.

§ log_determinant() [2/3]

template<typename T , int R, int C>
T stan::math::log_determinant ( const Eigen::Matrix< T, R, C > &  m)
inline

Returns the log absolute determinant of the specified square matrix.

Parameters
mSpecified matrix.
Returns
log absolute determinant of the matrix.
Exceptions
std::domain_errorif matrix is not square.

Definition at line 18 of file log_determinant.hpp.

§ log_determinant() [3/3]

template<typename T , int R, int C>
fvar<T> stan::math::log_determinant ( const Eigen::Matrix< fvar< T >, R, C > &  m)
inline

Definition at line 20 of file log_determinant.hpp.

§ log_determinant_ldlt() [1/2]

template<int R, int C, typename T >
T stan::math::log_determinant_ldlt ( LDLT_factor< T, R, C > &  A)
inline

Definition at line 12 of file log_determinant_ldlt.hpp.

§ log_determinant_ldlt() [2/2]

template<int R, int C>
var stan::math::log_determinant_ldlt ( LDLT_factor< var, R, C > &  A)

Definition at line 48 of file log_determinant_ldlt.hpp.

§ log_determinant_spd() [1/2]

template<int R, int C>
var stan::math::log_determinant_spd ( const Eigen::Matrix< var, R, C > &  m)
inline

Definition at line 14 of file log_determinant_spd.hpp.

§ log_determinant_spd() [2/2]

template<typename T , int R, int C>
T stan::math::log_determinant_spd ( const Eigen::Matrix< T, R, C > &  m)
inline

Returns the log absolute determinant of the specified square matrix.

Parameters
mSpecified matrix.
Returns
log absolute determinant of the matrix.
Exceptions
std::domain_errorif matrix is not square.

Definition at line 19 of file log_determinant_spd.hpp.

§ log_diff_exp() [1/7]

template<typename T >
fvar<T> stan::math::log_diff_exp ( const fvar< T > &  x1,
const fvar< T > &  x2 
)
inline

Definition at line 13 of file log_diff_exp.hpp.

§ log_diff_exp() [2/7]

template<typename T1 , typename T2 >
fvar<T2> stan::math::log_diff_exp ( const T1 &  x1,
const fvar< T2 > &  x2 
)
inline

Definition at line 23 of file log_diff_exp.hpp.

§ log_diff_exp() [3/7]

template<typename T1 , typename T2 >
fvar<T1> stan::math::log_diff_exp ( const fvar< T1 > &  x1,
const T2 &  x2 
)
inline

Definition at line 32 of file log_diff_exp.hpp.

§ log_diff_exp() [4/7]

var stan::math::log_diff_exp ( const var a,
const var b 
)
inline

Returns the log difference of the exponentiated arguments.

Parameters
[in]aFirst argument.
[in]bSecond argument.
Returns
Log difference of the expnoentiated arguments.

Definition at line 50 of file log_diff_exp.hpp.

§ log_diff_exp() [5/7]

template<typename T1 , typename T2 >
boost::math::tools::promote_args<T1, T2>::type stan::math::log_diff_exp ( const T1  x,
const T2  y 
)
inline

The natural logarithm of the difference of the natural exponentiation of x1 and the natural exponentiation of x2.

This function is only defined for x<0

\[ \mbox{log\_diff\_exp}(x, y) = \begin{cases} \textrm{NaN} & \mbox{if } x \leq y\\ \ln(\exp(x)-\exp(y)) & \mbox{if } x > y \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN or } y = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{log\_diff\_exp}(x, y)}{\partial x} = \begin{cases} \textrm{NaN} & \mbox{if } x \leq y\\ \frac{\exp(x)}{\exp(x)-\exp(y)} & \mbox{if } x > y \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN or } y = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{log\_diff\_exp}(x, y)}{\partial y} = \begin{cases} \textrm{NaN} & \mbox{if } x \leq y\\ -\frac{\exp(y)}{\exp(x)-\exp(y)} & \mbox{if } x > y \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN or } y = \textrm{NaN} \end{cases} \]

Definition at line 50 of file log_diff_exp.hpp.

§ log_diff_exp() [6/7]

var stan::math::log_diff_exp ( const var a,
double  b 
)
inline

Returns the log difference of the exponentiated arguments.

Parameters
[in]aFirst argument.
[in]bSecond argument.
Returns
Log difference of the expnoentiated arguments.

Definition at line 61 of file log_diff_exp.hpp.

§ log_diff_exp() [7/7]

var stan::math::log_diff_exp ( double  a,
const var b 
)
inline

Returns the log difference of the exponentiated arguments.

Parameters
[in]aFirst argument.
[in]bSecond argument.
Returns
Log difference of the expnoentiated arguments.

Definition at line 72 of file log_diff_exp.hpp.

§ log_falling_factorial() [1/7]

template<typename T >
fvar<T> stan::math::log_falling_factorial ( const fvar< T > &  x,
const fvar< T > &  n 
)
inline

Definition at line 14 of file log_falling_factorial.hpp.

§ log_falling_factorial() [2/7]

template<typename T >
fvar<T> stan::math::log_falling_factorial ( double  x,
const fvar< T > &  n 
)
inline

Definition at line 25 of file log_falling_factorial.hpp.

§ log_falling_factorial() [3/7]

template<typename T >
fvar<T> stan::math::log_falling_factorial ( const fvar< T > &  x,
double  n 
)
inline

Definition at line 34 of file log_falling_factorial.hpp.

§ log_falling_factorial() [4/7]

template<typename T1 , typename T2 >
boost::math::tools::promote_args<T1, T2>::type stan::math::log_falling_factorial ( const T1  x,
const T2  n 
)
inline

Return the natural log of the falling factorial of the specified arguments.

\[ \mbox{log\_falling\_factorial}(x, n) = \begin{cases} \textrm{error} & \mbox{if } x \leq 0\\ \ln (x)_n & \mbox{if } x > 0 \textrm{ and } -\infty \leq n \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN or } n = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{log\_falling\_factorial}(x, n)}{\partial x} = \begin{cases} \textrm{error} & \mbox{if } x \leq 0\\ \Psi(x) & \mbox{if } x > 0 \textrm{ and } -\infty \leq n \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN or } n = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{log\_falling\_factorial}(x, n)}{\partial n} = \begin{cases} \textrm{error} & \mbox{if } x \leq 0\\ -\Psi(n) & \mbox{if } x > 0 \textrm{ and } -\infty \leq n \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN or } n = \textrm{NaN} \end{cases} \]

Template Parameters
T1type of first argument
T2type of second argument
Parameters
[in]xFirst argument
[in]nSecond argument
Returns
log of falling factorial of arguments
Exceptions
std::domain_errorif the first argument is not positive

Definition at line 55 of file log_falling_factorial.hpp.

§ log_falling_factorial() [5/7]

var stan::math::log_falling_factorial ( const var a,
double  b 
)
inline

Definition at line 68 of file log_falling_factorial.hpp.

§ log_falling_factorial() [6/7]

var stan::math::log_falling_factorial ( const var a,
const var b 
)
inline

Definition at line 73 of file log_falling_factorial.hpp.

§ log_falling_factorial() [7/7]

var stan::math::log_falling_factorial ( double  a,
const var b 
)
inline

Definition at line 78 of file log_falling_factorial.hpp.

§ log_inv_logit() [1/5]

template<typename T >
fvar<T> stan::math::log_inv_logit ( const fvar< T > &  x)
inline

Definition at line 14 of file log_inv_logit.hpp.

§ log_inv_logit() [2/5]

var stan::math::log_inv_logit ( const var u)
inline

Return the natural logarithm of the inverse logit of the specified argument.

Parameters
uargument
Returns
log inverse logit of the argument

Definition at line 19 of file log_inv_logit.hpp.

§ log_inv_logit() [3/5]

double stan::math::log_inv_logit ( double  u)
inline

Returns the natural logarithm of the inverse logit of the specified argument.

\[ \mbox{log\_inv\_logit}(x) = \begin{cases} \ln\left(\frac{1}{1+\exp(-x)}\right)& \mbox{if } -\infty\leq x \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{log\_inv\_logit}(x)}{\partial x} = \begin{cases} \frac{1}{1+\exp(x)} & \mbox{if } -\infty\leq x\leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

Parameters
uargument
Returns
log of the inverse logit of argument

Definition at line 34 of file log_inv_logit.hpp.

§ log_inv_logit() [4/5]

template<typename T >
apply_scalar_unary<log_inv_logit_fun, T>::return_t stan::math::log_inv_logit ( const T &  x)
inline

Return the elementwise application of log_inv_logit() to specified argument container.

The return type promotes the underlying scalar argument type to double if it is an integer, and otherwise is the argument type.

Template Parameters
Tcontainer type
Parameters
xcontainer
Returns
elementwise log_inv_logit of members of container

Definition at line 40 of file log_inv_logit.hpp.

§ log_inv_logit() [5/5]

double stan::math::log_inv_logit ( int  u)
inline

Returns the natural logarithm of the inverse logit of the specified argument.

Parameters
uargument
Returns
log of the inverse logit of argument

Definition at line 48 of file log_inv_logit.hpp.

§ log_inv_logit_diff()

template<typename T >
T stan::math::log_inv_logit_diff ( const T &  alpha,
const T &  beta 
)
inline

Definition at line 25 of file ordered_logistic_lpmf.hpp.

§ log_mix() [1/9]

double stan::math::log_mix ( double  theta,
double  lambda1,
double  lambda2 
)
inline

Return the log mixture density with specified mixing proportion and log densities.

\[ \mbox{log\_mix}(\theta, \lambda_1, \lambda_2) = \log \left( \theta \lambda_1 + (1 - \theta) \lambda_2 \right). \]

\[ \frac{\partial}{\partial \theta} \mbox{log\_mix}(\theta, \lambda_1, \lambda_2) = FIXME \]

\[ \frac{\partial}{\partial \lambda_1} \mbox{log\_mix}(\theta, \lambda_1, \lambda_2) = FIXME \]

\[ \frac{\partial}{\partial \lambda_2} \mbox{log\_mix}(\theta, \lambda_1, \lambda_2) = FIXME \]

Parameters
[in]thetamixing proportion in [0, 1].
lambda1first log density.
lambda2second log density.
Returns
log mixture of densities in specified proportion

Definition at line 45 of file log_mix.hpp.

§ log_mix() [2/9]

template<typename T_theta , typename T_lambda1 , typename T_lambda2 >
return_type<T_theta, T_lambda1, T_lambda2>::type stan::math::log_mix ( const T_theta &  theta,
const T_lambda1 &  lambda1,
const T_lambda2 &  lambda2 
)
inline

Return the log mixture density with specified mixing proportion and log densities and its derivative at each.

\[ \mbox{log\_mix}(\theta, \lambda_1, \lambda_2) = \log \left( \theta \exp(\lambda_1) + (1 - \theta) \exp(\lambda_2) \right). \]

\[ \frac{\partial}{\partial \theta} \mbox{log\_mix}(\theta, \lambda_1, \lambda_2) = \dfrac{\exp(\lambda_1) - \exp(\lambda_2)} {\left( \theta \exp(\lambda_1) + (1 - \theta) \exp(\lambda_2) \right)} \]

\[ \frac{\partial}{\partial \lambda_1} \mbox{log\_mix}(\theta, \lambda_1, \lambda_2) = \dfrac{\theta \exp(\lambda_1)} {\left( \theta \exp(\lambda_1) + (1 - \theta) \exp(\lambda_2) \right)} \]

\[ \frac{\partial}{\partial \lambda_2} \mbox{log\_mix}(\theta, \lambda_1, \lambda_2) = \dfrac{\theta \exp(\lambda_2)} {\left( \theta \exp(\lambda_1) + (1 - \theta) \exp(\lambda_2) \right)} \]

Template Parameters
T_thetatheta scalar type.
T_lambda1lambda1 scalar type.
T_lambda2lambda2 scalar type.
Parameters
[in]thetamixing proportion in [0, 1].
[in]lambda1first log density.
[in]lambda2second log density.
Returns
log mixture of densities in specified proportion

Definition at line 87 of file log_mix.hpp.

§ log_mix() [3/9]

template<typename T >
fvar<T> stan::math::log_mix ( const fvar< T > &  theta,
const fvar< T > &  lambda1,
const fvar< T > &  lambda2 
)
inline

Return the log mixture density with specified mixing proportion and log densities and its derivative at each.

\[ \mbox{log\_mix}(\theta, \lambda_1, \lambda_2) = \log \left( \theta \exp(\lambda_1) + (1 - \theta) \exp(\lambda_2) \right). \]

\[ \frac{\partial}{\partial \theta} \mbox{log\_mix}(\theta, \lambda_1, \lambda_2) = \dfrac{\exp(\lambda_1) - \exp(\lambda_2)} {\left( \theta \exp(\lambda_1) + (1 - \theta) \exp(\lambda_2) \right)} \]

\[ \frac{\partial}{\partial \lambda_1} \mbox{log\_mix}(\theta, \lambda_1, \lambda_2) = \dfrac{\theta \exp(\lambda_1)} {\left( \theta \exp(\lambda_1) + (1 - \theta) \exp(\lambda_2) \right)} \]

\[ \frac{\partial}{\partial \lambda_2} \mbox{log\_mix}(\theta, \lambda_1, \lambda_2) = \dfrac{\theta \exp(\lambda_2)} {\left( \theta \exp(\lambda_1) + (1 - \theta) \exp(\lambda_2) \right)} \]

Template Parameters
Tscalar type.
Parameters
[in]thetamixing proportion in [0, 1].
[in]lambda1first log density.
[in]lambda2second log density.
Returns
log mixture of densities in specified proportion

Definition at line 116 of file log_mix.hpp.

§ log_mix() [4/9]

template<typename T >
fvar<T> stan::math::log_mix ( const fvar< T > &  theta,
const fvar< T > &  lambda1,
double  lambda2 
)
inline

Definition at line 139 of file log_mix.hpp.

§ log_mix() [5/9]

template<typename T >
fvar<T> stan::math::log_mix ( const fvar< T > &  theta,
double  lambda1,
const fvar< T > &  lambda2 
)
inline

Definition at line 161 of file log_mix.hpp.

§ log_mix() [6/9]

template<typename T >
fvar<T> stan::math::log_mix ( double  theta,
const fvar< T > &  lambda1,
const fvar< T > &  lambda2 
)
inline

Definition at line 183 of file log_mix.hpp.

§ log_mix() [7/9]

template<typename T >
fvar<T> stan::math::log_mix ( const fvar< T > &  theta,
double  lambda1,
double  lambda2 
)
inline

Definition at line 204 of file log_mix.hpp.

§ log_mix() [8/9]

template<typename T >
fvar<T> stan::math::log_mix ( double  theta,
const fvar< T > &  lambda1,
double  lambda2 
)
inline

Definition at line 222 of file log_mix.hpp.

§ log_mix() [9/9]

template<typename T >
fvar<T> stan::math::log_mix ( double  theta,
double  lambda1,
const fvar< T > &  lambda2 
)
inline

Definition at line 240 of file log_mix.hpp.

§ log_mix_partial_helper() [1/2]

void stan::math::log_mix_partial_helper ( double  theta_val,
double  lambda1_val,
double  lambda2_val,
double &  one_m_exp_lam2_m_lam1,
double &  one_m_t_prod_exp_lam2_m_lam1,
double &  one_d_t_plus_one_m_t_prod_exp_lam2_m_lam1 
)
inline

Definition at line 27 of file log_mix.hpp.

§ log_mix_partial_helper() [2/2]

template<typename T_theta , typename T_lambda1 , typename T_lambda2 , int N>
void stan::math::log_mix_partial_helper ( const T_theta &  theta,
const T_lambda1 &  lambda1,
const T_lambda2 &  lambda2,
typename boost::math::tools::promote_args< T_theta, T_lambda1, T_lambda2 >::type(&)  partials_array[N] 
)
inline

Definition at line 28 of file log_mix.hpp.

§ log_rising_factorial() [1/7]

template<typename T >
fvar<T> stan::math::log_rising_factorial ( const fvar< T > &  x,
const fvar< T > &  n 
)
inline

Definition at line 13 of file log_rising_factorial.hpp.

§ log_rising_factorial() [2/7]

template<typename T >
fvar<T> stan::math::log_rising_factorial ( const fvar< T > &  x,
double  n 
)
inline

Definition at line 20 of file log_rising_factorial.hpp.

§ log_rising_factorial() [3/7]

template<typename T >
fvar<T> stan::math::log_rising_factorial ( double  x,
const fvar< T > &  n 
)
inline

Definition at line 26 of file log_rising_factorial.hpp.

§ log_rising_factorial() [4/7]

var stan::math::log_rising_factorial ( const var a,
double  b 
)
inline

Definition at line 49 of file log_rising_factorial.hpp.

§ log_rising_factorial() [5/7]

template<typename T1 , typename T2 >
boost::math::tools::promote_args<T1, T2>::type stan::math::log_rising_factorial ( const T1 &  x,
const T2 &  n 
)
inline

Return the natural logarithm of the rising factorial from the first specified argument to the second.

\[ \mbox{log\_rising\_factorial}(x, n) = \begin{cases} \textrm{error} & \mbox{if } x \leq 0\\ \ln x^{(n)} & \mbox{if } x > 0 \textrm{ and } -\infty \leq n \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN or } n = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{log\_rising\_factorial}(x, n)}{\partial x} = \begin{cases} \textrm{error} & \mbox{if } x \leq 0\\ \Psi(x+n) - \Psi(x) & \mbox{if } x > 0 \textrm{ and } -\infty \leq n \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN or } n = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{log\_rising\_factorial}(x, n)}{\partial n} = \begin{cases} \textrm{error} & \mbox{if } x \leq 0\\ \Psi(x+n) & \mbox{if } x > 0 \textrm{ and } -\infty \leq n \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN or } n = \textrm{NaN} \end{cases} \]

Template Parameters
T1type of first argument x
T2type of second argument n
Parameters
[in]xfirst argument
[in]nsecond argument
Returns
natural logarithm of the rising factorial from x to n
Exceptions
std::domain_errorif the first argument is not positive

Definition at line 52 of file log_rising_factorial.hpp.

§ log_rising_factorial() [6/7]

var stan::math::log_rising_factorial ( const var a,
const var b 
)
inline

Definition at line 54 of file log_rising_factorial.hpp.

§ log_rising_factorial() [7/7]

var stan::math::log_rising_factorial ( double  a,
const var b 
)
inline

Definition at line 59 of file log_rising_factorial.hpp.

§ log_softmax() [1/3]

template<typename T >
Eigen::Matrix<fvar<T>, Eigen::Dynamic, 1> stan::math::log_softmax ( const Eigen::Matrix< fvar< T >, Eigen::Dynamic, 1 > &  alpha)
inline

Definition at line 16 of file log_softmax.hpp.

§ log_softmax() [2/3]

template<typename T >
Eigen::Matrix<T, Eigen::Dynamic, 1> stan::math::log_softmax ( const Eigen::Matrix< T, Eigen::Dynamic, 1 > &  v)
inline

Return the natural logarithm of the softmax of the specified vector.

$ \log \mbox{softmax}(y) \ = \ y - \log \sum_{k=1}^K \exp(y_k) \ = \ y - \mbox{log\_sum\_exp}(y). $

For the log softmax function, the entries in the Jacobian are $ \frac{\partial}{\partial y_m} \mbox{softmax}(y)[k] = \left\{ \begin{array}{ll} 1 - \mbox{softmax}(y)[m] & \mbox{ if } m = k, \mbox{ and} \\[6pt] \mbox{softmax}(y)[m] & \mbox{ if } m \neq k. \end{array} \right. $

Template Parameters
TScalar type of values in vector.
Parameters
[in]vVector to transform.
Returns
Unit simplex result of the softmax transform of the vector.

Definition at line 44 of file log_softmax.hpp.

§ log_softmax() [3/3]

Eigen::Matrix<var, Eigen::Dynamic, 1> stan::math::log_softmax ( const Eigen::Matrix< var, Eigen::Dynamic, 1 > &  alpha)
inline

Return the softmax of the specified Eigen vector.

Softmax is guaranteed to return a simplex.

The gradient calculations are unfolded.

Parameters
alphaUnconstrained input vector.
Returns
Softmax of the input.
Exceptions
std::domain_errorIf the input vector is size 0.

Definition at line 59 of file log_softmax.hpp.

§ log_sum_exp() [1/13]

template<typename T >
fvar<T> stan::math::log_sum_exp ( const std::vector< fvar< T > > &  v)

Definition at line 13 of file log_sum_exp.hpp.

§ log_sum_exp() [2/13]

template<typename T >
fvar<T> stan::math::log_sum_exp ( const fvar< T > &  x1,
const fvar< T > &  x2 
)
inline

Definition at line 14 of file log_sum_exp.hpp.

§ log_sum_exp() [3/13]

template<typename T , int R, int C>
fvar<T> stan::math::log_sum_exp ( const Eigen::Matrix< fvar< T >, R, C > &  v)

Definition at line 18 of file log_sum_exp.hpp.

§ log_sum_exp() [4/13]

double stan::math::log_sum_exp ( const std::vector< double > &  x)
inline

Return the log of the sum of the exponentiated values of the specified sequence of values.

The function is defined as follows to prevent overflow in exponential calculations.

$\log \sum_{n=1}^N \exp(x_n) = \max(x) + \log \sum_{n=1}^N \exp(x_n - \max(x))$.

Parameters
[in]xarray of specified values
Returns
The log of the sum of the exponentiated vector values.

Definition at line 24 of file log_sum_exp.hpp.

§ log_sum_exp() [5/13]

template<typename T >
fvar<T> stan::math::log_sum_exp ( double  x1,
const fvar< T > &  x2 
)
inline

Definition at line 24 of file log_sum_exp.hpp.

§ log_sum_exp() [6/13]

template<int R, int C>
double stan::math::log_sum_exp ( const Eigen::Matrix< double, R, C > &  x)

Return the log of the sum of the exponentiated values of the specified matrix of values.

The matrix may be a full matrix, a vector, or a row vector.

The function is defined as follows to prevent overflow in exponential calculations.

$\log \sum_{n=1}^N \exp(x_n) = \max(x) + \log \sum_{n=1}^N \exp(x_n - \max(x))$.

Parameters
[in]xMatrix of specified values
Returns
The log of the sum of the exponentiated vector values.

Definition at line 27 of file log_sum_exp.hpp.

§ log_sum_exp() [7/13]

template<typename T >
fvar<T> stan::math::log_sum_exp ( const fvar< T > &  x1,
double  x2 
)
inline

Definition at line 33 of file log_sum_exp.hpp.

§ log_sum_exp() [8/13]

var stan::math::log_sum_exp ( const std::vector< var > &  x)
inline

Returns the log sum of exponentials.

Definition at line 45 of file log_sum_exp.hpp.

§ log_sum_exp() [9/13]

template<typename T1 , typename T2 >
boost::math::tools::promote_args<T1, T2>::type stan::math::log_sum_exp ( const T2 &  a,
const T1 &  b 
)
inline

Calculates the log sum of exponetials without overflow.

$\log (\exp(a) + \exp(b)) = m + \log(\exp(a-m) + \exp(b-m))$,

where $m = max(a, b)$.

\[ \mbox{log\_sum\_exp}(x, y) = \begin{cases} \ln(\exp(x)+\exp(y)) & \mbox{if } -\infty\leq x, y \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN or } y = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{log\_sum\_exp}(x, y)}{\partial x} = \begin{cases} \frac{\exp(x)}{\exp(x)+\exp(y)} & \mbox{if } -\infty\leq x, y \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN or } y = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{log\_sum\_exp}(x, y)}{\partial y} = \begin{cases} \frac{\exp(y)}{\exp(x)+\exp(y)} & \mbox{if } -\infty\leq x, y \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN or } y = \textrm{NaN} \end{cases} \]

Parameters
athe first variable
bthe second variable

Definition at line 48 of file log_sum_exp.hpp.

§ log_sum_exp() [10/13]

var stan::math::log_sum_exp ( const var a,
const var b 
)
inline

Returns the log sum of exponentials.

Definition at line 50 of file log_sum_exp.hpp.

§ log_sum_exp() [11/13]

template<int R, int C>
var stan::math::log_sum_exp ( const Eigen::Matrix< var, R, C > &  x)
inline

Returns the log sum of exponentials.

Parameters
xmatrix

Definition at line 54 of file log_sum_exp.hpp.

§ log_sum_exp() [12/13]

var stan::math::log_sum_exp ( const var a,
double  b 
)
inline

Returns the log sum of exponentials.

Definition at line 57 of file log_sum_exp.hpp.

§ log_sum_exp() [13/13]

var stan::math::log_sum_exp ( double  a,
const var b 
)
inline

Returns the log sum of exponentials.

Definition at line 64 of file log_sum_exp.hpp.

§ logical_and()

template<typename T1 , typename T2 >
int stan::math::logical_and ( const T1  x1,
const T2  x2 
)
inline

The logical and function which returns 1 if both arguments are unequal to zero and 0 otherwise.

Equivalent to x1 != 0 && x2 != 0.

\[ \mbox{operator\&\&}(x, y) = \begin{cases} 0 & \mbox{if } x = 0 \textrm{ or } y=0 \\ 1 & \mbox{if } x, y \neq 0 \\[6pt] 1 & \mbox{if } x = \textrm{NaN or } y = \textrm{NaN} \end{cases} \]

Template Parameters
T1Type of first argument.
T2Type of second argument.
Parameters
x1First argument
x2Second argument
Returns
true if both x1 and x2 are not equal to 0.

Definition at line 30 of file logical_and.hpp.

§ logical_eq()

template<typename T1 , typename T2 >
int stan::math::logical_eq ( const T1  x1,
const T2  x2 
)
inline

Return 1 if the first argument is equal to the second.

Equivalent to x1 == x2.

Template Parameters
T1Type of first argument.
T2Type of second argument.
Parameters
x1First argument
x2Second argument
Returns
true iff x1 == x2

Definition at line 19 of file logical_eq.hpp.

§ logical_gt()

template<typename T1 , typename T2 >
int stan::math::logical_gt ( const T1  x1,
const T2  x2 
)
inline

Return 1 if the first argument is strictly greater than the second.

Equivalent to x1 < x2.

Template Parameters
T1Type of first argument.
T2Type of second argument.
Parameters
x1First argument
x2Second argument
Returns
true iff x1 > x2

Definition at line 19 of file logical_gt.hpp.

§ logical_gte()

template<typename T1 , typename T2 >
int stan::math::logical_gte ( const T1  x1,
const T2  x2 
)
inline

Return 1 if the first argument is greater than or equal to the second.

Equivalent to x1 >= x2.

Template Parameters
T1Type of first argument.
T2Type of second argument.
Parameters
x1First argument
x2Second argument
Returns
true iff x1 >= x2

Definition at line 19 of file logical_gte.hpp.

§ logical_lt()

template<typename T1 , typename T2 >
int stan::math::logical_lt ( T1  x1,
T2  x2 
)
inline

Return 1 if the first argument is strictly less than the second.

Equivalent to x1 < x2.

Template Parameters
T1Type of first argument.
T2Type of second argument.
Parameters
x1First argument
x2Second argument
Returns
true iff x1 < x2

Definition at line 20 of file logical_lt.hpp.

§ logical_lte()

template<typename T1 , typename T2 >
int stan::math::logical_lte ( const T1  x1,
const T2  x2 
)
inline

Return 1 if the first argument is less than or equal to the second.

Equivalent to x1 <= x2.

Template Parameters
T1Type of first argument.
T2Type of second argument.
Parameters
x1First argument
x2Second argument
Returns
true iff x1 <= x2

Definition at line 19 of file logical_lte.hpp.

§ logical_negation()

template<typename T >
int stan::math::logical_negation ( const T  x)
inline

The logical negation function which returns 1 if the input is equal to zero and 0 otherwise.

Template Parameters
TType to compare to zero.
Parameters
xValue to compare to zero.
Returns
1 if input is equal to zero.

Definition at line 17 of file logical_negation.hpp.

§ logical_neq()

template<typename T1 , typename T2 >
int stan::math::logical_neq ( const T1  x1,
const T2  x2 
)
inline

Return 1 if the first argument is unequal to the second.

Equivalent to x1 != x2.

Template Parameters
T1Type of first argument.
T2Type of second argument.
Parameters
x1First argument
x2Second argument
Returns
true iff x1 != x2

Definition at line 19 of file logical_neq.hpp.

§ logical_or()

template<typename T1 , typename T2 >
int stan::math::logical_or ( T1  x1,
T2  x2 
)
inline

The logical or function which returns 1 if either argument is unequal to zero and 0 otherwise.

Equivalent to x1 != 0 || x2 != 0.

\[ \mbox{operator||}(x, y) = \begin{cases} 0 & \mbox{if } x, y=0 \\ 1 & \mbox{if } x \neq 0 \textrm{ or } y\neq0\\[6pt] 1 & \mbox{if } x = \textrm{NaN or } y = \textrm{NaN} \end{cases} \]

Template Parameters
T1Type of first argument.
T2Type of second argument.
Parameters
x1First argument
x2Second argument
Returns
true if either x1 or x2 is not equal to 0.

Definition at line 29 of file logical_or.hpp.

§ logistic_ccdf_log()

template<typename T_y , typename T_loc , typename T_scale >
return_type<T_y, T_loc, T_scale>::type stan::math::logistic_ccdf_log ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma 
)

Definition at line 31 of file logistic_ccdf_log.hpp.

§ logistic_cdf()

template<typename T_y , typename T_loc , typename T_scale >
return_type<T_y, T_loc, T_scale>::type stan::math::logistic_cdf ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma 
)

Definition at line 31 of file logistic_cdf.hpp.

§ logistic_cdf_log()

template<typename T_y , typename T_loc , typename T_scale >
return_type<T_y, T_loc, T_scale>::type stan::math::logistic_cdf_log ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma 
)

Definition at line 30 of file logistic_cdf_log.hpp.

§ logistic_lccdf()

template<typename T_y , typename T_loc , typename T_scale >
return_type<T_y, T_loc, T_scale>::type stan::math::logistic_lccdf ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma 
)

Definition at line 31 of file logistic_lccdf.hpp.

§ logistic_lcdf()

template<typename T_y , typename T_loc , typename T_scale >
return_type<T_y, T_loc, T_scale>::type stan::math::logistic_lcdf ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma 
)

Definition at line 30 of file logistic_lcdf.hpp.

§ logistic_log() [1/2]

template<bool propto, typename T_y , typename T_loc , typename T_scale >
return_type<T_y, T_loc, T_scale>::type stan::math::logistic_log ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma 
)

Definition at line 31 of file logistic_log.hpp.

§ logistic_log() [2/2]

template<typename T_y , typename T_loc , typename T_scale >
return_type<T_y, T_loc, T_scale>::type stan::math::logistic_log ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma 
)
inline

Definition at line 129 of file logistic_log.hpp.

§ logistic_lpdf() [1/2]

template<bool propto, typename T_y , typename T_loc , typename T_scale >
return_type<T_y, T_loc, T_scale>::type stan::math::logistic_lpdf ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma 
)

Definition at line 31 of file logistic_lpdf.hpp.

§ logistic_lpdf() [2/2]

template<typename T_y , typename T_loc , typename T_scale >
return_type<T_y, T_loc, T_scale>::type stan::math::logistic_lpdf ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma 
)
inline

Definition at line 129 of file logistic_lpdf.hpp.

§ logistic_rng()

template<class RNG >
double stan::math::logistic_rng ( double  mu,
double  sigma,
RNG &  rng 
)
inline

Definition at line 24 of file logistic_rng.hpp.

§ logit() [1/5]

template<typename T >
fvar<T> stan::math::logit ( const fvar< T > &  x)
inline

Definition at line 16 of file logit.hpp.

§ logit() [2/5]

var stan::math::logit ( const var u)
inline

Return the log odds of the specified argument.

Parameters
uargument
Returns
log odds of argument

Definition at line 17 of file logit.hpp.

§ logit() [3/5]

template<typename T >
apply_scalar_unary<logit_fun, T>::return_t stan::math::logit ( const T &  x)
inline

Return the elementwise application of logit() to specified argument container.

The return type promotes the underlying scalar argument type to double if it is an integer, and otherwise is the argument type.

Template Parameters
Tcontainer type
Parameters
xcontainer
Returns
elementwise logit of container elements

Definition at line 39 of file logit.hpp.

§ logit() [4/5]

double stan::math::logit ( double  u)
inline

Return the log odds of the argument.

The logit function is defined as for $x \in [0, 1]$ by returning the log odds of $x$ treated as a probability,

$\mbox{logit}(x) = \log \left( \frac{x}{1 - x} \right)$.

The inverse to this function is inv_logit.

\[ \mbox{logit}(x) = \begin{cases} \textrm{NaN}& \mbox{if } x < 0 \textrm{ or } x > 1\\ \ln\frac{x}{1-x} & \mbox{if } 0\leq x \leq 1 \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{logit}(x)}{\partial x} = \begin{cases} \textrm{NaN}& \mbox{if } x < 0 \textrm{ or } x > 1\\ \frac{1}{x-x^2}& \mbox{if } 0\leq x\leq 1 \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

Parameters
uargument
Returns
log odds of argument

Definition at line 41 of file logit.hpp.

§ logit() [5/5]

double stan::math::logit ( int  u)
inline

Return the log odds of the argument.

Parameters
uargument
Returns
log odds of argument

Definition at line 52 of file logit.hpp.

§ lognormal_ccdf_log()

template<typename T_y , typename T_loc , typename T_scale >
return_type<T_y, T_loc, T_scale>::type stan::math::lognormal_ccdf_log ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma 
)

Definition at line 25 of file lognormal_ccdf_log.hpp.

§ lognormal_cdf()

template<typename T_y , typename T_loc , typename T_scale >
return_type<T_y, T_loc, T_scale>::type stan::math::lognormal_cdf ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma 
)

Definition at line 25 of file lognormal_cdf.hpp.

§ lognormal_cdf_log()

template<typename T_y , typename T_loc , typename T_scale >
return_type<T_y, T_loc, T_scale>::type stan::math::lognormal_cdf_log ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma 
)

Definition at line 25 of file lognormal_cdf_log.hpp.

§ lognormal_lccdf()

template<typename T_y , typename T_loc , typename T_scale >
return_type<T_y, T_loc, T_scale>::type stan::math::lognormal_lccdf ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma 
)

Definition at line 25 of file lognormal_lccdf.hpp.

§ lognormal_lcdf()

template<typename T_y , typename T_loc , typename T_scale >
return_type<T_y, T_loc, T_scale>::type stan::math::lognormal_lcdf ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma 
)

Definition at line 25 of file lognormal_lcdf.hpp.

§ lognormal_log() [1/2]

template<bool propto, typename T_y , typename T_loc , typename T_scale >
return_type<T_y, T_loc, T_scale>::type stan::math::lognormal_log ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma 
)

Definition at line 32 of file lognormal_log.hpp.

§ lognormal_log() [2/2]

template<typename T_y , typename T_loc , typename T_scale >
return_type<T_y, T_loc, T_scale>::type stan::math::lognormal_log ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma 
)
inline

Definition at line 140 of file lognormal_log.hpp.

§ lognormal_lpdf() [1/2]

template<bool propto, typename T_y , typename T_loc , typename T_scale >
return_type<T_y, T_loc, T_scale>::type stan::math::lognormal_lpdf ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma 
)

Definition at line 32 of file lognormal_lpdf.hpp.

§ lognormal_lpdf() [2/2]

template<typename T_y , typename T_loc , typename T_scale >
return_type<T_y, T_loc, T_scale>::type stan::math::lognormal_lpdf ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma 
)
inline

Definition at line 140 of file lognormal_lpdf.hpp.

§ lognormal_rng()

template<class RNG >
double stan::math::lognormal_rng ( double  mu,
double  sigma,
RNG &  rng 
)
inline

Definition at line 21 of file lognormal_rng.hpp.

§ lub_constrain() [1/2]

template<typename T , typename TL , typename TU >
boost::math::tools::promote_args<T, TL, TU>::type stan::math::lub_constrain ( const T  x,
TL  lb,
TU  ub 
)
inline

Return the lower- and upper-bounded scalar derived by transforming the specified free scalar given the specified lower and upper bounds.

The transform is the transformed and scaled inverse logit,

$f(x) = L + (U - L) \mbox{logit}^{-1}(x)$

If the lower bound is negative infinity and upper bound finite, this function reduces to ub_constrain(x, ub). If the upper bound is positive infinity and the lower bound finite, this function reduces to lb_constrain(x, lb). If the upper bound is positive infinity and the lower bound negative infinity, this function reduces to identity_constrain(x).

Parameters
xFree scalar to transform.
lbLower bound.
ubUpper bound.
Returns
Lower- and upper-bounded scalar derived from transforming the free scalar.
Template Parameters
TType of scalar.
TLType of lower bound.
TUType of upper bound.
Exceptions
std::domain_errorif ub <= lb

Definition at line 44 of file lub_constrain.hpp.

§ lub_constrain() [2/2]

template<typename T , typename TL , typename TU >
boost::math::tools::promote_args<T, TL, TU>::type stan::math::lub_constrain ( const T  x,
const TL  lb,
const TU  ub,
T &  lp 
)

Return the lower- and upper-bounded scalar derived by transforming the specified free scalar given the specified lower and upper bounds and increment the specified log probability with the log absolute Jacobian determinant.

The transform is as defined in lub_constrain(T, double, double). The log absolute Jacobian determinant is given by

$\log \left| \frac{d}{dx} \left( L + (U-L) \mbox{logit}^{-1}(x) \right) \right|$

$ {} = \log | (U-L) \, (\mbox{logit}^{-1}(x)) \, (1 - \mbox{logit}^{-1}(x)) |$

$ {} = \log (U - L) + \log (\mbox{logit}^{-1}(x)) + \log (1 - \mbox{logit}^{-1}(x))$

If the lower bound is negative infinity and upper bound finite, this function reduces to ub_constrain(x, ub, lp). If the upper bound is positive infinity and the lower bound finite, this function reduces to lb_constrain(x, lb, lp). If the upper bound is positive infinity and the lower bound negative infinity, this function reduces to identity_constrain(x, lp).

Parameters
xFree scalar to transform.
lbLower bound.
ubUpper bound.
lpLog probability scalar reference.
Returns
Lower- and upper-bounded scalar derived from transforming the free scalar.
Template Parameters
TType of scalar.
TLType of lower bound.
TUType of upper bound.
Exceptions
std::domain_errorif ub <= lb

Definition at line 114 of file lub_constrain.hpp.

§ lub_free()

template<typename T , typename TL , typename TU >
boost::math::tools::promote_args<T, TL, TU>::type stan::math::lub_free ( const T  y,
TL  lb,
TU  ub 
)
inline

Return the unconstrained scalar that transforms to the specified lower- and upper-bounded scalar given the specified bounds.

The transfrom in lub_constrain(T, double, double), is reversed by a transformed and scaled logit,

$f^{-1}(y) = \mbox{logit}(\frac{y - L}{U - L})$

where $U$ and $L$ are the lower and upper bounds.

If the lower bound is negative infinity and upper bound finite, this function reduces to ub_free(y, ub). If the upper bound is positive infinity and the lower bound finite, this function reduces to lb_free(x, lb). If the upper bound is positive infinity and the lower bound negative infinity, this function reduces to identity_free(y).

Template Parameters
TType of scalar.
Parameters
yScalar input.
lbLower bound.
ubUpper bound.
Returns
The free scalar that transforms to the input scalar given the bounds.
Exceptions
std::invalid_argumentif the lower bound is greater than the upper bound, y is less than the lower bound, or y is greater than the upper bound

Definition at line 46 of file lub_free.hpp.

§ machine_precision()

double stan::math::machine_precision ( )
inline

Returns the difference between 1.0 and the next value representable.

Returns
Minimum positive number.

Definition at line 149 of file constants.hpp.

§ make_nu()

template<typename T >
const Eigen::Array<T, Eigen::Dynamic, 1> stan::math::make_nu ( const T  eta,
size_t  K 
)

This function calculates the degrees of freedom for the t distribution that corresponds to the shape parameter in the Lewandowski et.

al. distribution

Parameters
etahyperparameter on (0, inf), eta = 1 <-> correlation matrix is uniform
Knumber of variables in covariance matrix

Definition at line 21 of file make_nu.hpp.

§ matrix_exp()

template<typename T >
Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> stan::math::matrix_exp ( const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic >  A)
inline

Return the matrix exponential of the input matrix.

Template Parameters
Ttype of scalar of the elements of input matrix.
Parameters
[in]AMatrix to exponentiate.
Returns
Matrix exponential.

Definition at line 22 of file matrix_exp.hpp.

§ matrix_exp_2x2()

template<typename T >
Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> stan::math::matrix_exp_2x2 ( const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &  A)

Return the matrix exponential of a 2x2 matrix.

Reference for algorithm: http://mathworld.wolfram.com/MatrixExponential.html Note: algorithm only works if delta > 0;

Template Parameters
Ttype of scalar of the elements of input matrix.
Parameters
[in]A2x2 matrix to exponentiate.
Returns
Matrix exponential of A.

Definition at line 21 of file matrix_exp_2x2.hpp.

§ matrix_exp_pade()

template<typename MatrixType >
MatrixType stan::math::matrix_exp_pade ( const MatrixType &  arg)

Computes the matrix exponential, using a Pade approximation, coupled with scaling and squaring.

Template Parameters
MatrixTypescalar type of the elements in the input matrix.
Parameters
[in]argmatrix to exponentiate.
Returns
Matrix exponential of input matrix.

Definition at line 21 of file matrix_exp_pade.hpp.

§ matrix_normal_prec_log() [1/2]

template<bool propto, typename T_y , typename T_Mu , typename T_Sigma , typename T_D >
boost::math::tools::promote_args<T_y, T_Mu, T_Sigma, T_D>::type stan::math::matrix_normal_prec_log ( const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &  y,
const Eigen::Matrix< T_Mu, Eigen::Dynamic, Eigen::Dynamic > &  Mu,
const Eigen::Matrix< T_Sigma, Eigen::Dynamic, Eigen::Dynamic > &  Sigma,
const Eigen::Matrix< T_D, Eigen::Dynamic, Eigen::Dynamic > &  D 
)

The log of the matrix normal density for the given y, mu, Sigma and D where Sigma and D are given as precision matrices, not covariance matrices.

Parameters
yAn mxn matrix.
MuThe mean matrix.
SigmaThe mxm inverse covariance matrix (i.e., the precision matrix) of the rows of y.
DThe nxn inverse covariance matrix (i.e., the precision matrix) of the columns of y.
Returns
The log of the matrix normal density.
Exceptions
std::domain_errorif Sigma or D are not square, not symmetric, or not semi-positive definite.
Template Parameters
T_yType of scalar.
T_MuType of location.
T_SigmaType of Sigma.
T_DType of D.

Definition at line 42 of file matrix_normal_prec_log.hpp.

§ matrix_normal_prec_log() [2/2]

template<typename T_y , typename T_Mu , typename T_Sigma , typename T_D >
boost::math::tools::promote_args<T_y, T_Mu, T_Sigma, T_D>::type stan::math::matrix_normal_prec_log ( const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &  y,
const Eigen::Matrix< T_Mu, Eigen::Dynamic, Eigen::Dynamic > &  Mu,
const Eigen::Matrix< T_Sigma, Eigen::Dynamic, Eigen::Dynamic > &  Sigma,
const Eigen::Matrix< T_D, Eigen::Dynamic, Eigen::Dynamic > &  D 
)

Definition at line 100 of file matrix_normal_prec_log.hpp.

§ matrix_normal_prec_lpdf() [1/2]

template<bool propto, typename T_y , typename T_Mu , typename T_Sigma , typename T_D >
boost::math::tools::promote_args<T_y, T_Mu, T_Sigma, T_D>::type stan::math::matrix_normal_prec_lpdf ( const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &  y,
const Eigen::Matrix< T_Mu, Eigen::Dynamic, Eigen::Dynamic > &  Mu,
const Eigen::Matrix< T_Sigma, Eigen::Dynamic, Eigen::Dynamic > &  Sigma,
const Eigen::Matrix< T_D, Eigen::Dynamic, Eigen::Dynamic > &  D 
)

The log of the matrix normal density for the given y, mu, Sigma and D where Sigma and D are given as precision matrices, not covariance matrices.

Parameters
yAn mxn matrix.
MuThe mean matrix.
SigmaThe mxm inverse covariance matrix (i.e., the precision matrix) of the rows of y.
DThe nxn inverse covariance matrix (i.e., the precision matrix) of the columns of y.
Returns
The log of the matrix normal density.
Exceptions
std::domain_errorif Sigma or D are not square, not symmetric, or not semi-positive definite.
Template Parameters
T_yType of scalar.
T_MuType of location.
T_SigmaType of Sigma.
T_DType of D.

Definition at line 42 of file matrix_normal_prec_lpdf.hpp.

§ matrix_normal_prec_lpdf() [2/2]

template<typename T_y , typename T_Mu , typename T_Sigma , typename T_D >
boost::math::tools::promote_args<T_y, T_Mu, T_Sigma, T_D>::type stan::math::matrix_normal_prec_lpdf ( const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &  y,
const Eigen::Matrix< T_Mu, Eigen::Dynamic, Eigen::Dynamic > &  Mu,
const Eigen::Matrix< T_Sigma, Eigen::Dynamic, Eigen::Dynamic > &  Sigma,
const Eigen::Matrix< T_D, Eigen::Dynamic, Eigen::Dynamic > &  D 
)

Definition at line 100 of file matrix_normal_prec_lpdf.hpp.

§ max() [1/3]

int stan::math::max ( const std::vector< int > &  x)
inline

Returns the maximum coefficient in the specified column vector.

Parameters
xSpecified vector.
Returns
Maximum coefficient value in the vector.
Template Parameters
Typeof values being compared and returned
Exceptions
std::domain_errorIf the size of the vector is zero.

Definition at line 22 of file max.hpp.

§ max() [2/3]

template<typename T >
T stan::math::max ( const std::vector< T > &  x)
inline

Returns the maximum coefficient in the specified column vector.

Parameters
xSpecified vector.
Returns
Maximum coefficient value in the vector.
Template Parameters
TType of values being compared and returned

Definition at line 39 of file max.hpp.

§ max() [3/3]

template<typename T , int R, int C>
T stan::math::max ( const Eigen::Matrix< T, R, C > &  m)
inline

Returns the maximum coefficient in the specified vector, row vector, or matrix.

Parameters
mSpecified vector, row vector, or matrix.
Returns
Maximum coefficient value in the vector.

Definition at line 56 of file max.hpp.

§ mdivide_left() [1/7]

template<typename T , int R1, int C1, int R2, int C2>
Eigen::Matrix<fvar<T>, R1, C2> stan::math::mdivide_left ( const Eigen::Matrix< fvar< T >, R1, C1 > &  A,
const Eigen::Matrix< fvar< T >, R2, C2 > &  b 
)
inline

Definition at line 24 of file mdivide_left.hpp.

§ mdivide_left() [2/7]

template<typename T1 , typename T2 , int R1, int C1, int R2, int C2>
Eigen::Matrix<typename boost::math::tools::promote_args<T1, T2>::type, R1, C2> stan::math::mdivide_left ( const Eigen::Matrix< T1, R1, C1 > &  A,
const Eigen::Matrix< T2, R2, C2 > &  b 
)
inline

Returns the solution of the system Ax=b.

Parameters
AMatrix.
bRight hand side matrix or vector.
Returns
x = A^-1 b, solution of the linear system.
Exceptions
std::domain_errorif A is not square or the rows of b don't match the size of A.

Definition at line 25 of file mdivide_left.hpp.

§ mdivide_left() [3/7]

template<typename T , int R1, int C1, int R2, int C2>
Eigen::Matrix<fvar<T>, R1, C2> stan::math::mdivide_left ( const Eigen::Matrix< double, R1, C1 > &  A,
const Eigen::Matrix< fvar< T >, R2, C2 > &  b 
)
inline

Definition at line 64 of file mdivide_left.hpp.

§ mdivide_left() [4/7]

template<typename T , int R1, int C1, int R2, int C2>
Eigen::Matrix<fvar<T>, R1, C2> stan::math::mdivide_left ( const Eigen::Matrix< fvar< T >, R1, C1 > &  A,
const Eigen::Matrix< double, R2, C2 > &  b 
)
inline

Definition at line 86 of file mdivide_left.hpp.

§ mdivide_left() [5/7]

template<int R1, int C1, int R2, int C2>
Eigen::Matrix<var, R1, C2> stan::math::mdivide_left ( const Eigen::Matrix< var, R1, C1 > &  A,
const Eigen::Matrix< var, R2, C2 > &  b 
)
inline

Definition at line 273 of file mdivide_left.hpp.

§ mdivide_left() [6/7]

template<int R1, int C1, int R2, int C2>
Eigen::Matrix<var, R1, C2> stan::math::mdivide_left ( const Eigen::Matrix< var, R1, C1 > &  A,
const Eigen::Matrix< double, R2, C2 > &  b 
)
inline

Definition at line 300 of file mdivide_left.hpp.

§ mdivide_left() [7/7]

template<int R1, int C1, int R2, int C2>
Eigen::Matrix<var, R1, C2> stan::math::mdivide_left ( const Eigen::Matrix< double, R1, C1 > &  A,
const Eigen::Matrix< var, R2, C2 > &  b 
)
inline

Definition at line 327 of file mdivide_left.hpp.

§ mdivide_left_ldlt() [1/5]

template<int R1, int C1, int R2, int C2, typename T2 >
Eigen::Matrix<fvar<T2>, R1, C2> stan::math::mdivide_left_ldlt ( const LDLT_factor< double, R1, C1 > &  A,
const Eigen::Matrix< fvar< T2 >, R2, C2 > &  b 
)
inline

Returns the solution of the system Ax=b given an LDLT_factor of A.

Parameters
ALDLT_factor
bRight hand side matrix or vector.
Returns
x = b A^-1, solution of the linear system.
Exceptions
std::domain_errorif rows of b don't match the size of A.

Definition at line 25 of file mdivide_left_ldlt.hpp.

§ mdivide_left_ldlt() [2/5]

template<int R1, int C1, int R2, int C2, typename T1 , typename T2 >
Eigen::Matrix<typename boost::math::tools::promote_args<T1, T2>::type, R1, C2> stan::math::mdivide_left_ldlt ( const LDLT_factor< T1, R1, C1 > &  A,
const Eigen::Matrix< T2, R2, C2 > &  b 
)
inline

Returns the solution of the system Ax=b given an LDLT_factor of A.

Parameters
ALDLT_factor
bRight hand side matrix or vector.
Returns
x = b A^-1, solution of the linear system.
Exceptions
std::domain_errorif rows of b don't match the size of A.

Definition at line 26 of file mdivide_left_ldlt.hpp.

§ mdivide_left_ldlt() [3/5]

template<int R1, int C1, int R2, int C2>
Eigen::Matrix<var, R1, C2> stan::math::mdivide_left_ldlt ( const LDLT_factor< var, R1, C1 > &  A,
const Eigen::Matrix< var, R2, C2 > &  b 
)
inline

Returns the solution of the system Ax=b given an LDLT_factor of A.

Parameters
ALDLT_factor
bRight hand side matrix or vector.
Returns
x = b A^-1, solution of the linear system.
Exceptions
std::domain_errorif rows of b don't match the size of A.

Definition at line 246 of file mdivide_left_ldlt.hpp.

§ mdivide_left_ldlt() [4/5]

template<int R1, int C1, int R2, int C2>
Eigen::Matrix<var, R1, C2> stan::math::mdivide_left_ldlt ( const LDLT_factor< var, R1, C1 > &  A,
const Eigen::Matrix< double, R2, C2 > &  b 
)
inline

Returns the solution of the system Ax=b given an LDLT_factor of A.

Parameters
ALDLT_factor
bRight hand side matrix or vector.
Returns
x = b A^-1, solution of the linear system.
Exceptions
std::domain_errorif rows of b don't match the size of A.

Definition at line 274 of file mdivide_left_ldlt.hpp.

§ mdivide_left_ldlt() [5/5]

template<int R1, int C1, int R2, int C2>
Eigen::Matrix<var, R1, C2> stan::math::mdivide_left_ldlt ( const LDLT_factor< double, R1, C1 > &  A,
const Eigen::Matrix< var, R2, C2 > &  b 
)
inline

Returns the solution of the system Ax=b given an LDLT_factor of A.

Parameters
ALDLT_factor
bRight hand side matrix or vector.
Returns
x = b A^-1, solution of the linear system.
Exceptions
std::domain_errorif rows of b don't match the size of A.

Definition at line 302 of file mdivide_left_ldlt.hpp.

§ mdivide_left_spd() [1/4]

template<typename T1 , typename T2 , int R1, int C1, int R2, int C2>
Eigen::Matrix<typename boost::math::tools::promote_args<T1, T2>::type, R1, C2> stan::math::mdivide_left_spd ( const Eigen::Matrix< T1, R1, C1 > &  A,
const Eigen::Matrix< T2, R2, C2 > &  b 
)
inline

Returns the solution of the system Ax=b where A is symmetric positive definite.

Parameters
AMatrix.
bRight hand side matrix or vector.
Returns
x = A^-1 b, solution of the linear system.
Exceptions
std::domain_errorif A is not square or the rows of b don't match the size of A.

Definition at line 28 of file mdivide_left_spd.hpp.

§ mdivide_left_spd() [2/4]

template<int R1, int C1, int R2, int C2>
Eigen::Matrix<var, R1, C2> stan::math::mdivide_left_spd ( const Eigen::Matrix< var, R1, C1 > &  A,
const Eigen::Matrix< var, R2, C2 > &  b 
)
inline

Definition at line 248 of file mdivide_left_spd.hpp.

§ mdivide_left_spd() [3/4]

template<int R1, int C1, int R2, int C2>
Eigen::Matrix<var, R1, C2> stan::math::mdivide_left_spd ( const Eigen::Matrix< var, R1, C1 > &  A,
const Eigen::Matrix< double, R2, C2 > &  b 
)
inline

Definition at line 275 of file mdivide_left_spd.hpp.

§ mdivide_left_spd() [4/4]

template<int R1, int C1, int R2, int C2>
Eigen::Matrix<var, R1, C2> stan::math::mdivide_left_spd ( const Eigen::Matrix< double, R1, C1 > &  A,
const Eigen::Matrix< var, R2, C2 > &  b 
)
inline

Definition at line 302 of file mdivide_left_spd.hpp.

§ mdivide_left_tri() [1/5]

template<int TriView, typename T1 , typename T2 , int R1, int C1, int R2, int C2>
Eigen::Matrix<typename boost::math::tools::promote_args<T1, T2>::type, R1, C2> stan::math::mdivide_left_tri ( const Eigen::Matrix< T1, R1, C1 > &  A,
const Eigen::Matrix< T2, R2, C2 > &  b 
)
inline

Returns the solution of the system Ax=b when A is triangular.

Parameters
ATriangular matrix. Specify upper or lower with TriView being Eigen::Upper or Eigen::Lower.
bRight hand side matrix or vector.
Returns
x = A^-1 b, solution of the linear system.
Exceptions
std::domain_errorif A is not square or the rows of b don't match the size of A.

Definition at line 27 of file mdivide_left_tri.hpp.

§ mdivide_left_tri() [2/5]

template<int TriView, typename T , int R1, int C1>
Eigen::Matrix<T, R1, C1> stan::math::mdivide_left_tri ( const Eigen::Matrix< T, R1, C1 > &  A)
inline

Returns the solution of the system Ax=b when A is triangular and b=I.

Parameters
ATriangular matrix. Specify upper or lower with TriView being Eigen::Upper or Eigen::Lower.
Returns
x = A^-1 .
Exceptions
std::domain_errorif A is not square

Definition at line 48 of file mdivide_left_tri.hpp.

§ mdivide_left_tri() [3/5]

template<int TriView, int R1, int C1, int R2, int C2>
Eigen::Matrix<var, R1, C2> stan::math::mdivide_left_tri ( const Eigen::Matrix< var, R1, C1 > &  A,
const Eigen::Matrix< var, R2, C2 > &  b 
)
inline

Definition at line 304 of file mdivide_left_tri.hpp.

§ mdivide_left_tri() [4/5]

template<int TriView, int R1, int C1, int R2, int C2>
Eigen::Matrix<var, R1, C2> stan::math::mdivide_left_tri ( const Eigen::Matrix< double, R1, C1 > &  A,
const Eigen::Matrix< var, R2, C2 > &  b 
)
inline

Definition at line 330 of file mdivide_left_tri.hpp.

§ mdivide_left_tri() [5/5]

template<int TriView, int R1, int C1, int R2, int C2>
Eigen::Matrix<var, R1, C2> stan::math::mdivide_left_tri ( const Eigen::Matrix< var, R1, C1 > &  A,
const Eigen::Matrix< double, R2, C2 > &  b 
)
inline

Definition at line 356 of file mdivide_left_tri.hpp.

§ mdivide_left_tri_low() [1/5]

template<typename T1 , typename T2 , int R1, int C1, int R2, int C2>
Eigen::Matrix<typename boost::math::tools::promote_args<T1, T2>::type, R1, C2> stan::math::mdivide_left_tri_low ( const Eigen::Matrix< T1, R1, C1 > &  A,
const Eigen::Matrix< T2, R2, C2 > &  b 
)
inline

Definition at line 16 of file mdivide_left_tri_low.hpp.

§ mdivide_left_tri_low() [2/5]

template<typename T , int R1, int C1, int R2, int C2>
Eigen::Matrix<fvar<T>, R1, C1> stan::math::mdivide_left_tri_low ( const Eigen::Matrix< fvar< T >, R1, C1 > &  A,
const Eigen::Matrix< fvar< T >, R2, C2 > &  b 
)
inline

Definition at line 22 of file mdivide_left_tri_low.hpp.

§ mdivide_left_tri_low() [3/5]

template<typename T , int R1, int C1>
Eigen::Matrix<T, R1, C1> stan::math::mdivide_left_tri_low ( const Eigen::Matrix< T, R1, C1 > &  A)
inline

Definition at line 25 of file mdivide_left_tri_low.hpp.

§ mdivide_left_tri_low() [4/5]

template<typename T , int R1, int C1, int R2, int C2>
Eigen::Matrix<fvar<T>, R1, C1> stan::math::mdivide_left_tri_low ( const Eigen::Matrix< double, R1, C1 > &  A,
const Eigen::Matrix< fvar< T >, R2, C2 > &  b 
)
inline

Definition at line 64 of file mdivide_left_tri_low.hpp.

§ mdivide_left_tri_low() [5/5]

template<typename T , int R1, int C1, int R2, int C2>
Eigen::Matrix<fvar<T>, R1, C1> stan::math::mdivide_left_tri_low ( const Eigen::Matrix< fvar< T >, R1, C1 > &  A,
const Eigen::Matrix< double, R2, C2 > &  b 
)
inline

Definition at line 101 of file mdivide_left_tri_low.hpp.

§ mdivide_right() [1/4]

template<typename T , int R1, int C1, int R2, int C2>
Eigen::Matrix<fvar<T>, R1, C2> stan::math::mdivide_right ( const Eigen::Matrix< fvar< T >, R1, C1 > &  A,
const Eigen::Matrix< fvar< T >, R2, C2 > &  b 
)
inline

Definition at line 24 of file mdivide_right.hpp.

§ mdivide_right() [2/4]

template<typename T1 , typename T2 , int R1, int C1, int R2, int C2>
Eigen::Matrix<typename boost::math::tools::promote_args<T1, T2>::type, R1, C2> stan::math::mdivide_right ( const Eigen::Matrix< T1, R1, C1 > &  b,
const Eigen::Matrix< T2, R2, C2 > &  A 
)
inline

Returns the solution of the system Ax=b.

Parameters
AMatrix.
bRight hand side matrix or vector.
Returns
x = b A^-1, solution of the linear system.
Exceptions
std::domain_errorif A is not square or the rows of b don't match the size of A.

Definition at line 26 of file mdivide_right.hpp.

§ mdivide_right() [3/4]

template<typename T , int R1, int C1, int R2, int C2>
Eigen::Matrix<fvar<T>, R1, C2> stan::math::mdivide_right ( const Eigen::Matrix< fvar< T >, R1, C1 > &  A,
const Eigen::Matrix< double, R2, C2 > &  b 
)
inline

Definition at line 64 of file mdivide_right.hpp.

§ mdivide_right() [4/4]

template<typename T , int R1, int C1, int R2, int C2>
Eigen::Matrix<fvar<T>, R1, C2> stan::math::mdivide_right ( const Eigen::Matrix< double, R1, C1 > &  A,
const Eigen::Matrix< fvar< T >, R2, C2 > &  b 
)
inline

Definition at line 87 of file mdivide_right.hpp.

§ mdivide_right_ldlt() [1/2]

template<typename T1 , typename T2 , int R1, int C1, int R2, int C2>
Eigen::Matrix<typename boost::math::tools::promote_args<T1, T2>::type, R1, C2> stan::math::mdivide_right_ldlt ( const Eigen::Matrix< T1, R1, C1 > &  b,
const LDLT_factor< T2, R2, C2 > &  A 
)
inline

Returns the solution of the system xA=b given an LDLT_factor of A.

Parameters
ALDLT_factor
bRight hand side matrix or vector.
Returns
x = A^-1 b, solution of the linear system.
Exceptions
std::domain_errorif rows of b don't match the size of A.

Definition at line 26 of file mdivide_right_ldlt.hpp.

§ mdivide_right_ldlt() [2/2]

template<int R1, int C1, int R2, int C2>
Eigen::Matrix<double, R1, C2> stan::math::mdivide_right_ldlt ( const Eigen::Matrix< double, R1, C1 > &  b,
const LDLT_factor< double, R2, C2 > &  A 
)
inline

Definition at line 35 of file mdivide_right_ldlt.hpp.

§ mdivide_right_spd()

template<typename T1 , typename T2 , int R1, int C1, int R2, int C2>
Eigen::Matrix<typename boost::math::tools::promote_args<T1, T2>::type, R1, C2> stan::math::mdivide_right_spd ( const Eigen::Matrix< T1, R1, C1 > &  b,
const Eigen::Matrix< T2, R2, C2 > &  A 
)
inline

Returns the solution of the system Ax=b where A is symmetric positive definite.

Parameters
AMatrix.
bRight hand side matrix or vector.
Returns
x = b A^-1, solution of the linear system.
Exceptions
std::domain_errorif A is not square or the rows of b don't match the size of A.

Definition at line 29 of file mdivide_right_spd.hpp.

§ mdivide_right_tri()

template<int TriView, typename T1 , typename T2 , int R1, int C1, int R2, int C2>
Eigen::Matrix<typename boost::math::tools::promote_args<T1, T2>::type, R1, C2> stan::math::mdivide_right_tri ( const Eigen::Matrix< T1, R1, C1 > &  b,
const Eigen::Matrix< T2, R2, C2 > &  A 
)
inline

Returns the solution of the system Ax=b when A is triangular.

Parameters
ATriangular matrix. Specify upper or lower with TriView being Eigen::Upper or Eigen::Lower.
bRight hand side matrix or vector.
Returns
x = b A^-1, solution of the linear system.
Exceptions
std::domain_errorif A is not square or the rows of b don't match the size of A.

Definition at line 29 of file mdivide_right_tri.hpp.

§ mdivide_right_tri_low() [1/4]

template<typename T , int R1, int C1, int R2, int C2>
Eigen::Matrix<fvar<T>, R1, C1> stan::math::mdivide_right_tri_low ( const Eigen::Matrix< fvar< T >, R1, C1 > &  A,
const Eigen::Matrix< fvar< T >, R2, C2 > &  b 
)
inline

Definition at line 22 of file mdivide_right_tri_low.hpp.

§ mdivide_right_tri_low() [2/4]

template<typename T1 , typename T2 , int R1, int C1, int R2, int C2>
Eigen::Matrix<typename boost::math::tools::promote_args<T1, T2>::type, R1, C2> stan::math::mdivide_right_tri_low ( const Eigen::Matrix< T1, R1, C1 > &  b,
const Eigen::Matrix< T2, R2, C2 > &  A 
)
inline

Returns the solution of the system tri(A)x=b when tri(A) is a lower triangular view of the matrix A.

Parameters
AMatrix.
bRight hand side matrix or vector.
Returns
x = b * tri(A)^-1, solution of the linear system.
Exceptions
std::domain_errorif A is not square or the rows of b don't match the size of A.

Definition at line 25 of file mdivide_right_tri_low.hpp.

§ mdivide_right_tri_low() [3/4]

template<typename T , int R1, int C1, int R2, int C2>
Eigen::Matrix<fvar<T>, R1, C2> stan::math::mdivide_right_tri_low ( const Eigen::Matrix< fvar< T >, R1, C1 > &  A,
const Eigen::Matrix< double, R2, C2 > &  b 
)
inline

Definition at line 64 of file mdivide_right_tri_low.hpp.

§ mdivide_right_tri_low() [4/4]

template<typename T , int R1, int C1, int R2, int C2>
Eigen::Matrix<fvar<T>, R1, C2> stan::math::mdivide_right_tri_low ( const Eigen::Matrix< double, R1, C1 > &  A,
const Eigen::Matrix< fvar< T >, R2, C2 > &  b 
)
inline

Definition at line 95 of file mdivide_right_tri_low.hpp.

§ mean() [1/2]

template<typename T >
boost::math::tools::promote_args<T>::type stan::math::mean ( const std::vector< T > &  v)
inline

Returns the sample mean (i.e., average) of the coefficients in the specified standard vector.

Parameters
vSpecified vector.
Returns
Sample mean of vector coefficients.
Exceptions
std::domain_errorif the size of the vector is less than 1.

Definition at line 23 of file mean.hpp.

§ mean() [2/2]

template<typename T , int R, int C>
boost::math::tools::promote_args<T>::type stan::math::mean ( const Eigen::Matrix< T, R, C > &  m)
inline

Returns the sample mean (i.e., average) of the coefficients in the specified vector, row vector, or matrix.

Parameters
mSpecified vector, row vector, or matrix.
Returns
Sample mean of vector coefficients.

Definition at line 40 of file mean.hpp.

§ min() [1/3]

int stan::math::min ( const std::vector< int > &  x)
inline

Returns the minimum coefficient in the specified column vector.

Parameters
xSpecified vector.
Returns
Minimum coefficient value in the vector.
Template Parameters
Typeof values being compared and returned

Definition at line 20 of file min.hpp.

§ min() [2/3]

template<typename T >
T stan::math::min ( const std::vector< T > &  x)
inline

Returns the minimum coefficient in the specified column vector.

Parameters
xSpecified vector.
Returns
Minimum coefficient value in the vector.
Template Parameters
Typeof values being compared and returned

Definition at line 37 of file min.hpp.

§ min() [3/3]

template<typename T , int R, int C>
T stan::math::min ( const Eigen::Matrix< T, R, C > &  m)
inline

Returns the minimum coefficient in the specified matrix, vector, or row vector.

Parameters
mSpecified matrix, vector, or row vector.
Returns
Minimum coefficient value in the vector.

Definition at line 54 of file min.hpp.

§ minus()

template<typename T >
T stan::math::minus ( const T &  x)
inline

Returns the negation of the specified scalar or matrix.

Template Parameters
TType of subtrahend.
Parameters
xSubtrahend.
Returns
Negation of subtrahend.

Definition at line 16 of file minus.hpp.

§ modified_bessel_first_kind() [1/3]

template<typename T >
fvar<T> stan::math::modified_bessel_first_kind ( int  v,
const fvar< T > &  z 
)
inline

Definition at line 13 of file modified_bessel_first_kind.hpp.

§ modified_bessel_first_kind() [2/3]

var stan::math::modified_bessel_first_kind ( int  v,
const var a 
)
inline

Definition at line 27 of file modified_bessel_first_kind.hpp.

§ modified_bessel_first_kind() [3/3]

template<typename T2 >
T2 stan::math::modified_bessel_first_kind ( int  v,
const T2  z 
)
inline

\[ \mbox{modified\_bessel\_first\_kind}(v, z) = \begin{cases} I_v(z) & \mbox{if } -\infty\leq z \leq \infty \\[6pt] \textrm{error} & \mbox{if } z = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{modified\_bessel\_first\_kind}(v, z)}{\partial z} = \begin{cases} \frac{\partial\, I_v(z)}{\partial z} & \mbox{if } -\infty\leq z\leq \infty \\[6pt] \textrm{error} & \mbox{if } z = \textrm{NaN} \end{cases} \]

\[ {I_v}(z) = \left(\frac{1}{2}z\right)^v\sum_{k=0}^\infty \frac{\left(\frac{1}{4}z^2\right)^k}{k!\Gamma(v+k+1)} \]

\[ \frac{\partial \, I_v(z)}{\partial z} = I_{v-1}(z)-\frac{v}{z}I_v(z) \]

Definition at line 39 of file modified_bessel_first_kind.hpp.

§ modified_bessel_second_kind() [1/3]

template<typename T >
fvar<T> stan::math::modified_bessel_second_kind ( int  v,
const fvar< T > &  z 
)
inline

Definition at line 13 of file modified_bessel_second_kind.hpp.

§ modified_bessel_second_kind() [2/3]

var stan::math::modified_bessel_second_kind ( int  v,
const var a 
)
inline

Definition at line 27 of file modified_bessel_second_kind.hpp.

§ modified_bessel_second_kind() [3/3]

template<typename T2 >
T2 stan::math::modified_bessel_second_kind ( int  v,
const T2  z 
)
inline

\[ \mbox{modified\_bessel\_second\_kind}(v, z) = \begin{cases} \textrm{error} & \mbox{if } z \leq 0 \\ K_v(z) & \mbox{if } z > 0 \\[6pt] \textrm{NaN} & \mbox{if } z = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{modified\_bessel\_second\_kind}(v, z)}{\partial z} = \begin{cases} \textrm{error} & \mbox{if } z \leq 0 \\ \frac{\partial\, K_v(z)}{\partial z} & \mbox{if } z > 0 \\[6pt] \textrm{NaN} & \mbox{if } z = \textrm{NaN} \end{cases} \]

\[ {K_v}(z) = \frac{\pi}{2}\cdot\frac{I_{-v}(z) - I_{v}(z)}{\sin(v\pi)} \]

\[ \frac{\partial \, K_v(z)}{\partial z} = -\frac{v}{z}K_v(z)-K_{v-1}(z) \]

Definition at line 42 of file modified_bessel_second_kind.hpp.

§ modulus()

int stan::math::modulus ( int  x,
int  y 
)
inline

Definition at line 12 of file modulus.hpp.

§ multi_gp_cholesky_log() [1/2]

template<bool propto, typename T_y , typename T_covar , typename T_w >
boost::math::tools::promote_args<T_y, T_covar, T_w>::type stan::math::multi_gp_cholesky_log ( const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &  y,
const Eigen::Matrix< T_covar, Eigen::Dynamic, Eigen::Dynamic > &  L,
const Eigen::Matrix< T_w, Eigen::Dynamic, 1 > &  w 
)

The log of a multivariate Gaussian Process for the given y, w, and a Cholesky factor L of the kernel matrix Sigma.

Sigma = LL', a square, semi-positive definite matrix. y is a dxN matrix, where each column is a different observation and each row is a different output dimension. The Gaussian Process is assumed to have a scaled kernel matrix with a different scale for each output dimension. This distribution is equivalent to: for (i in 1:d) row(y, i) ~ multi_normal(0, (1/w[i])*LL').

Parameters
yA dxN matrix
LThe Cholesky decomposition of a kernel matrix
wA d-dimensional vector of positve inverse scale parameters for each output.
Returns
The log of the multivariate GP density.
Exceptions
std::domain_errorif Sigma is not square, not symmetric, or not semi-positive definite.
Template Parameters
T_yType of scalar.
T_covarType of kernel.
T_wType of weight.

Definition at line 41 of file multi_gp_cholesky_log.hpp.

§ multi_gp_cholesky_log() [2/2]

template<typename T_y , typename T_covar , typename T_w >
boost::math::tools::promote_args<T_y, T_covar, T_w>::type stan::math::multi_gp_cholesky_log ( const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &  y,
const Eigen::Matrix< T_covar, Eigen::Dynamic, Eigen::Dynamic > &  L,
const Eigen::Matrix< T_w, Eigen::Dynamic, 1 > &  w 
)
inline

Definition at line 96 of file multi_gp_cholesky_log.hpp.

§ multi_gp_cholesky_lpdf() [1/2]

template<bool propto, typename T_y , typename T_covar , typename T_w >
boost::math::tools::promote_args<T_y, T_covar, T_w>::type stan::math::multi_gp_cholesky_lpdf ( const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &  y,
const Eigen::Matrix< T_covar, Eigen::Dynamic, Eigen::Dynamic > &  L,
const Eigen::Matrix< T_w, Eigen::Dynamic, 1 > &  w 
)

The log of a multivariate Gaussian Process for the given y, w, and a Cholesky factor L of the kernel matrix Sigma.

Sigma = LL', a square, semi-positive definite matrix. y is a dxN matrix, where each column is a different observation and each row is a different output dimension. The Gaussian Process is assumed to have a scaled kernel matrix with a different scale for each output dimension. This distribution is equivalent to: for (i in 1:d) row(y, i) ~ multi_normal(0, (1/w[i])*LL').

Parameters
yA dxN matrix
LThe Cholesky decomposition of a kernel matrix
wA d-dimensional vector of positve inverse scale parameters for each output.
Returns
The log of the multivariate GP density.
Exceptions
std::domain_errorif Sigma is not square, not symmetric, or not semi-positive definite.
Template Parameters
T_yType of scalar.
T_covarType of kernel.
T_wType of weight.

Definition at line 41 of file multi_gp_cholesky_lpdf.hpp.

§ multi_gp_cholesky_lpdf() [2/2]

template<typename T_y , typename T_covar , typename T_w >
boost::math::tools::promote_args<T_y, T_covar, T_w>::type stan::math::multi_gp_cholesky_lpdf ( const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &  y,
const Eigen::Matrix< T_covar, Eigen::Dynamic, Eigen::Dynamic > &  L,
const Eigen::Matrix< T_w, Eigen::Dynamic, 1 > &  w 
)
inline

Definition at line 96 of file multi_gp_cholesky_lpdf.hpp.

§ multi_gp_log() [1/2]

template<bool propto, typename T_y , typename T_covar , typename T_w >
boost::math::tools::promote_args<T_y, T_covar, T_w>::type stan::math::multi_gp_log ( const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &  y,
const Eigen::Matrix< T_covar, Eigen::Dynamic, Eigen::Dynamic > &  Sigma,
const Eigen::Matrix< T_w, Eigen::Dynamic, 1 > &  w 
)

The log of a multivariate Gaussian Process for the given y, Sigma, and w.

y is a dxN matrix, where each column is a different observation and each row is a different output dimension. The Gaussian Process is assumed to have a scaled kernel matrix with a different scale for each output dimension. This distribution is equivalent to: for (i in 1:d) row(y, i) ~ multi_normal(0, (1/w[i])*Sigma).

Parameters
yA dxN matrix
SigmaThe NxN kernel matrix
wA d-dimensional vector of positve inverse scale parameters for each output.
Returns
The log of the multivariate GP density.
Exceptions
std::domain_errorif Sigma is not square, not symmetric, or not semi-positive definite.
Template Parameters
T_yType of scalar.
T_covarType of kernel.
T_wType of weight.

Definition at line 42 of file multi_gp_log.hpp.

§ multi_gp_log() [2/2]

template<typename T_y , typename T_covar , typename T_w >
boost::math::tools::promote_args<T_y, T_covar, T_w>::type stan::math::multi_gp_log ( const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &  y,
const Eigen::Matrix< T_covar, Eigen::Dynamic, Eigen::Dynamic > &  Sigma,
const Eigen::Matrix< T_w, Eigen::Dynamic, 1 > &  w 
)
inline

Definition at line 96 of file multi_gp_log.hpp.

§ multi_gp_lpdf() [1/2]

template<bool propto, typename T_y , typename T_covar , typename T_w >
boost::math::tools::promote_args<T_y, T_covar, T_w>::type stan::math::multi_gp_lpdf ( const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &  y,
const Eigen::Matrix< T_covar, Eigen::Dynamic, Eigen::Dynamic > &  Sigma,
const Eigen::Matrix< T_w, Eigen::Dynamic, 1 > &  w 
)

The log of a multivariate Gaussian Process for the given y, Sigma, and w.

y is a dxN matrix, where each column is a different observation and each row is a different output dimension. The Gaussian Process is assumed to have a scaled kernel matrix with a different scale for each output dimension. This distribution is equivalent to: for (i in 1:d) row(y, i) ~ multi_normal(0, (1/w[i])*Sigma).

Parameters
yA dxN matrix
SigmaThe NxN kernel matrix
wA d-dimensional vector of positve inverse scale parameters for each output.
Returns
The log of the multivariate GP density.
Exceptions
std::domain_errorif Sigma is not square, not symmetric, or not semi-positive definite.
Template Parameters
T_yType of scalar.
T_covarType of kernel.
T_wType of weight.

Definition at line 42 of file multi_gp_lpdf.hpp.

§ multi_gp_lpdf() [2/2]

template<typename T_y , typename T_covar , typename T_w >
boost::math::tools::promote_args<T_y, T_covar, T_w>::type stan::math::multi_gp_lpdf ( const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &  y,
const Eigen::Matrix< T_covar, Eigen::Dynamic, Eigen::Dynamic > &  Sigma,
const Eigen::Matrix< T_w, Eigen::Dynamic, 1 > &  w 
)
inline

Definition at line 96 of file multi_gp_lpdf.hpp.

§ multi_normal_cholesky_log() [1/2]

template<bool propto, typename T_y , typename T_loc , typename T_covar >
return_type<T_y, T_loc, T_covar>::type stan::math::multi_normal_cholesky_log ( const T_y &  y,
const T_loc &  mu,
const T_covar &  L 
)

The log of the multivariate normal density for the given y, mu, and a Cholesky factor L of the variance matrix.

Sigma = LL', a square, semi-positive definite matrix.

Parameters
yA scalar vector
muThe mean vector of the multivariate normal distribution.
LThe Cholesky decomposition of a variance matrix of the multivariate normal distribution
Returns
The log of the multivariate normal density.
Exceptions
std::domain_errorif LL' is not square, not symmetric, or not semi-positive definite.
Template Parameters
T_yType of scalar.
T_locType of location.
T_covarType of scale.

Definition at line 48 of file multi_normal_cholesky_log.hpp.

§ multi_normal_cholesky_log() [2/2]

template<typename T_y , typename T_loc , typename T_covar >
return_type<T_y, T_loc, T_covar>::type stan::math::multi_normal_cholesky_log ( const T_y &  y,
const T_loc &  mu,
const T_covar &  L 
)
inline

Definition at line 143 of file multi_normal_cholesky_log.hpp.

§ multi_normal_cholesky_lpdf() [1/2]

template<bool propto, typename T_y , typename T_loc , typename T_covar >
return_type<T_y, T_loc, T_covar>::type stan::math::multi_normal_cholesky_lpdf ( const T_y &  y,
const T_loc &  mu,
const T_covar &  L 
)

The log of the multivariate normal density for the given y, mu, and a Cholesky factor L of the variance matrix.

Sigma = LL', a square, semi-positive definite matrix.

Parameters
yA scalar vector
muThe mean vector of the multivariate normal distribution.
LThe Cholesky decomposition of a variance matrix of the multivariate normal distribution
Returns
The log of the multivariate normal density.
Exceptions
std::domain_errorif LL' is not square, not symmetric, or not semi-positive definite.
Template Parameters
T_yType of scalar.
T_locType of location.
T_covarType of scale.

Definition at line 48 of file multi_normal_cholesky_lpdf.hpp.

§ multi_normal_cholesky_lpdf() [2/2]

template<typename T_y , typename T_loc , typename T_covar >
return_type<T_y, T_loc, T_covar>::type stan::math::multi_normal_cholesky_lpdf ( const T_y &  y,
const T_loc &  mu,
const T_covar &  L 
)
inline

Definition at line 143 of file multi_normal_cholesky_lpdf.hpp.

§ multi_normal_cholesky_rng()

template<class RNG >
Eigen::VectorXd stan::math::multi_normal_cholesky_rng ( const Eigen::Matrix< double, Eigen::Dynamic, 1 > &  mu,
const Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > &  S,
RNG &  rng 
)
inline

Definition at line 28 of file multi_normal_cholesky_rng.hpp.

§ multi_normal_log() [1/2]

template<bool propto, typename T_y , typename T_loc , typename T_covar >
return_type<T_y, T_loc, T_covar>::type stan::math::multi_normal_log ( const T_y &  y,
const T_loc &  mu,
const T_covar &  Sigma 
)

Definition at line 26 of file multi_normal_log.hpp.

§ multi_normal_log() [2/2]

template<typename T_y , typename T_loc , typename T_covar >
return_type<T_y, T_loc, T_covar>::type stan::math::multi_normal_log ( const T_y &  y,
const T_loc &  mu,
const T_covar &  Sigma 
)
inline

Definition at line 119 of file multi_normal_log.hpp.

§ multi_normal_lpdf() [1/2]

template<bool propto, typename T_y , typename T_loc , typename T_covar >
return_type<T_y, T_loc, T_covar>::type stan::math::multi_normal_lpdf ( const T_y &  y,
const T_loc &  mu,
const T_covar &  Sigma 
)

Definition at line 26 of file multi_normal_lpdf.hpp.

§ multi_normal_lpdf() [2/2]

template<typename T_y , typename T_loc , typename T_covar >
return_type<T_y, T_loc, T_covar>::type stan::math::multi_normal_lpdf ( const T_y &  y,
const T_loc &  mu,
const T_covar &  Sigma 
)
inline

Definition at line 119 of file multi_normal_lpdf.hpp.

§ multi_normal_prec_log() [1/2]

template<bool propto, typename T_y , typename T_loc , typename T_covar >
return_type<T_y, T_loc, T_covar>::type stan::math::multi_normal_prec_log ( const T_y &  y,
const T_loc &  mu,
const T_covar &  Sigma 
)

Definition at line 35 of file multi_normal_prec_log.hpp.

§ multi_normal_prec_log() [2/2]

template<typename T_y , typename T_loc , typename T_covar >
return_type<T_y, T_loc, T_covar>::type stan::math::multi_normal_prec_log ( const T_y &  y,
const T_loc &  mu,
const T_covar &  Sigma 
)
inline

Definition at line 129 of file multi_normal_prec_log.hpp.

§ multi_normal_prec_lpdf() [1/2]

template<bool propto, typename T_y , typename T_loc , typename T_covar >
return_type<T_y, T_loc, T_covar>::type stan::math::multi_normal_prec_lpdf ( const T_y &  y,
const T_loc &  mu,
const T_covar &  Sigma 
)

Definition at line 35 of file multi_normal_prec_lpdf.hpp.

§ multi_normal_prec_lpdf() [2/2]

template<typename T_y , typename T_loc , typename T_covar >
return_type<T_y, T_loc, T_covar>::type stan::math::multi_normal_prec_lpdf ( const T_y &  y,
const T_loc &  mu,
const T_covar &  Sigma 
)
inline

Definition at line 129 of file multi_normal_prec_lpdf.hpp.

§ multi_normal_rng()

template<class RNG >
Eigen::VectorXd stan::math::multi_normal_rng ( const Eigen::VectorXd &  mu,
const Eigen::MatrixXd &  S,
RNG &  rng 
)
inline

Return a pseudo-random vector with a multi-variate normal distribution given the specified location parameter and covariance matrix and pseudo-random number generator.

If calculating more than one multivariate-normal random draw then it is more efficient to calculate the Cholesky factor of the covariance matrix and use the function stan::math::multi_normal_cholesky_rng.

Template Parameters
RNGType of pseudo-random number generator.
Parameters
muLocation parameter.
SCovariance parameter.
rngPseudo-random number generator.

Definition at line 35 of file multi_normal_rng.hpp.

§ multi_student_t_log() [1/2]

template<bool propto, typename T_y , typename T_dof , typename T_loc , typename T_scale >
return_type<T_y, T_dof, T_loc, T_scale>::type stan::math::multi_student_t_log ( const T_y &  y,
const T_dof &  nu,
const T_loc &  mu,
const T_scale &  Sigma 
)

Return the log of the multivariate Student t distribution at the specified arguments.

Template Parameters
proptoCarry out calculations up to a proportion

Definition at line 36 of file multi_student_t_log.hpp.

§ multi_student_t_log() [2/2]

template<typename T_y , typename T_dof , typename T_loc , typename T_scale >
return_type<T_y, T_dof, T_loc, T_scale>::type stan::math::multi_student_t_log ( const T_y &  y,
const T_dof &  nu,
const T_loc &  mu,
const T_scale &  Sigma 
)
inline

Definition at line 150 of file multi_student_t_log.hpp.

§ multi_student_t_lpdf() [1/2]

template<bool propto, typename T_y , typename T_dof , typename T_loc , typename T_scale >
return_type<T_y, T_dof, T_loc, T_scale>::type stan::math::multi_student_t_lpdf ( const T_y &  y,
const T_dof &  nu,
const T_loc &  mu,
const T_scale &  Sigma 
)

Return the log of the multivariate Student t distribution at the specified arguments.

Template Parameters
proptoCarry out calculations up to a proportion

Definition at line 36 of file multi_student_t_lpdf.hpp.

§ multi_student_t_lpdf() [2/2]

template<typename T_y , typename T_dof , typename T_loc , typename T_scale >
return_type<T_y, T_dof, T_loc, T_scale>::type stan::math::multi_student_t_lpdf ( const T_y &  y,
const T_dof &  nu,
const T_loc &  mu,
const T_scale &  Sigma 
)
inline

Definition at line 150 of file multi_student_t_lpdf.hpp.

§ multi_student_t_rng()

template<class RNG >
Eigen::VectorXd stan::math::multi_student_t_rng ( double  nu,
const Eigen::Matrix< double, Eigen::Dynamic, 1 > &  mu,
const Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > &  s,
RNG &  rng 
)
inline

Definition at line 27 of file multi_student_t_rng.hpp.

§ multinomial_log() [1/2]

template<bool propto, typename T_prob >
boost::math::tools::promote_args<T_prob>::type stan::math::multinomial_log ( const std::vector< int > &  ns,
const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &  theta 
)

Definition at line 23 of file multinomial_log.hpp.

§ multinomial_log() [2/2]

template<typename T_prob >
boost::math::tools::promote_args<T_prob>::type stan::math::multinomial_log ( const std::vector< int > &  ns,
const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &  theta 
)

Definition at line 54 of file multinomial_log.hpp.

§ multinomial_lpmf() [1/2]

template<bool propto, typename T_prob >
boost::math::tools::promote_args<T_prob>::type stan::math::multinomial_lpmf ( const std::vector< int > &  ns,
const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &  theta 
)

Definition at line 23 of file multinomial_lpmf.hpp.

§ multinomial_lpmf() [2/2]

template<typename T_prob >
boost::math::tools::promote_args<T_prob>::type stan::math::multinomial_lpmf ( const std::vector< int > &  ns,
const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &  theta 
)

Definition at line 54 of file multinomial_lpmf.hpp.

§ multinomial_rng()

template<class RNG >
std::vector<int> stan::math::multinomial_rng ( const Eigen::Matrix< double, Eigen::Dynamic, 1 > &  theta,
int  N,
RNG &  rng 
)
inline

Definition at line 22 of file multinomial_rng.hpp.

§ multiply() [1/21]

template<typename T , int R1, int C1>
Eigen::Matrix<fvar<T>, R1, C1> stan::math::multiply ( const Eigen::Matrix< fvar< T >, R1, C1 > &  m,
const fvar< T > &  c 
)
inline

Definition at line 20 of file multiply.hpp.

§ multiply() [2/21]

template<int R, int C, typename T >
boost::enable_if_c<boost::is_arithmetic<T>::value, Eigen::Matrix<double, R, C> >::type stan::math::multiply ( const Eigen::Matrix< double, R, C > &  m,
c 
)
inline

Return specified matrix multiplied by specified scalar.

Template Parameters
RRow type for matrix.
CColumn type for matrix.
Parameters
mMatrix.
cScalar.
Returns
Product of matrix and scalar.

Definition at line 25 of file multiply.hpp.

§ multiply() [3/21]

template<typename T , int R2, int C2>
Eigen::Matrix<fvar<T>, R2, C2> stan::math::multiply ( const Eigen::Matrix< fvar< T >, R2, C2 > &  m,
double  c 
)
inline

Definition at line 32 of file multiply.hpp.

§ multiply() [4/21]

template<int R, int C, typename T >
boost::enable_if_c<boost::is_arithmetic<T>::value, Eigen::Matrix<double, R, C> >::type stan::math::multiply ( c,
const Eigen::Matrix< double, R, C > &  m 
)
inline

Return specified scalar multiplied by specified matrix.

Template Parameters
RRow type for matrix.
CColumn type for matrix.
Parameters
cScalar.
mMatrix.
Returns
Product of scalar and matrix.

Definition at line 42 of file multiply.hpp.

§ multiply() [5/21]

template<typename T , int R1, int C1>
Eigen::Matrix<fvar<T>, R1, C1> stan::math::multiply ( const Eigen::Matrix< double, R1, C1 > &  m,
const fvar< T > &  c 
)
inline

Definition at line 44 of file multiply.hpp.

§ multiply() [6/21]

template<typename T , int R1, int C1>
Eigen::Matrix<fvar<T>, R1, C1> stan::math::multiply ( const fvar< T > &  c,
const Eigen::Matrix< fvar< T >, R1, C1 > &  m 
)
inline

Definition at line 56 of file multiply.hpp.

§ multiply() [7/21]

template<int R1, int C1, int R2, int C2>
Eigen::Matrix<double, R1, C2> stan::math::multiply ( const Eigen::Matrix< double, R1, C1 > &  m1,
const Eigen::Matrix< double, R2, C2 > &  m2 
)
inline

Return the product of the specified matrices.

The number of columns in the first matrix must be the same as the number of rows in the second matrix.

Parameters
m1First matrix.
m2Second matrix.
Returns
The product of the first and second matrices.
Exceptions
std::domain_errorif the number of columns of m1 does not match the number of rows of m2.

Definition at line 59 of file multiply.hpp.

§ multiply() [8/21]

template<typename T , int R1, int C1>
Eigen::Matrix<fvar<T>, R1, C1> stan::math::multiply ( double  c,
const Eigen::Matrix< fvar< T >, R1, C1 > &  m 
)
inline

Definition at line 63 of file multiply.hpp.

§ multiply() [9/21]

template<typename T , int R1, int C1>
Eigen::Matrix<fvar<T>, R1, C1> stan::math::multiply ( const fvar< T > &  c,
const Eigen::Matrix< double, R1, C1 > &  m 
)
inline

Definition at line 70 of file multiply.hpp.

§ multiply() [10/21]

template<typename T , int R1, int C1, int R2, int C2>
Eigen::Matrix<fvar<T>, R1, C2> stan::math::multiply ( const Eigen::Matrix< fvar< T >, R1, C1 > &  m1,
const Eigen::Matrix< fvar< T >, R2, C2 > &  m2 
)
inline

Definition at line 77 of file multiply.hpp.

§ multiply() [11/21]

template<int C1, int R2>
double stan::math::multiply ( const Eigen::Matrix< double, 1, C1 > &  rv,
const Eigen::Matrix< double, R2, 1 > &  v 
)
inline

Return the scalar product of the specified row vector and specified column vector.

The return is the same as the dot product. The two vectors must be the same size.

Parameters
rvRow vector.
vColumn vector.
Returns
Scalar result of multiplying row vector by column vector.
Exceptions
std::domain_errorif rv and v are not the same size.

Definition at line 77 of file multiply.hpp.

§ multiply() [12/21]

template<typename T , int R1, int C1, int R2, int C2>
Eigen::Matrix<fvar<T>, R1, C2> stan::math::multiply ( const Eigen::Matrix< fvar< T >, R1, C1 > &  m1,
const Eigen::Matrix< double, R2, C2 > &  m2 
)
inline

Definition at line 94 of file multiply.hpp.

§ multiply() [13/21]

template<typename T , int R1, int C1, int R2, int C2>
Eigen::Matrix<fvar<T>, R1, C2> stan::math::multiply ( const Eigen::Matrix< double, R1, C1 > &  m1,
const Eigen::Matrix< fvar< T >, R2, C2 > &  m2 
)
inline

Definition at line 111 of file multiply.hpp.

§ multiply() [14/21]

template<typename T , int C1, int R2>
fvar<T> stan::math::multiply ( const Eigen::Matrix< fvar< T >, 1, C1 > &  rv,
const Eigen::Matrix< fvar< T >, R2, 1 > &  v 
)
inline

Definition at line 130 of file multiply.hpp.

§ multiply() [15/21]

template<typename T , int C1, int R2>
fvar<T> stan::math::multiply ( const Eigen::Matrix< fvar< T >, 1, C1 > &  rv,
const Eigen::Matrix< double, R2, 1 > &  v 
)
inline

Definition at line 139 of file multiply.hpp.

§ multiply() [16/21]

template<typename T , int C1, int R2>
fvar<T> stan::math::multiply ( const Eigen::Matrix< double, 1, C1 > &  rv,
const Eigen::Matrix< fvar< T >, R2, 1 > &  v 
)
inline

Definition at line 148 of file multiply.hpp.

§ multiply() [17/21]

template<typename T1 , typename T2 >
boost::enable_if_c< (boost::is_scalar<T1>::value || boost::is_same<T1, var>::value) && (boost::is_scalar<T2>::value || boost::is_same<T2, var>::value), typename boost::math::tools::promote_args<T1, T2>::type>::type stan::math::multiply ( const T1 &  v,
const T2 &  c 
)
inline

Return the product of two scalars.

Template Parameters
T1scalar type of v
T2scalar type of c
Parameters
[in]vFirst scalar
[in]cSpecified scalar
Returns
Product of scalars

Definition at line 529 of file multiply.hpp.

§ multiply() [18/21]

template<typename T1 , typename T2 , int R2, int C2>
Eigen::Matrix<var, R2, C2> stan::math::multiply ( const T1 &  c,
const Eigen::Matrix< T2, R2, C2 > &  m 
)
inline

Return the product of scalar and matrix.

Template Parameters
T1scalar type v
T2scalar type matrix m
R2Rows matrix m
C2Columns matrix m
Parameters
[in]cSpecified scalar
[in]mMatrix
Returns
Product of scalar and matrix

Definition at line 545 of file multiply.hpp.

§ multiply() [19/21]

template<typename T1 , int R1, int C1, typename T2 >
Eigen::Matrix<var, R1, C1> stan::math::multiply ( const Eigen::Matrix< T1, R1, C1 > &  m,
const T2 &  c 
)
inline

Return the product of scalar and matrix.

Template Parameters
T1scalar type matrix m
T2scalar type v
R1Rows matrix m
C1Columns matrix m
Parameters
[in]cSpecified scalar
[in]mMatrix
Returns
Product of scalar and matrix

Definition at line 563 of file multiply.hpp.

§ multiply() [20/21]

template<typename TA , int RA, int CA, typename TB , int CB>
boost::enable_if_c<boost::is_same<TA, var>::value || boost::is_same<TB, var>::value, Eigen::Matrix<var, RA, CB> >::type stan::math::multiply ( const Eigen::Matrix< TA, RA, CA > &  A,
const Eigen::Matrix< TB, CA, CB > &  B 
)
inline

Return the product of two matrices.

Template Parameters
TAscalar type matrix A
RARows matrix A
CAColumns matrix A
TBscalar type matrix B
RBRows matrix B
CBColumns matrix B
Parameters
[in]AMatrix
[in]BMatrix
Returns
Product of scalar and matrix.

Definition at line 586 of file multiply.hpp.

§ multiply() [21/21]

template<typename TA , int CA, typename TB >
boost::enable_if_c<boost::is_same<TA, var>::value || boost::is_same<TB, var>::value, var>::type stan::math::multiply ( const Eigen::Matrix< TA, 1, CA > &  A,
const Eigen::Matrix< TB, CA, 1 > &  B 
)
inline

Return the scalar product of a row vector and a vector.

Template Parameters
TAscalar type row vector A
CAColumns matrix A
TBscalar type vector B
Parameters
[in]ARow vector
[in]BColumn vector
Returns
Scalar product of row vector and vector

Definition at line 616 of file multiply.hpp.

§ multiply_log() [1/7]

template<typename T >
fvar<T> stan::math::multiply_log ( const fvar< T > &  x1,
const fvar< T > &  x2 
)
inline

Definition at line 14 of file multiply_log.hpp.

§ multiply_log() [2/7]

template<typename T >
fvar<T> stan::math::multiply_log ( double  x1,
const fvar< T > &  x2 
)
inline

Definition at line 23 of file multiply_log.hpp.

§ multiply_log() [3/7]

template<typename T >
fvar<T> stan::math::multiply_log ( const fvar< T > &  x1,
double  x2 
)
inline

Definition at line 32 of file multiply_log.hpp.

§ multiply_log() [4/7]

template<typename T_a , typename T_b >
boost::math::tools::promote_args<T_a, T_b>::type stan::math::multiply_log ( const T_a  a,
const T_b  b 
)
inline

Calculated the value of the first argument times log of the second argument while behaving properly with 0 inputs.

$ a * \log b $.

\[ \mbox{multiply\_log}(x, y) = \begin{cases} 0 & \mbox{if } x=y=0\\ x\ln y & \mbox{if } x, y\neq0 \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN or } y = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{multiply\_log}(x, y)}{\partial x} = \begin{cases} \infty & \mbox{if } x=y=0\\ \ln y & \mbox{if } x, y\neq 0 \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN or } y = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{multiply\_log}(x, y)}{\partial y} = \begin{cases} \infty & \mbox{if } x=y=0\\ \frac{x}{y} & \mbox{if } x, y\neq 0 \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN or } y = \textrm{NaN} \end{cases} \]

Parameters
athe first variable
bthe second variable
Returns
a * log(b)

Definition at line 51 of file multiply_log.hpp.

§ multiply_log() [5/7]

var stan::math::multiply_log ( const var a,
const var b 
)
inline

Return the value of a*log(b).

When both a and b are 0, the value returned is 0. The partial deriviative with respect to a is log(b). The partial deriviative with respect to b is a/b. When a and b are both 0, this is set to Inf.

Parameters
aFirst variable.
bSecond variable.
Returns
Value of a*log(b)

Definition at line 73 of file multiply_log.hpp.

§ multiply_log() [6/7]

var stan::math::multiply_log ( const var a,
double  b 
)
inline

Return the value of a*log(b).

When both a and b are 0, the value returned is 0. The partial deriviative with respect to a is log(b).

Parameters
aFirst variable.
bSecond scalar.
Returns
Value of a*log(b)

Definition at line 86 of file multiply_log.hpp.

§ multiply_log() [7/7]

var stan::math::multiply_log ( double  a,
const var b 
)
inline

Return the value of a*log(b).

When both a and b are 0, the value returned is 0. The partial deriviative with respect to b is a/b. When a and b are both 0, this is set to Inf.

Parameters
aFirst scalar.
bSecond variable.
Returns
Value of a*log(b)

Definition at line 100 of file multiply_log.hpp.

§ multiply_lower_tri_self_transpose() [1/3]

template<typename T , int R, int C>
Eigen::Matrix<fvar<T>, R, R> stan::math::multiply_lower_tri_self_transpose ( const Eigen::Matrix< fvar< T >, R, C > &  m)
inline

Definition at line 17 of file multiply_lower_tri_self_transpose.hpp.

§ multiply_lower_tri_self_transpose() [2/3]

matrix_v stan::math::multiply_lower_tri_self_transpose ( const matrix_v L)
inline

Definition at line 19 of file multiply_lower_tri_self_transpose.hpp.

§ multiply_lower_tri_self_transpose() [3/3]

matrix_d stan::math::multiply_lower_tri_self_transpose ( const matrix_d L)
inline

Returns the result of multiplying the lower triangular portion of the input matrix by its own transpose.

Parameters
LMatrix to multiply.
Returns
The lower triangular values in L times their own transpose.
Exceptions
std::domain_errorIf the input matrix is not square.

Definition at line 19 of file multiply_lower_tri_self_transpose.hpp.

§ neg_binomial_2_ccdf_log()

template<typename T_n , typename T_location , typename T_precision >
return_type<T_location, T_precision>::type stan::math::neg_binomial_2_ccdf_log ( const T_n &  n,
const T_location &  mu,
const T_precision &  phi 
)

Definition at line 18 of file neg_binomial_2_ccdf_log.hpp.

§ neg_binomial_2_cdf()

template<typename T_n , typename T_location , typename T_precision >
return_type<T_location, T_precision>::type stan::math::neg_binomial_2_cdf ( const T_n &  n,
const T_location &  mu,
const T_precision &  phi 
)

Definition at line 26 of file neg_binomial_2_cdf.hpp.

§ neg_binomial_2_cdf_log()

template<typename T_n , typename T_location , typename T_precision >
return_type<T_location, T_precision>::type stan::math::neg_binomial_2_cdf_log ( const T_n &  n,
const T_location &  mu,
const T_precision &  phi 
)

Definition at line 19 of file neg_binomial_2_cdf_log.hpp.

§ neg_binomial_2_lccdf()

template<typename T_n , typename T_location , typename T_precision >
return_type<T_location, T_precision>::type stan::math::neg_binomial_2_lccdf ( const T_n &  n,
const T_location &  mu,
const T_precision &  phi 
)

Definition at line 18 of file neg_binomial_2_lccdf.hpp.

§ neg_binomial_2_lcdf()

template<typename T_n , typename T_location , typename T_precision >
return_type<T_location, T_precision>::type stan::math::neg_binomial_2_lcdf ( const T_n &  n,
const T_location &  mu,
const T_precision &  phi 
)

Definition at line 19 of file neg_binomial_2_lcdf.hpp.

§ neg_binomial_2_log() [1/2]

template<bool propto, typename T_n , typename T_location , typename T_precision >
return_type<T_location, T_precision>::type stan::math::neg_binomial_2_log ( const T_n &  n,
const T_location &  mu,
const T_precision &  phi 
)

Definition at line 37 of file neg_binomial_2_log.hpp.

§ neg_binomial_2_log() [2/2]

template<typename T_n , typename T_location , typename T_precision >
return_type<T_location, T_precision>::type stan::math::neg_binomial_2_log ( const T_n &  n,
const T_location &  mu,
const T_precision &  phi 
)
inline

Definition at line 134 of file neg_binomial_2_log.hpp.

§ neg_binomial_2_log_log() [1/2]

template<bool propto, typename T_n , typename T_log_location , typename T_precision >
return_type<T_log_location, T_precision>::type stan::math::neg_binomial_2_log_log ( const T_n &  n,
const T_log_location &  eta,
const T_precision &  phi 
)

Definition at line 34 of file neg_binomial_2_log_log.hpp.

§ neg_binomial_2_log_log() [2/2]

template<typename T_n , typename T_log_location , typename T_precision >
return_type<T_log_location, T_precision>::type stan::math::neg_binomial_2_log_log ( const T_n &  n,
const T_log_location &  eta,
const T_precision &  phi 
)
inline

Definition at line 126 of file neg_binomial_2_log_log.hpp.

§ neg_binomial_2_log_lpmf() [1/2]

template<bool propto, typename T_n , typename T_log_location , typename T_precision >
return_type<T_log_location, T_precision>::type stan::math::neg_binomial_2_log_lpmf ( const T_n &  n,
const T_log_location &  eta,
const T_precision &  phi 
)

Definition at line 34 of file neg_binomial_2_log_lpmf.hpp.

§ neg_binomial_2_log_lpmf() [2/2]

template<typename T_n , typename T_log_location , typename T_precision >
return_type<T_log_location, T_precision>::type stan::math::neg_binomial_2_log_lpmf ( const T_n &  n,
const T_log_location &  eta,
const T_precision &  phi 
)
inline

Definition at line 126 of file neg_binomial_2_log_lpmf.hpp.

§ neg_binomial_2_log_rng()

template<class RNG >
int stan::math::neg_binomial_2_log_rng ( double  eta,
double  phi,
RNG &  rng 
)
inline

Definition at line 27 of file neg_binomial_2_log_rng.hpp.

§ neg_binomial_2_lpmf() [1/2]

template<bool propto, typename T_n , typename T_location , typename T_precision >
return_type<T_location, T_precision>::type stan::math::neg_binomial_2_lpmf ( const T_n &  n,
const T_location &  mu,
const T_precision &  phi 
)

Definition at line 36 of file neg_binomial_2_lpmf.hpp.

§ neg_binomial_2_lpmf() [2/2]

template<typename T_n , typename T_location , typename T_precision >
return_type<T_location, T_precision>::type stan::math::neg_binomial_2_lpmf ( const T_n &  n,
const T_location &  mu,
const T_precision &  phi 
)
inline

Definition at line 128 of file neg_binomial_2_lpmf.hpp.

§ neg_binomial_2_rng()

template<class RNG >
int stan::math::neg_binomial_2_rng ( double  mu,
double  phi,
RNG &  rng 
)
inline

Definition at line 27 of file neg_binomial_2_rng.hpp.

§ neg_binomial_ccdf_log()

template<typename T_n , typename T_shape , typename T_inv_scale >
return_type<T_shape, T_inv_scale>::type stan::math::neg_binomial_ccdf_log ( const T_n &  n,
const T_shape &  alpha,
const T_inv_scale &  beta 
)

Definition at line 33 of file neg_binomial_ccdf_log.hpp.

§ neg_binomial_cdf()

template<typename T_n , typename T_shape , typename T_inv_scale >
return_type<T_shape, T_inv_scale>::type stan::math::neg_binomial_cdf ( const T_n &  n,
const T_shape &  alpha,
const T_inv_scale &  beta 
)

Definition at line 28 of file neg_binomial_cdf.hpp.

§ neg_binomial_cdf_log()

template<typename T_n , typename T_shape , typename T_inv_scale >
return_type<T_shape, T_inv_scale>::type stan::math::neg_binomial_cdf_log ( const T_n &  n,
const T_shape &  alpha,
const T_inv_scale &  beta 
)

Definition at line 33 of file neg_binomial_cdf_log.hpp.

§ neg_binomial_lccdf()

template<typename T_n , typename T_shape , typename T_inv_scale >
return_type<T_shape, T_inv_scale>::type stan::math::neg_binomial_lccdf ( const T_n &  n,
const T_shape &  alpha,
const T_inv_scale &  beta 
)

Definition at line 33 of file neg_binomial_lccdf.hpp.

§ neg_binomial_lcdf()

template<typename T_n , typename T_shape , typename T_inv_scale >
return_type<T_shape, T_inv_scale>::type stan::math::neg_binomial_lcdf ( const T_n &  n,
const T_shape &  alpha,
const T_inv_scale &  beta 
)

Definition at line 33 of file neg_binomial_lcdf.hpp.

§ neg_binomial_log() [1/2]

template<bool propto, typename T_n , typename T_shape , typename T_inv_scale >
return_type<T_shape, T_inv_scale>::type stan::math::neg_binomial_log ( const T_n &  n,
const T_shape &  alpha,
const T_inv_scale &  beta 
)

Definition at line 38 of file neg_binomial_log.hpp.

§ neg_binomial_log() [2/2]

template<typename T_n , typename T_shape , typename T_inv_scale >
return_type<T_shape, T_inv_scale>::type stan::math::neg_binomial_log ( const T_n &  n,
const T_shape &  alpha,
const T_inv_scale &  beta 
)
inline

Definition at line 169 of file neg_binomial_log.hpp.

§ neg_binomial_lpmf() [1/2]

template<bool propto, typename T_n , typename T_shape , typename T_inv_scale >
return_type<T_shape, T_inv_scale>::type stan::math::neg_binomial_lpmf ( const T_n &  n,
const T_shape &  alpha,
const T_inv_scale &  beta 
)

Definition at line 38 of file neg_binomial_lpmf.hpp.

§ neg_binomial_lpmf() [2/2]

template<typename T_n , typename T_shape , typename T_inv_scale >
return_type<T_shape, T_inv_scale>::type stan::math::neg_binomial_lpmf ( const T_n &  n,
const T_shape &  alpha,
const T_inv_scale &  beta 
)
inline

Definition at line 169 of file neg_binomial_lpmf.hpp.

§ neg_binomial_rng()

template<class RNG >
int stan::math::neg_binomial_rng ( double  alpha,
double  beta,
RNG &  rng 
)
inline

Definition at line 28 of file neg_binomial_rng.hpp.

§ negative_infinity()

double stan::math::negative_infinity ( )
inline

Return negative infinity.

Returns
Negative infinity.

Definition at line 130 of file constants.hpp.

§ nested_size()

static size_t stan::math::nested_size ( )
inlinestatic

Definition at line 10 of file nested_size.hpp.

§ normal_ccdf_log()

template<typename T_y , typename T_loc , typename T_scale >
return_type<T_y, T_loc, T_scale>::type stan::math::normal_ccdf_log ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma 
)

Definition at line 25 of file normal_ccdf_log.hpp.

§ normal_cdf()

template<typename T_y , typename T_loc , typename T_scale >
return_type<T_y, T_loc, T_scale>::type stan::math::normal_cdf ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma 
)

Calculates the normal cumulative distribution function for the given variate, location, and scale.

$\Phi(x) = \frac{1}{\sqrt{2 \pi}} \int_{-\inf}^x e^{-t^2/2} dt$.

Parameters
yA scalar variate.
muThe location of the normal distribution.
sigmaThe scale of the normal distriubtion
Returns
The unit normal cdf evaluated at the specified arguments.
Template Parameters
T_yType of y.
T_locType of mean parameter.
T_scaleType of standard deviation paramater.

Definition at line 38 of file normal_cdf.hpp.

§ normal_cdf_log()

template<typename T_y , typename T_loc , typename T_scale >
return_type<T_y, T_loc, T_scale>::type stan::math::normal_cdf_log ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma 
)

Definition at line 25 of file normal_cdf_log.hpp.

§ normal_lccdf()

template<typename T_y , typename T_loc , typename T_scale >
return_type<T_y, T_loc, T_scale>::type stan::math::normal_lccdf ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma 
)

Definition at line 25 of file normal_lccdf.hpp.

§ normal_lcdf()

template<typename T_y , typename T_loc , typename T_scale >
return_type<T_y, T_loc, T_scale>::type stan::math::normal_lcdf ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma 
)

Definition at line 25 of file normal_lcdf.hpp.

§ normal_log() [1/2]

template<bool propto, typename T_y , typename T_loc , typename T_scale >
return_type<T_y, T_loc, T_scale>::type stan::math::normal_log ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma 
)

The log of the normal density for the specified scalar(s) given the specified mean(s) and deviation(s).

y, mu, or sigma can each be either a scalar or a vector. Any vector inputs must be the same length.

The result log probability is defined to be the sum of the log probabilities for each observation/mean/deviation triple.

Parameters
y(Sequence of) scalar(s).
mu(Sequence of) location parameter(s) for the normal distribution.
sigma(Sequence of) scale parameters for the normal distribution.
Returns
The log of the product of the densities.
Exceptions
std::domain_errorif the scale is not positive.
Template Parameters
T_yUnderlying type of scalar in sequence.
T_locType of location parameter.

Definition at line 44 of file normal_log.hpp.

§ normal_log() [2/2]

template<typename T_y , typename T_loc , typename T_scale >
return_type<T_y, T_loc, T_scale>::type stan::math::normal_log ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma 
)
inline

Definition at line 120 of file normal_log.hpp.

§ normal_lpdf() [1/2]

template<bool propto, typename T_y , typename T_loc , typename T_scale >
return_type<T_y, T_loc, T_scale>::type stan::math::normal_lpdf ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma 
)

The log of the normal density for the specified scalar(s) given the specified mean(s) and deviation(s).

y, mu, or sigma can each be either a scalar or a vector. Any vector inputs must be the same length.

The result log probability is defined to be the sum of the log probabilities for each observation/mean/deviation triple.

Parameters
y(Sequence of) scalar(s).
mu(Sequence of) location parameter(s) for the normal distribution.
sigma(Sequence of) scale parameters for the normal distribution.
Returns
The log of the product of the densities.
Exceptions
std::domain_errorif the scale is not positive.
Template Parameters
T_yUnderlying type of scalar in sequence.
T_locType of location parameter.

Definition at line 44 of file normal_lpdf.hpp.

§ normal_lpdf() [2/2]

template<typename T_y , typename T_loc , typename T_scale >
return_type<T_y, T_loc, T_scale>::type stan::math::normal_lpdf ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma 
)
inline

Definition at line 120 of file normal_lpdf.hpp.

§ normal_rng()

template<class RNG >
double stan::math::normal_rng ( double  mu,
double  sigma,
RNG &  rng 
)
inline

Definition at line 18 of file normal_rng.hpp.

§ not_a_number()

double stan::math::not_a_number ( )
inline

Return (quiet) not-a-number.

Returns
Quiet not-a-number.

Definition at line 139 of file constants.hpp.

§ num_elements() [1/3]

template<typename T >
int stan::math::num_elements ( const T &  x)
inline

Returns 1, the number of elements in a primitive type.

Parameters
xArgument of primitive type.
Returns
1

Definition at line 18 of file num_elements.hpp.

§ num_elements() [2/3]

template<typename T , int R, int C>
int stan::math::num_elements ( const Eigen::Matrix< T, R, C > &  m)
inline

Returns the size of the specified matrix.

Parameters
margument matrix
Returns
size of matrix

Definition at line 30 of file num_elements.hpp.

§ num_elements() [3/3]

template<typename T >
int stan::math::num_elements ( const std::vector< T > &  v)
inline

Returns the number of elements in the specified vector.

This assumes it is not ragged and that each of its contained elements has the same number of elements.

Parameters
vargument vector
Returns
number of contained arguments

Definition at line 44 of file num_elements.hpp.

§ operator!()

bool stan::math::operator! ( const var a)
inline

Prefix logical negation for the value of variables (C++).

The expression (!a) is equivalent to negating the scalar value of the variable a.

Note that this is the only logical operator defined for variables. Overridden logical conjunction (&&) and disjunction (||) operators do not apply the same "short circuit" rules as the built-in logical operators.

\[ \mbox{operator!}(x) = \begin{cases} 0 & \mbox{if } x \neq 0 \\ 1 & \mbox{if } x = 0 \\[6pt] 0 & \mbox{if } x = \textrm{NaN} \end{cases} \]

Parameters
aVariable to negate.
Returns
True if variable is non-zero.

Definition at line 31 of file operator_unary_not.hpp.

§ operator!=() [1/6]

template<typename T >
bool stan::math::operator!= ( const fvar< T > &  x,
const fvar< T > &  y 
)
inline

Definition at line 12 of file operator_not_equal.hpp.

§ operator!=() [2/6]

template<typename T >
bool stan::math::operator!= ( const fvar< T > &  x,
double  y 
)
inline

Definition at line 19 of file operator_not_equal.hpp.

§ operator!=() [3/6]

template<typename T >
bool stan::math::operator!= ( double  x,
const fvar< T > &  y 
)
inline

Definition at line 26 of file operator_not_equal.hpp.

§ operator!=() [4/6]

bool stan::math::operator!= ( const var a,
const var b 
)
inline

Inequality operator comparing two variables' values (C++).

\[ \mbox{operator!=}(x, y) = \begin{cases} 0 & \mbox{if } x = y\\ 1 & \mbox{if } x \neq y \\[6pt] 0 & \mbox{if } x = \textrm{NaN or } y = \textrm{NaN} \end{cases} \]

Parameters
aFirst variable.
bSecond variable.
Returns
True if the first variable's value is not the same as the second's.

Definition at line 26 of file operator_not_equal.hpp.

§ operator!=() [5/6]

bool stan::math::operator!= ( const var a,
double  b 
)
inline

Inequality operator comparing a variable's value and a double (C++).

Parameters
aFirst variable.
bSecond value.
Returns
True if the first variable's value is not the same as the second value.

Definition at line 39 of file operator_not_equal.hpp.

§ operator!=() [6/6]

bool stan::math::operator!= ( double  a,
const var b 
)
inline

Inequality operator comparing a double and a variable's value (C++).

Parameters
aFirst value.
bSecond variable.
Returns
True if the first value is not the same as the second variable's value.

Definition at line 52 of file operator_not_equal.hpp.

§ operator*() [1/6]

template<typename T >
fvar<T> stan::math::operator* ( const fvar< T > &  x1,
const fvar< T > &  x2 
)
inline

Definition at line 12 of file operator_multiplication.hpp.

§ operator*() [2/6]

template<typename T >
fvar<T> stan::math::operator* ( double  x1,
const fvar< T > &  x2 
)
inline

Definition at line 20 of file operator_multiplication.hpp.

§ operator*() [3/6]

template<typename T >
fvar<T> stan::math::operator* ( const fvar< T > &  x1,
double  x2 
)
inline

Definition at line 27 of file operator_multiplication.hpp.

§ operator*() [4/6]

var stan::math::operator* ( const var a,
const var b 
)
inline

Multiplication operator for two variables (C++).

The partial derivatives are

$\frac{\partial}{\partial x} (x * y) = y$, and

$\frac{\partial}{\partial y} (x * y) = x$.

\[ \mbox{operator*}(x, y) = \begin{cases} xy & \mbox{if } -\infty\leq x, y \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN or } y = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{operator*}(x, y)}{\partial x} = \begin{cases} y & \mbox{if } -\infty\leq x, y \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN or } y = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{operator*}(x, y)}{\partial y} = \begin{cases} x & \mbox{if } -\infty\leq x, y \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN or } y = \textrm{NaN} \end{cases} \]

Parameters
aFirst variable operand.
bSecond variable operand.
Returns
Variable result of multiplying operands.

Definition at line 83 of file operator_multiplication.hpp.

§ operator*() [5/6]

var stan::math::operator* ( const var a,
double  b 
)
inline

Multiplication operator for a variable and a scalar (C++).

The partial derivative for the variable is

$\frac{\partial}{\partial x} (x * c) = c$, and

Parameters
aVariable operand.
bScalar operand.
Returns
Variable result of multiplying operands.

Definition at line 98 of file operator_multiplication.hpp.

§ operator*() [6/6]

var stan::math::operator* ( double  a,
const var b 
)
inline

Multiplication operator for a scalar and a variable (C++).

The partial derivative for the variable is

$\frac{\partial}{\partial y} (c * y) = c$.

Parameters
aScalar operand.
bVariable operand.
Returns
Variable result of multiplying the operands.

Definition at line 115 of file operator_multiplication.hpp.

§ operator+() [1/7]

template<typename T >
fvar<T> stan::math::operator+ ( const fvar< T > &  x1,
const fvar< T > &  x2 
)
inline

Definition at line 12 of file operator_addition.hpp.

§ operator+() [2/7]

template<typename T >
fvar<T> stan::math::operator+ ( double  x1,
const fvar< T > &  x2 
)
inline

Definition at line 19 of file operator_addition.hpp.

§ operator+() [3/7]

template<typename T >
fvar<T> stan::math::operator+ ( const fvar< T > &  x1,
double  x2 
)
inline

Definition at line 26 of file operator_addition.hpp.

§ operator+() [4/7]

var stan::math::operator+ ( const var a)
inline

Unary plus operator for variables (C++).

The function simply returns its input, because

$\frac{d}{dx} +x = \frac{d}{dx} x = 1$.

The effect of unary plus on a built-in C++ scalar type is integer promotion. Because variables are all double-precision floating point already, promotion is not necessary.

\[ \mbox{operator+}(x) = \begin{cases} x & \mbox{if } -\infty\leq x \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{operator+}(x)}{\partial x} = \begin{cases} 1 & \mbox{if } -\infty\leq x\leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

Parameters
aArgument variable.
Returns
The input reference.

Definition at line 43 of file operator_unary_plus.hpp.

§ operator+() [5/7]

var stan::math::operator+ ( const var a,
const var b 
)
inline

Addition operator for variables (C++).

The partial derivatives are defined by

$\frac{\partial}{\partial x} (x+y) = 1$, and

$\frac{\partial}{\partial y} (x+y) = 1$.

\[ \mbox{operator+}(x, y) = \begin{cases} x+y & \mbox{if } -\infty\leq x, y \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN or } y = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{operator+}(x, y)}{\partial x} = \begin{cases} 1 & \mbox{if } -\infty\leq x, y \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN or } y = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{operator+}(x, y)}{\partial y} = \begin{cases} 1 & \mbox{if } -\infty\leq x, y \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN or } y = \textrm{NaN} \end{cases} \]

Parameters
aFirst variable operand.
bSecond variable operand.
Returns
Variable result of adding two variables.

Definition at line 84 of file operator_addition.hpp.

§ operator+() [6/7]

var stan::math::operator+ ( const var a,
double  b 
)
inline

Addition operator for variable and scalar (C++).

The derivative with respect to the variable is

$\frac{d}{dx} (x + c) = 1$.

Parameters
aFirst variable operand.
bSecond scalar operand.
Returns
Result of adding variable and scalar.

Definition at line 99 of file operator_addition.hpp.

§ operator+() [7/7]

var stan::math::operator+ ( double  a,
const var b 
)
inline

Addition operator for scalar and variable (C++).

The derivative with respect to the variable is

$\frac{d}{dy} (c + y) = 1$.

Parameters
aFirst scalar operand.
bSecond variable operand.
Returns
Result of adding variable and scalar.

Definition at line 116 of file operator_addition.hpp.

§ operator++() [1/2]

var& stan::math::operator++ ( var a)
inline

Prefix increment operator for variables (C++).

Following C++, (++a) is defined to behave exactly as (a = a + 1.0) does, but is faster and uses less memory. In particular, the result is an assignable lvalue.

Parameters
aVariable to increment.
Returns
Reference the result of incrementing this input variable.

Definition at line 36 of file operator_unary_increment.hpp.

§ operator++() [2/2]

var stan::math::operator++ ( var a,
int   
)
inline

Postfix increment operator for variables (C++).

Following C++, the expression (a++) is defined to behave like the sequence of operations

var temp = a; a = a + 1.0; return temp;

Parameters
aVariable to increment.
Returns
Input variable.

Definition at line 52 of file operator_unary_increment.hpp.

§ operator-() [1/8]

template<typename T >
fvar<T> stan::math::operator- ( const fvar< T > &  x1,
const fvar< T > &  x2 
)
inline

Definition at line 12 of file operator_subtraction.hpp.

§ operator-() [2/8]

template<typename T >
fvar<T> stan::math::operator- ( const fvar< T > &  x)
inline

Definition at line 12 of file operator_unary_minus.hpp.

§ operator-() [3/8]

template<typename T >
fvar<T> stan::math::operator- ( double  x1,
const fvar< T > &  x2 
)
inline

Definition at line 19 of file operator_subtraction.hpp.

§ operator-() [4/8]

template<typename T >
fvar<T> stan::math::operator- ( const fvar< T > &  x1,
double  x2 
)
inline

Definition at line 26 of file operator_subtraction.hpp.

§ operator-() [5/8]

var stan::math::operator- ( const var a)
inline

Unary negation operator for variables (C++).

$\frac{d}{dx} -x = -1$.

\[ \mbox{operator-}(x) = \begin{cases} -x & \mbox{if } -\infty\leq x \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{operator-}(x)}{\partial x} = \begin{cases} -1 & \mbox{if } -\infty\leq x\leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

Parameters
aArgument variable.
Returns
Negation of variable.

Definition at line 51 of file operator_unary_negative.hpp.

§ operator-() [6/8]

var stan::math::operator- ( const var a,
const var b 
)
inline

Subtraction operator for variables (C++).

The partial derivatives are defined by

$\frac{\partial}{\partial x} (x-y) = 1$, and

$\frac{\partial}{\partial y} (x-y) = -1$.

\[ \mbox{operator-}(x, y) = \begin{cases} x-y & \mbox{if } -\infty\leq x, y \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN or } y = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{operator-}(x, y)}{\partial x} = \begin{cases} 1 & \mbox{if } -\infty\leq x, y \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN or } y = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{operator-}(x, y)}{\partial y} = \begin{cases} -1 & \mbox{if } -\infty\leq x, y \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN or } y = \textrm{NaN} \end{cases} \]

Parameters
aFirst variable operand.
bSecond variable operand.
Returns
Variable result of subtracting the second variable from the first.

Definition at line 99 of file operator_subtraction.hpp.

§ operator-() [7/8]

var stan::math::operator- ( const var a,
double  b 
)
inline

Subtraction operator for variable and scalar (C++).

The derivative for the variable is

$\frac{\partial}{\partial x} (x-c) = 1$, and

Parameters
aFirst variable operand.
bSecond scalar operand.
Returns
Result of subtracting the scalar from the variable.

Definition at line 114 of file operator_subtraction.hpp.

§ operator-() [8/8]

var stan::math::operator- ( double  a,
const var b 
)
inline

Subtraction operator for scalar and variable (C++).

The derivative for the variable is

$\frac{\partial}{\partial y} (c-y) = -1$, and

Parameters
aFirst scalar operand.
bSecond variable operand.
Returns
Result of sutracting a variable from a scalar.

Definition at line 131 of file operator_subtraction.hpp.

§ operator--() [1/2]

var& stan::math::operator-- ( var a)
inline

Prefix decrement operator for variables (C++).

Following C++, (–a) is defined to behave exactly as

a = a - 1.0)

does, but is faster and uses less memory. In particular, the result is an assignable lvalue.

Parameters
aVariable to decrement.
Returns
Reference the result of decrementing this input variable.

Definition at line 40 of file operator_unary_decrement.hpp.

§ operator--() [2/2]

var stan::math::operator-- ( var a,
int   
)
inline

Postfix decrement operator for variables (C++).

Following C++, the expression (a–) is defined to behave like the sequence of operations

var temp = a; a = a - 1.0; return temp;

Parameters
aVariable to decrement.
Returns
Input variable.

Definition at line 56 of file operator_unary_decrement.hpp.

§ operator/() [1/9]

template<typename T >
fvar<T> stan::math::operator/ ( const fvar< T > &  x1,
const fvar< T > &  x2 
)
inline

Definition at line 12 of file operator_division.hpp.

§ operator/() [2/9]

template<typename T >
fvar<T> stan::math::operator/ ( const fvar< T > &  x1,
double  x2 
)
inline

Definition at line 20 of file operator_division.hpp.

§ operator/() [3/9]

template<typename T >
fvar<T> stan::math::operator/ ( double  x1,
const fvar< T > &  x2 
)
inline

Definition at line 28 of file operator_division.hpp.

§ operator/() [4/9]

template<typename T , int R, int C>
Eigen::Matrix<fvar<T>, R, C> stan::math::operator/ ( const Eigen::Matrix< fvar< T >, R, C > &  v,
const fvar< T > &  c 
)
inline

Definition at line 51 of file divide.hpp.

§ operator/() [5/9]

template<typename T , int R, int C>
Eigen::Matrix<fvar<T>, R, C> stan::math::operator/ ( const Eigen::Matrix< fvar< T >, R, C > &  v,
double  c 
)
inline

Definition at line 57 of file divide.hpp.

§ operator/() [6/9]

template<typename T , int R, int C>
Eigen::Matrix<fvar<T>, R, C> stan::math::operator/ ( const Eigen::Matrix< double, R, C > &  v,
const fvar< T > &  c 
)
inline

Definition at line 63 of file divide.hpp.

§ operator/() [7/9]

var stan::math::operator/ ( const var a,
const var b 
)
inline

Division operator for two variables (C++).

The partial derivatives for the variables are

$\frac{\partial}{\partial x} (x/y) = 1/y$, and

$\frac{\partial}{\partial y} (x/y) = -x / y^2$.

\[ \mbox{operator/}(x, y) = \begin{cases} \frac{x}{y} & \mbox{if } -\infty\leq x, y \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN or } y = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{operator/}(x, y)}{\partial x} = \begin{cases} \frac{1}{y} & \mbox{if } -\infty\leq x, y \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN or } y = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{operator/}(x, y)}{\partial y} = \begin{cases} -\frac{x}{y^2} & \mbox{if } -\infty\leq x, y \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN or } y = \textrm{NaN} \end{cases} \]

Parameters
aFirst variable operand.
bSecond variable operand.
Returns
Variable result of dividing the first variable by the second.

Definition at line 96 of file operator_division.hpp.

§ operator/() [8/9]

var stan::math::operator/ ( const var a,
double  b 
)
inline

Division operator for dividing a variable by a scalar (C++).

The derivative with respect to the variable is

$\frac{\partial}{\partial x} (x/c) = 1/c$.

Parameters
aVariable operand.
bScalar operand.
Returns
Variable result of dividing the variable by the scalar.

Definition at line 111 of file operator_division.hpp.

§ operator/() [9/9]

var stan::math::operator/ ( double  a,
const var b 
)
inline

Division operator for dividing a scalar by a variable (C++).

The derivative with respect to the variable is

$\frac{d}{d y} (c/y) = -c / y^2$.

Parameters
aScalar operand.
bVariable operand.
Returns
Variable result of dividing the scalar by the variable.

Definition at line 128 of file operator_division.hpp.

§ operator<() [1/6]

template<typename T >
bool stan::math::operator< ( const fvar< T > &  x,
double  y 
)
inline

Definition at line 10 of file operator_less_than.hpp.

§ operator<() [2/6]

template<typename T >
bool stan::math::operator< ( double  x,
const fvar< T > &  y 
)
inline

Definition at line 16 of file operator_less_than.hpp.

§ operator<() [3/6]

template<typename T >
bool stan::math::operator< ( const fvar< T > &  x,
const fvar< T > &  y 
)
inline

Definition at line 22 of file operator_less_than.hpp.

§ operator<() [4/6]

bool stan::math::operator< ( const var a,
const var b 
)
inline

Less than operator comparing variables' values (C++).

\[ \mbox{operator\textless}(x, y) = \begin{cases} 0 & \mbox{if } x \geq y \\ 1 & \mbox{if } x < y \\[6pt] 0 & \mbox{if } x = \textrm{NaN or } y = \textrm{NaN} \end{cases} \]

Parameters
aFirst variable.
bSecond variable.
Returns
True if first variable's value is less than second's.

Definition at line 24 of file operator_less_than.hpp.

§ operator<() [5/6]

bool stan::math::operator< ( const var a,
double  b 
)
inline

Less than operator comparing variable's value and a double (C++).

Parameters
aFirst variable.
bSecond value.
Returns
True if first variable's value is less than second value.

Definition at line 36 of file operator_less_than.hpp.

§ operator<() [6/6]

bool stan::math::operator< ( double  a,
const var b 
)
inline

Less than operator comparing a double and variable's value (C++).

Parameters
aFirst value.
bSecond variable.
Returns
True if first value is less than second variable's value.

Definition at line 48 of file operator_less_than.hpp.

§ operator<=() [1/6]

template<typename T >
bool stan::math::operator<= ( const fvar< T > &  x,
const fvar< T > &  y 
)
inline

Definition at line 12 of file operator_less_than_or_equal.hpp.

§ operator<=() [2/6]

template<typename T >
bool stan::math::operator<= ( const fvar< T > &  x,
double  y 
)
inline

Definition at line 19 of file operator_less_than_or_equal.hpp.

§ operator<=() [3/6]

template<typename T >
bool stan::math::operator<= ( double  x,
const fvar< T > &  y 
)
inline

Definition at line 26 of file operator_less_than_or_equal.hpp.

§ operator<=() [4/6]

bool stan::math::operator<= ( const var a,
const var b 
)
inline

Less than or equal operator comparing two variables' values (C++).

\[ \mbox{operator\textless=}(x, y) = \begin{cases} 0 & \mbox{if } x > y\\ 1 & \mbox{if } x \leq y \\[6pt] 0 & \mbox{if } x = \textrm{NaN or } y = \textrm{NaN} \end{cases} \]

Parameters
aFirst variable.
bSecond variable.
Returns
True if first variable's value is less than or equal to the second's.

Definition at line 26 of file operator_less_than_or_equal.hpp.

§ operator<=() [5/6]

bool stan::math::operator<= ( const var a,
double  b 
)
inline

Less than or equal operator comparing a variable's value and a scalar (C++).

Parameters
aFirst variable.
bSecond value.
Returns
True if first variable's value is less than or equal to the second value.

Definition at line 39 of file operator_less_than_or_equal.hpp.

§ operator<=() [6/6]

bool stan::math::operator<= ( double  a,
const var b 
)
inline

Less than or equal operator comparing a double and variable's value (C++).

Parameters
aFirst value.
bSecond variable.
Returns
True if first value is less than or equal to the second variable's value.

Definition at line 52 of file operator_less_than_or_equal.hpp.

§ operator==() [1/6]

template<typename T >
bool stan::math::operator== ( const fvar< T > &  x,
const fvar< T > &  y 
)
inline

Definition at line 12 of file operator_equal.hpp.

§ operator==() [2/6]

template<typename T >
bool stan::math::operator== ( const fvar< T > &  x,
double  y 
)
inline

Definition at line 19 of file operator_equal.hpp.

§ operator==() [3/6]

bool stan::math::operator== ( const var a,
const var b 
)
inline

Equality operator comparing two variables' values (C++).

\[ \mbox{operator==}(x, y) = \begin{cases} 0 & \mbox{if } x \neq y\\ 1 & \mbox{if } x = y \\[6pt] 0 & \mbox{if } x = \textrm{NaN or } y = \textrm{NaN} \end{cases} \]

Parameters
aFirst variable.
bSecond variable.
Returns
True if the first variable's value is the same as the second's.

Definition at line 26 of file operator_equal.hpp.

§ operator==() [4/6]

template<typename T >
bool stan::math::operator== ( double  x,
const fvar< T > &  y 
)
inline

Definition at line 26 of file operator_equal.hpp.

§ operator==() [5/6]

bool stan::math::operator== ( const var a,
double  b 
)
inline

Equality operator comparing a variable's value and a double (C++).

Parameters
aFirst variable.
bSecond value.
Returns
True if the first variable's value is the same as the second value.

Definition at line 39 of file operator_equal.hpp.

§ operator==() [6/6]

bool stan::math::operator== ( double  a,
const var b 
)
inline

Equality operator comparing a scalar and a variable's value (C++).

Parameters
aFirst scalar.
bSecond variable.
Returns
True if the variable's value is equal to the scalar.

Definition at line 51 of file operator_equal.hpp.

§ operator>() [1/6]

template<typename T >
bool stan::math::operator> ( const fvar< T > &  x,
const fvar< T > &  y 
)
inline

Definition at line 12 of file operator_greater_than.hpp.

§ operator>() [2/6]

template<typename T >
bool stan::math::operator> ( const fvar< T > &  x,
double  y 
)
inline

Definition at line 19 of file operator_greater_than.hpp.

§ operator>() [3/6]

bool stan::math::operator> ( const var a,
const var b 
)
inline

Greater than operator comparing variables' values (C++).

\[ \mbox{operator\textgreater}(x, y) = \begin{cases} 0 & \mbox{if } x \leq y\\ 1 & \mbox{if } x > y \\[6pt] 0 & \mbox{if } x = \textrm{NaN or } y = \textrm{NaN} \end{cases} \]

Parameters
aFirst variable.
bSecond variable.
Returns
True if first variable's value is greater than second's.

Definition at line 25 of file operator_greater_than.hpp.

§ operator>() [4/6]

template<typename T >
bool stan::math::operator> ( double  x,
const fvar< T > &  y 
)
inline

Definition at line 26 of file operator_greater_than.hpp.

§ operator>() [5/6]

bool stan::math::operator> ( const var a,
double  b 
)
inline

Greater than operator comparing variable's value and double (C++).

Parameters
aFirst variable.
bSecond value.
Returns
True if first variable's value is greater than second value.

Definition at line 37 of file operator_greater_than.hpp.

§ operator>() [6/6]

bool stan::math::operator> ( double  a,
const var b 
)
inline

Greater than operator comparing a double and a variable's value (C++).

Parameters
aFirst value.
bSecond variable.
Returns
True if first value is greater than second variable's value.

Definition at line 49 of file operator_greater_than.hpp.

§ operator>=() [1/6]

template<typename T >
bool stan::math::operator>= ( const fvar< T > &  x,
const fvar< T > &  y 
)
inline

Definition at line 12 of file operator_greater_than_or_equal.hpp.

§ operator>=() [2/6]

template<typename T >
bool stan::math::operator>= ( const fvar< T > &  x,
double  y 
)
inline

Definition at line 19 of file operator_greater_than_or_equal.hpp.

§ operator>=() [3/6]

template<typename T >
bool stan::math::operator>= ( double  x,
const fvar< T > &  y 
)
inline

Definition at line 26 of file operator_greater_than_or_equal.hpp.

§ operator>=() [4/6]

bool stan::math::operator>= ( const var a,
const var b 
)
inline

Greater than or equal operator comparing two variables' values (C++).

\[ \mbox{operator\textgreater=}(x, y) = \begin{cases} 0 & \mbox{if } x < y\\ 1 & \mbox{if } x \geq y \\[6pt] 0 & \mbox{if } x = \textrm{NaN or } y = \textrm{NaN} \end{cases} \]

Parameters
aFirst variable.
bSecond variable.
Returns
True if first variable's value is greater than or equal to the second's.

Definition at line 27 of file operator_greater_than_or_equal.hpp.

§ operator>=() [5/6]

bool stan::math::operator>= ( const var a,
double  b 
)
inline

Greater than or equal operator comparing variable's value and double (C++).

Parameters
aFirst variable.
bSecond value.
Returns
True if first variable's value is greater than or equal to second value.

Definition at line 40 of file operator_greater_than_or_equal.hpp.

§ operator>=() [6/6]

bool stan::math::operator>= ( double  a,
const var b 
)
inline

Greater than or equal operator comparing double and variable's value (C++).

Parameters
aFirst value.
bSecond variable.
Returns
True if the first value is greater than or equal to the second variable's value.

Definition at line 53 of file operator_greater_than_or_equal.hpp.

§ ordered_constrain() [1/2]

template<typename T >
Eigen::Matrix<T, Eigen::Dynamic, 1> stan::math::ordered_constrain ( const Eigen::Matrix< T, Eigen::Dynamic, 1 > &  x)

Return an increasing ordered vector derived from the specified free vector.

The returned constrained vector will have the same dimensionality as the specified free vector.

Parameters
xFree vector of scalars.
Returns
Positive, increasing ordered vector.
Template Parameters
TType of scalar.

Definition at line 22 of file ordered_constrain.hpp.

§ ordered_constrain() [2/2]

template<typename T >
Eigen::Matrix<T, Eigen::Dynamic, 1> stan::math::ordered_constrain ( const Eigen::Matrix< T, Eigen::Dynamic, 1 > &  x,
T &  lp 
)
inline

Return a positive valued, increasing ordered vector derived from the specified free vector and increment the specified log probability reference with the log absolute Jacobian determinant of the transform.

The returned constrained vector will have the same dimensionality as the specified free vector.

Parameters
xFree vector of scalars.
lpLog probability reference.
Returns
Positive, increasing ordered vector.
Template Parameters
TType of scalar.

Definition at line 54 of file ordered_constrain.hpp.

§ ordered_free()

template<typename T >
Eigen::Matrix<T, Eigen::Dynamic, 1> stan::math::ordered_free ( const Eigen::Matrix< T, Eigen::Dynamic, 1 > &  y)

Return the vector of unconstrained scalars that transform to the specified positive ordered vector.

This function inverts the constraining operation defined in ordered_constrain(Matrix),

Parameters
yVector of positive, ordered scalars.
Returns
Free vector that transforms into the input vector.
Template Parameters
TType of scalar.
Exceptions
std::domain_errorif y is not a vector of positive, ordered scalars.

Definition at line 26 of file ordered_free.hpp.

§ ordered_logistic_log() [1/2]

template<bool propto, typename T_lambda , typename T_cut >
boost::math::tools::promote_args<T_lambda, T_cut>::type stan::math::ordered_logistic_log ( int  y,
const T_lambda &  lambda,
const Eigen::Matrix< T_cut, Eigen::Dynamic, 1 > &  c 
)

Returns the (natural) log probability of the specified integer outcome given the continuous location and specified cutpoints in an ordered logistic model.

Typically the continous location will be the dot product of a vector of regression coefficients and a vector of predictors for the outcome.

Template Parameters
proptoTrue if calculating up to a proportion.
T_locLocation type.
T_cutCut-point type.
Parameters
yOutcome.
lambdaLocation.
cPositive increasing vector of cutpoints.
Returns
Log probability of outcome given location and cutpoints.
Exceptions
std::domain_errorIf the outcome is not between 1 and the number of cutpoints plus 2; if the cutpoint vector is empty; if the cutpoint vector contains a non-positive, non-finite value; or if the cutpoint vector is not sorted in ascending order.

Definition at line 51 of file ordered_logistic_log.hpp.

§ ordered_logistic_log() [2/2]

template<typename T_lambda , typename T_cut >
boost::math::tools::promote_args<T_lambda, T_cut>::type stan::math::ordered_logistic_log ( int  y,
const T_lambda &  lambda,
const Eigen::Matrix< T_cut, Eigen::Dynamic, 1 > &  c 
)

Definition at line 86 of file ordered_logistic_log.hpp.

§ ordered_logistic_lpmf() [1/2]

template<bool propto, typename T_lambda , typename T_cut >
boost::math::tools::promote_args<T_lambda, T_cut>::type stan::math::ordered_logistic_lpmf ( int  y,
const T_lambda &  lambda,
const Eigen::Matrix< T_cut, Eigen::Dynamic, 1 > &  c 
)

Returns the (natural) log probability of the specified integer outcome given the continuous location and specified cutpoints in an ordered logistic model.

Typically the continous location will be the dot product of a vector of regression coefficients and a vector of predictors for the outcome.

Template Parameters
proptoTrue if calculating up to a proportion.
T_locLocation type.
T_cutCut-point type.
Parameters
yOutcome.
lambdaLocation.
cPositive increasing vector of cutpoints.
Returns
Log probability of outcome given location and cutpoints.
Exceptions
std::domain_errorIf the outcome is not between 1 and the number of cutpoints plus 2; if the cutpoint vector is empty; if the cutpoint vector contains a non-positive, non-finite value; or if the cutpoint vector is not sorted in ascending order.

Definition at line 57 of file ordered_logistic_lpmf.hpp.

§ ordered_logistic_lpmf() [2/2]

template<typename T_lambda , typename T_cut >
boost::math::tools::promote_args<T_lambda, T_cut>::type stan::math::ordered_logistic_lpmf ( int  y,
const T_lambda &  lambda,
const Eigen::Matrix< T_cut, Eigen::Dynamic, 1 > &  c 
)

Definition at line 92 of file ordered_logistic_lpmf.hpp.

§ ordered_logistic_rng()

template<class RNG >
int stan::math::ordered_logistic_rng ( double  eta,
const Eigen::Matrix< double, Eigen::Dynamic, 1 > &  c,
RNG &  rng 
)
inline

Definition at line 23 of file ordered_logistic_rng.hpp.

§ out_of_range()

void stan::math::out_of_range ( const char *  function,
int  max,
int  index,
const char *  msg1 = "",
const char *  msg2 = "" 
)
inline

Throw an out_of_range exception with a consistently formatted message.

This is an abstraction for all Stan functions to use when throwing out of range. This will allow us to change the behavior for all functions at once.

The message is: "<function>: index <index> out of range; expecting index to be between " "1 and <max><msg1><msg2>"

Parameters
functionName of the function
maxMax
indexIndex
msg1Message to print. Default is "".
msg2Message to print. Default is "".
Exceptions
std::out_of_rangewith message.

Definition at line 31 of file out_of_range.hpp.

§ owens_t() [1/7]

template<typename T >
fvar<T> stan::math::owens_t ( const fvar< T > &  x1,
const fvar< T > &  x2 
)
inline

Return Owen's T function applied to the specified arguments.

Parameters
x1First argument.
x2Second argument.
Returns
Owen's T function applied to the specified arguments.

Definition at line 23 of file owens_t.hpp.

§ owens_t() [2/7]

template<typename T >
fvar<T> stan::math::owens_t ( double  x1,
const fvar< T > &  x2 
)
inline

Return Owen's T function applied to the specified arguments.

Parameters
x1First argument.
x2Second argument.
Returns
Owen's T function applied to the specified arguments.

Definition at line 44 of file owens_t.hpp.

§ owens_t() [3/7]

double stan::math::owens_t ( double  h,
double  a 
)
inline

Return the result of applying Owen's T function to the specified arguments.

Used to compute the cumulative density function for the skew normal distribution.

\[ \mbox{owens\_t}(h, a) = \begin{cases} \mbox{owens\_t}(h, a) & \mbox{if } -\infty\leq h, a \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } h = \textrm{NaN or } a = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{owens\_t}(h, a)}{\partial h} = \begin{cases} \frac{\partial\, \mbox{owens\_t}(h, a)}{\partial h} & \mbox{if } -\infty\leq h, a\leq \infty \\[6pt] \textrm{NaN} & \mbox{if } h = \textrm{NaN or } a = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{owens\_t}(h, a)}{\partial a} = \begin{cases} \frac{\partial\, \mbox{owens\_t}(h, a)}{\partial a} & \mbox{if } -\infty\leq h, a\leq \infty \\[6pt] \textrm{NaN} & \mbox{if } h = \textrm{NaN or } a = \textrm{NaN} \end{cases} \]

\[ \mbox{owens\_t}(h, a) = \frac{1}{2\pi} \int_0^a \frac{\exp(-\frac{1}{2}h^2(1+x^2))}{1+x^2}dx \]

\[ \frac{\partial \, \mbox{owens\_t}(h, a)}{\partial h} = -\frac{1}{2\sqrt{2\pi}} \operatorname{erf}\left(\frac{ha}{\sqrt{2}}\right) \exp\left(-\frac{h^2}{2}\right) \]

\[ \frac{\partial \, \mbox{owens\_t}(h, a)}{\partial a} = \frac{\exp\left(-\frac{1}{2}h^2(1+a^2)\right)}{2\pi (1+a^2)} \]

Parameters
hFirst argument
aSecond argument
Returns
Owen's T function applied to the arguments.

Definition at line 59 of file owens_t.hpp.

§ owens_t() [4/7]

template<typename T >
fvar<T> stan::math::owens_t ( const fvar< T > &  x1,
double  x2 
)
inline

Return Owen's T function applied to the specified arguments.

Parameters
x1First argument.
x2Second argument.
Returns
Owen's T function applied to the specified arguments.

Definition at line 62 of file owens_t.hpp.

§ owens_t() [5/7]

var stan::math::owens_t ( const var h,
const var a 
)
inline

The Owen's T function of h and a.

Used to compute the cumulative density function for the skew normal distribution.

Parameters
hvar parameter.
avar parameter.
Returns
The Owen's T function.

Definition at line 66 of file owens_t.hpp.

§ owens_t() [6/7]

var stan::math::owens_t ( const var h,
double  a 
)
inline

The Owen's T function of h and a.

Used to compute the cumulative density function for the skew normal distribution.

Parameters
hvar parameter.
adouble parameter.
Returns
The Owen's T function.

Definition at line 80 of file owens_t.hpp.

§ owens_t() [7/7]

var stan::math::owens_t ( double  h,
const var a 
)
inline

The Owen's T function of h and a.

Used to compute the cumulative density function for the skew normal distribution.

Parameters
hdouble parameter.
avar parameter.
Returns
The Owen's T function.

Definition at line 94 of file owens_t.hpp.

§ pareto_ccdf_log()

template<typename T_y , typename T_scale , typename T_shape >
return_type<T_y, T_scale, T_shape>::type stan::math::pareto_ccdf_log ( const T_y &  y,
const T_scale &  y_min,
const T_shape &  alpha 
)

Definition at line 25 of file pareto_ccdf_log.hpp.

§ pareto_cdf()

template<typename T_y , typename T_scale , typename T_shape >
return_type<T_y, T_scale, T_shape>::type stan::math::pareto_cdf ( const T_y &  y,
const T_scale &  y_min,
const T_shape &  alpha 
)

Definition at line 25 of file pareto_cdf.hpp.

§ pareto_cdf_log()

template<typename T_y , typename T_scale , typename T_shape >
return_type<T_y, T_scale, T_shape>::type stan::math::pareto_cdf_log ( const T_y &  y,
const T_scale &  y_min,
const T_shape &  alpha 
)

Definition at line 25 of file pareto_cdf_log.hpp.

§ pareto_lccdf()

template<typename T_y , typename T_scale , typename T_shape >
return_type<T_y, T_scale, T_shape>::type stan::math::pareto_lccdf ( const T_y &  y,
const T_scale &  y_min,
const T_shape &  alpha 
)

Definition at line 25 of file pareto_lccdf.hpp.

§ pareto_lcdf()

template<typename T_y , typename T_scale , typename T_shape >
return_type<T_y, T_scale, T_shape>::type stan::math::pareto_lcdf ( const T_y &  y,
const T_scale &  y_min,
const T_shape &  alpha 
)

Definition at line 25 of file pareto_lcdf.hpp.

§ pareto_log() [1/2]

template<bool propto, typename T_y , typename T_scale , typename T_shape >
return_type<T_y, T_scale, T_shape>::type stan::math::pareto_log ( const T_y &  y,
const T_scale &  y_min,
const T_shape &  alpha 
)

Definition at line 29 of file pareto_log.hpp.

§ pareto_log() [2/2]

template<typename T_y , typename T_scale , typename T_shape >
return_type<T_y, T_scale, T_shape>::type stan::math::pareto_log ( const T_y &  y,
const T_scale &  y_min,
const T_shape &  alpha 
)
inline

Definition at line 119 of file pareto_log.hpp.

§ pareto_lpdf() [1/2]

template<bool propto, typename T_y , typename T_scale , typename T_shape >
return_type<T_y, T_scale, T_shape>::type stan::math::pareto_lpdf ( const T_y &  y,
const T_scale &  y_min,
const T_shape &  alpha 
)

Definition at line 29 of file pareto_lpdf.hpp.

§ pareto_lpdf() [2/2]

template<typename T_y , typename T_scale , typename T_shape >
return_type<T_y, T_scale, T_shape>::type stan::math::pareto_lpdf ( const T_y &  y,
const T_scale &  y_min,
const T_shape &  alpha 
)
inline

Definition at line 119 of file pareto_lpdf.hpp.

§ pareto_rng()

template<class RNG >
double stan::math::pareto_rng ( double  y_min,
double  alpha,
RNG &  rng 
)
inline

Definition at line 20 of file pareto_rng.hpp.

§ pareto_type_2_ccdf_log()

template<typename T_y , typename T_loc , typename T_scale , typename T_shape >
return_type<T_y, T_loc, T_scale, T_shape>::type stan::math::pareto_type_2_ccdf_log ( const T_y &  y,
const T_loc &  mu,
const T_scale &  lambda,
const T_shape &  alpha 
)

Definition at line 26 of file pareto_type_2_ccdf_log.hpp.

§ pareto_type_2_cdf()

template<typename T_y , typename T_loc , typename T_scale , typename T_shape >
return_type<T_y, T_loc, T_scale, T_shape>::type stan::math::pareto_type_2_cdf ( const T_y &  y,
const T_loc &  mu,
const T_scale &  lambda,
const T_shape &  alpha 
)

Definition at line 27 of file pareto_type_2_cdf.hpp.

§ pareto_type_2_cdf_log()

template<typename T_y , typename T_loc , typename T_scale , typename T_shape >
return_type<T_y, T_loc, T_scale, T_shape>::type stan::math::pareto_type_2_cdf_log ( const T_y &  y,
const T_loc &  mu,
const T_scale &  lambda,
const T_shape &  alpha 
)

Definition at line 26 of file pareto_type_2_cdf_log.hpp.

§ pareto_type_2_lccdf()

template<typename T_y , typename T_loc , typename T_scale , typename T_shape >
return_type<T_y, T_loc, T_scale, T_shape>::type stan::math::pareto_type_2_lccdf ( const T_y &  y,
const T_loc &  mu,
const T_scale &  lambda,
const T_shape &  alpha 
)

Definition at line 26 of file pareto_type_2_lccdf.hpp.

§ pareto_type_2_lcdf()

template<typename T_y , typename T_loc , typename T_scale , typename T_shape >
return_type<T_y, T_loc, T_scale, T_shape>::type stan::math::pareto_type_2_lcdf ( const T_y &  y,
const T_loc &  mu,
const T_scale &  lambda,
const T_shape &  alpha 
)

Definition at line 26 of file pareto_type_2_lcdf.hpp.

§ pareto_type_2_log() [1/2]

template<bool propto, typename T_y , typename T_loc , typename T_scale , typename T_shape >
return_type<T_y, T_loc, T_scale, T_shape>::type stan::math::pareto_type_2_log ( const T_y &  y,
const T_loc &  mu,
const T_scale &  lambda,
const T_shape &  alpha 
)

Definition at line 29 of file pareto_type_2_log.hpp.

§ pareto_type_2_log() [2/2]

template<typename T_y , typename T_loc , typename T_scale , typename T_shape >
return_type<T_y, T_loc, T_scale, T_shape>::type stan::math::pareto_type_2_log ( const T_y &  y,
const T_loc &  mu,
const T_scale &  lambda,
const T_shape &  alpha 
)
inline

Definition at line 133 of file pareto_type_2_log.hpp.

§ pareto_type_2_lpdf() [1/2]

template<bool propto, typename T_y , typename T_loc , typename T_scale , typename T_shape >
return_type<T_y, T_loc, T_scale, T_shape>::type stan::math::pareto_type_2_lpdf ( const T_y &  y,
const T_loc &  mu,
const T_scale &  lambda,
const T_shape &  alpha 
)

Definition at line 29 of file pareto_type_2_lpdf.hpp.

§ pareto_type_2_lpdf() [2/2]

template<typename T_y , typename T_loc , typename T_scale , typename T_shape >
return_type<T_y, T_loc, T_scale, T_shape>::type stan::math::pareto_type_2_lpdf ( const T_y &  y,
const T_loc &  mu,
const T_scale &  lambda,
const T_shape &  alpha 
)
inline

Definition at line 133 of file pareto_type_2_lpdf.hpp.

§ pareto_type_2_rng()

template<class RNG >
double stan::math::pareto_type_2_rng ( double  mu,
double  lambda,
double  alpha,
RNG &  rng 
)
inline

Definition at line 21 of file pareto_type_2_rng.hpp.

§ partial_derivative()

template<typename T , typename F >
void stan::math::partial_derivative ( const F &  f,
const Eigen::Matrix< T, Eigen::Dynamic, 1 > &  x,
int  n,
T &  fx,
T &  dfx_dxn 
)

Return the partial derivative of the specified multiivariate function at the specified argument.

Template Parameters
TArgument type
FFunction type
Parameters
fFunction
[in]xArgument vector
[in]nIndex of argument with which to take derivative
[out]fxValue of function applied to argument
[out]dfx_dxnValue of partial derivative

Definition at line 26 of file partial_derivative.hpp.

§ Phi() [1/4]

template<typename T >
fvar<T> stan::math::Phi ( const fvar< T > &  x)
inline

Definition at line 12 of file Phi.hpp.

§ Phi() [2/4]

double stan::math::Phi ( double  x)
inline

The unit normal cumulative distribution function.

The return value for a specified input is the probability that a random unit normal variate is less than or equal to the specified value, defined by

$\Phi(x) = \int_{-\infty}^x \mbox{\sf Norm}(x|0, 1) \ dx$

This function can be used to implement the inverse link function for probit regression.

Phi will underflow to 0 below -37.5 and overflow to 1 above 8

Parameters
xArgument.
Returns
Probability random sample is less than or equal to argument.

Definition at line 28 of file Phi.hpp.

§ Phi() [3/4]

template<typename T >
apply_scalar_unary<Phi_fun, T>::return_t stan::math::Phi ( const T &  x)
inline

Vectorized version of Phi().

Parameters
xContainer.
Template Parameters
TContainer type.
Returns
Unit normal CDF of each value in x.

Definition at line 31 of file Phi.hpp.

§ Phi() [4/4]

var stan::math::Phi ( const var a)
inline

The unit normal cumulative density function for variables (stan).

See Phi() for the double-based version.

The derivative is the unit normal density function,

$\frac{d}{dx} \Phi(x) = \mbox{\sf Norm}(x|0, 1) = \frac{1}{\sqrt{2\pi}} \exp(-\frac{1}{2} x^2)$.

\[ \mbox{Phi}(x) = \begin{cases} 0 & \mbox{if } x < -37.5 \\ \Phi(x) & \mbox{if } -37.5 \leq x \leq 8.25 \\ 1 & \mbox{if } x > 8.25 \\[6pt] \textrm{error} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{Phi}(x)}{\partial x} = \begin{cases} 0 & \mbox{if } x < -27.5 \\ \frac{\partial\, \Phi(x)}{\partial x} & \mbox{if } -27.5 \leq x \leq 27.5 \\ 0 & \mbox{if } x > 27.5 \\[6pt] \textrm{error} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \Phi(x) = \frac{1}{\sqrt{2\pi}} \int_{0}^{x} e^{-t^2/2} dt \]

\[ \frac{\partial \, \Phi(x)}{\partial x} = \frac{e^{-x^2/2}}{\sqrt{2\pi}} \]

Parameters
aVariable argument.
Returns
The unit normal cdf evaluated at the specified argument.

Definition at line 66 of file Phi.hpp.

§ Phi_approx() [1/5]

double stan::math::Phi_approx ( double  x)
inline

Return an approximation of the unit normal CDF.

http://www.jiem.org/index.php/jiem/article/download/60/27

This function can be used to implement the inverse link function for probit regression.

Parameters
xArgument.
Returns
Probability random sample is less than or equal to argument.

Definition at line 21 of file Phi_approx.hpp.

§ Phi_approx() [2/5]

template<typename T >
fvar<T> stan::math::Phi_approx ( const fvar< T > &  x)
inline

Return an approximation of the unit normal cumulative distribution function (CDF).

Template Parameters
Tscalar type of forward-mode autodiff variable argument.
Parameters
xargument
Returns
approximate probability random sample is less than or equal to argument

Definition at line 22 of file Phi_approx.hpp.

§ Phi_approx() [3/5]

double stan::math::Phi_approx ( int  x)
inline

Return an approximation of the unit normal CDF.

Parameters
xargument.
Returns
approximate probability random sample is less than or equal to argument.

Definition at line 33 of file Phi_approx.hpp.

§ Phi_approx() [4/5]

template<typename T >
apply_scalar_unary<Phi_approx_fun, T>::return_t stan::math::Phi_approx ( const T &  x)
inline

Return the elementwise application of Phi_approx() to specified argument container.

The return type promotes the underlying scalar argument type to double if it is an integer, and otherwise is the argument type.

Template Parameters
Tcontainer type
Parameters
xcontainer
Returns
elementwise Phi_approx of container elements

Definition at line 40 of file Phi_approx.hpp.

§ Phi_approx() [5/5]

var stan::math::Phi_approx ( const var a)
inline

Approximation of the unit normal CDF for variables (stan).

http://www.jiem.org/index.php/jiem/article/download/60/27

\[ \mbox{Phi\_approx}(x) = \begin{cases} \Phi_{\mbox{\footnotesize approx}}(x) & \mbox{if } -\infty\leq x\leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{Phi\_approx}(x)}{\partial x} = \begin{cases} \frac{\partial\, \Phi_{\mbox{\footnotesize approx}}(x)}{\partial x} & \mbox{if } -\infty\leq x\leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \Phi_{\mbox{\footnotesize approx}}(x) = \mbox{logit}^{-1}(0.07056 \, x^3 + 1.5976 \, x) \]

\[ \frac{\partial \, \Phi_{\mbox{\footnotesize approx}}(x)}{\partial x} = -\Phi_{\mbox{\footnotesize approx}}^2(x) e^{-0.07056x^3 - 1.5976x}(-0.21168x^2-1.5976) \]

Parameters
aVariable argument.
Returns
The corresponding unit normal cdf approximation.

Definition at line 47 of file Phi_approx.hpp.

§ pi()

double stan::math::pi ( )
inline

Return the value of pi.

Returns
Pi.

Definition at line 85 of file constants.hpp.

§ poisson_ccdf_log()

template<typename T_n , typename T_rate >
return_type<T_rate>::type stan::math::poisson_ccdf_log ( const T_n &  n,
const T_rate &  lambda 
)

Definition at line 27 of file poisson_ccdf_log.hpp.

§ poisson_cdf()

template<typename T_n , typename T_rate >
return_type<T_rate>::type stan::math::poisson_cdf ( const T_n &  n,
const T_rate &  lambda 
)

Definition at line 27 of file poisson_cdf.hpp.

§ poisson_cdf_log()

template<typename T_n , typename T_rate >
return_type<T_rate>::type stan::math::poisson_cdf_log ( const T_n &  n,
const T_rate &  lambda 
)

Definition at line 26 of file poisson_cdf_log.hpp.

§ poisson_lccdf()

template<typename T_n , typename T_rate >
return_type<T_rate>::type stan::math::poisson_lccdf ( const T_n &  n,
const T_rate &  lambda 
)

Definition at line 27 of file poisson_lccdf.hpp.

§ poisson_lcdf()

template<typename T_n , typename T_rate >
return_type<T_rate>::type stan::math::poisson_lcdf ( const T_n &  n,
const T_rate &  lambda 
)

Definition at line 26 of file poisson_lcdf.hpp.

§ poisson_log() [1/2]

template<bool propto, typename T_n , typename T_rate >
return_type<T_rate>::type stan::math::poisson_log ( const T_n &  n,
const T_rate &  lambda 
)

Definition at line 29 of file poisson_log.hpp.

§ poisson_log() [2/2]

template<typename T_n , typename T_rate >
return_type<T_rate>::type stan::math::poisson_log ( const T_n &  n,
const T_rate &  lambda 
)
inline

Definition at line 84 of file poisson_log.hpp.

§ poisson_log_log() [1/2]

template<bool propto, typename T_n , typename T_log_rate >
return_type<T_log_rate>::type stan::math::poisson_log_log ( const T_n &  n,
const T_log_rate &  alpha 
)

Definition at line 31 of file poisson_log_log.hpp.

§ poisson_log_log() [2/2]

template<typename T_n , typename T_log_rate >
return_type<T_log_rate>::type stan::math::poisson_log_log ( const T_n &  n,
const T_log_rate &  alpha 
)
inline

Definition at line 96 of file poisson_log_log.hpp.

§ poisson_log_lpmf() [1/2]

template<bool propto, typename T_n , typename T_log_rate >
return_type<T_log_rate>::type stan::math::poisson_log_lpmf ( const T_n &  n,
const T_log_rate &  alpha 
)

Definition at line 31 of file poisson_log_lpmf.hpp.

§ poisson_log_lpmf() [2/2]

template<typename T_n , typename T_log_rate >
return_type<T_log_rate>::type stan::math::poisson_log_lpmf ( const T_n &  n,
const T_log_rate &  alpha 
)
inline

Definition at line 96 of file poisson_log_lpmf.hpp.

§ poisson_log_rng()

template<class RNG >
int stan::math::poisson_log_rng ( double  alpha,
RNG &  rng 
)
inline

Definition at line 21 of file poisson_log_rng.hpp.

§ poisson_lpmf() [1/2]

template<bool propto, typename T_n , typename T_rate >
return_type<T_rate>::type stan::math::poisson_lpmf ( const T_n &  n,
const T_rate &  lambda 
)

Definition at line 29 of file poisson_lpmf.hpp.

§ poisson_lpmf() [2/2]

template<typename T_n , typename T_rate >
return_type<T_rate>::type stan::math::poisson_lpmf ( const T_n &  n,
const T_rate &  lambda 
)
inline

Definition at line 84 of file poisson_lpmf.hpp.

§ poisson_rng()

template<class RNG >
int stan::math::poisson_rng ( double  lambda,
RNG &  rng 
)
inline

Definition at line 22 of file poisson_rng.hpp.

§ positive_constrain() [1/2]

template<typename T >
T stan::math::positive_constrain ( const T  x)
inline

Return the positive value for the specified unconstrained input.

The transform applied is

$f(x) = \exp(x)$.

Parameters
xArbitrary input scalar.
Returns
Input transformed to be positive.

Definition at line 20 of file positive_constrain.hpp.

§ positive_constrain() [2/2]

template<typename T >
T stan::math::positive_constrain ( const T  x,
T &  lp 
)
inline

Return the positive value for the specified unconstrained input, incrementing the scalar reference with the log absolute Jacobian determinant.

See positive_constrain(T) for details of the transform. The log absolute Jacobian determinant is

$\log | \frac{d}{dx} \mbox{exp}(x) | = \log | \mbox{exp}(x) | = x$.

Parameters
xArbitrary input scalar.
lpLog probability reference.
Returns
Input transformed to be positive.
Template Parameters
TType of scalar.

Definition at line 42 of file positive_constrain.hpp.

§ positive_free()

template<typename T >
T stan::math::positive_free ( const T  y)
inline

Return the unconstrained value corresponding to the specified positive-constrained value.

The transform is the inverse of the transform $f$ applied by positive_constrain(T), namely

$f^{-1}(x) = \log(x)$.

The input is validated using check_positive().

Parameters
yInput scalar.
Returns
Unconstrained value that produces the input when constrained.
Template Parameters
TType of scalar.
Exceptions
std::domain_errorif the variable is negative.

Definition at line 28 of file positive_free.hpp.

§ positive_infinity()

double stan::math::positive_infinity ( )
inline

Return positive infinity.

Returns
Positive infinity.

Definition at line 121 of file constants.hpp.

§ positive_ordered_constrain() [1/2]

template<typename T >
Eigen::Matrix<T, Eigen::Dynamic, 1> stan::math::positive_ordered_constrain ( const Eigen::Matrix< T, Eigen::Dynamic, 1 > &  x)

Return an increasing positive ordered vector derived from the specified free vector.

The returned constrained vector will have the same dimensionality as the specified free vector.

Parameters
xFree vector of scalars.
Returns
Positive, increasing ordered vector.
Template Parameters
TType of scalar.

Definition at line 22 of file positive_ordered_constrain.hpp.

§ positive_ordered_constrain() [2/2]

template<typename T >
Eigen::Matrix<T, Eigen::Dynamic, 1> stan::math::positive_ordered_constrain ( const Eigen::Matrix< T, Eigen::Dynamic, 1 > &  x,
T &  lp 
)
inline

Return a positive valued, increasing positive ordered vector derived from the specified free vector and increment the specified log probability reference with the log absolute Jacobian determinant of the transform.

The returned constrained vector will have the same dimensionality as the specified free vector.

Parameters
xFree vector of scalars.
lpLog probability reference.
Returns
Positive, increasing ordered vector.
Template Parameters
TType of scalar.

Definition at line 53 of file positive_ordered_constrain.hpp.

§ positive_ordered_free()

template<typename T >
Eigen::Matrix<T, Eigen::Dynamic, 1> stan::math::positive_ordered_free ( const Eigen::Matrix< T, Eigen::Dynamic, 1 > &  y)

Return the vector of unconstrained scalars that transform to the specified positive ordered vector.

This function inverts the constraining operation defined in positive_ordered_constrain(Matrix),

Parameters
yVector of positive, ordered scalars.
Returns
Free vector that transforms into the input vector.
Template Parameters
TType of scalar.
Exceptions
std::domain_errorif y is not a vector of positive, ordered scalars.

Definition at line 26 of file positive_ordered_free.hpp.

§ pow() [1/6]

template<typename T >
fvar<T> stan::math::pow ( const fvar< T > &  x1,
const fvar< T > &  x2 
)
inline

Definition at line 17 of file pow.hpp.

§ pow() [2/6]

template<typename T >
fvar<T> stan::math::pow ( double  x1,
const fvar< T > &  x2 
)
inline

Definition at line 29 of file pow.hpp.

§ pow() [3/6]

template<typename T >
fvar<T> stan::math::pow ( const fvar< T > &  x1,
double  x2 
)
inline

Definition at line 39 of file pow.hpp.

§ pow() [4/6]

var stan::math::pow ( const var base,
const var exponent 
)
inline

Return the base raised to the power of the exponent (cmath).

The partial derivatives are

$\frac{\partial}{\partial x} \mbox{pow}(x, y) = y x^{y-1}$, and

$\frac{\partial}{\partial y} \mbox{pow}(x, y) = x^y \ \log x$.

\[ \mbox{pow}(x, y) = \begin{cases} x^y & \mbox{if } -\infty\leq x, y \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN or } y = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{pow}(x, y)}{\partial x} = \begin{cases} yx^{y-1} & \mbox{if } -\infty\leq x\leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN or } y = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{pow}(x, y)}{\partial y} = \begin{cases} x^y\ln x & \mbox{if } -\infty\leq x\leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN or } y = \textrm{NaN} \end{cases} \]

Parameters
baseBase variable.
exponentExponent variable.
Returns
Base raised to the exponent.

Definition at line 103 of file pow.hpp.

§ pow() [5/6]

var stan::math::pow ( const var base,
double  exponent 
)
inline

Return the base variable raised to the power of the exponent scalar (cmath).

The derivative for the variable is

$\frac{d}{dx} \mbox{pow}(x, c) = c x^{c-1}$.

Parameters
baseBase variable.
exponentExponent scalar.
Returns
Base raised to the exponent.

Definition at line 119 of file pow.hpp.

§ pow() [6/6]

var stan::math::pow ( double  base,
const var exponent 
)
inline

Return the base scalar raised to the power of the exponent variable (cmath).

The derivative for the variable is

$\frac{d}{d y} \mbox{pow}(c, y) = c^y \log c $.

Parameters
baseBase scalar.
exponentExponent variable.
Returns
Base raised to the exponent.

Definition at line 141 of file pow.hpp.

§ precomputed_gradients()

var stan::math::precomputed_gradients ( double  value,
const std::vector< var > &  operands,
const std::vector< double > &  gradients 
)
inline

This function returns a var for an expression that has the specified value, vector of operands, and vector of partial derivatives of value with respect to the operands.

Parameters
[in]valueThe value of the resulting dependent variable.
[in]operandsoperands.
[in]gradientsvector of partial derivatives of result with respect to operands.
Returns
An auto-diff variable that uses the precomputed gradients provided.

Definition at line 95 of file precomputed_gradients.hpp.

§ primitive_value() [1/4]

double stan::math::primitive_value ( const var v)
inline

Return the primitive double value for the specified auto-diff variable.

Parameters
vinput variable.
Returns
value of input.

Definition at line 17 of file primitive_value.hpp.

§ primitive_value() [2/4]

template<typename T >
double stan::math::primitive_value ( const fvar< T > &  v)
inline

Return the primitive value of the specified forward-mode autodiff variable.

This function applies recursively to higher-order autodiff types to return a primitive double value.

Template Parameters
Tscalar type for autodiff variable.
Parameters
vinput variable.
Returns
primitive value of input.

Definition at line 20 of file primitive_value.hpp.

§ primitive_value() [3/4]

template<typename T >
boost::enable_if<boost::is_arithmetic<T>, T>::type stan::math::primitive_value ( x)
inline

Return the value of the specified arithmetic argument unmodified with its own declared type.

This template function can only be instantiated with arithmetic types as defined by Boost's is_arithmetic trait metaprogram.

This function differs from value_of in that it does not cast all return types to double.

Template Parameters
Ttype of arithmetic input.
Parameters
xinput.
Returns
input unmodified.

Definition at line 29 of file primitive_value.hpp.

§ primitive_value() [4/4]

template<typename T >
boost::disable_if<boost::is_arithmetic<T>, double>::type stan::math::primitive_value ( const T &  x)
inline

Return the primitive value of the specified argument.

This implementation only applies to non-arithmetic types as defined by Boost's is_arithmetic trait metaprogram.

Template Parameters
Ttype of non-arithmetic input.
Parameters
xinput.
Returns
value of input.

Definition at line 46 of file primitive_value.hpp.

§ print_mat_size()

void stan::math::print_mat_size ( int  n,
std::ostream &  o 
)
inline

Helper function to return the matrix size as either "dynamic" or "1".

Parameters
nEigen matrix size specification.
oOutput stream.
Returns
String representing size.

Definition at line 25 of file assign.hpp.

§ print_stack()

void stan::math::print_stack ( std::ostream &  o)
inline

Prints the auto-dif variable stack.

This function is used for debugging purposes.

Only works if all members of stack are vari* as it casts to vari*.

Parameters
oostream to modify

Definition at line 20 of file print_stack.hpp.

§ prob_constrain() [1/2]

template<typename T >
T stan::math::prob_constrain ( const T  x)
inline

Return a probability value constrained to fall between 0 and 1 (inclusive) for the specified free scalar.

The transform is the inverse logit,

$f(x) = \mbox{logit}^{-1}(x) = \frac{1}{1 + \exp(x)}$.

Parameters
xFree scalar.
Returns
Probability-constrained result of transforming the free scalar.
Template Parameters
TType of scalar.

Definition at line 26 of file prob_constrain.hpp.

§ prob_constrain() [2/2]

template<typename T >
T stan::math::prob_constrain ( const T  x,
T &  lp 
)
inline

Return a probability value constrained to fall between 0 and 1 (inclusive) for the specified free scalar and increment the specified log probability reference with the log absolute Jacobian determinant of the transform.

The transform is as defined for prob_constrain(T). The log absolute Jacobian determinant is

The log absolute Jacobian determinant is

$\log | \frac{d}{dx} \mbox{logit}^{-1}(x) |$

$\log ((\mbox{logit}^{-1}(x)) (1 - \mbox{logit}^{-1}(x))$

$\log (\mbox{logit}^{-1}(x)) + \log (1 - \mbox{logit}^{-1}(x))$.

Parameters
xFree scalar.
lpLog probability reference.
Returns
Probability-constrained result of transforming the free scalar.
Template Parameters
TType of scalar.

Definition at line 53 of file prob_constrain.hpp.

§ prob_free()

template<typename T >
T stan::math::prob_free ( const T  y)
inline

Return the free scalar that when transformed to a probability produces the specified scalar.

The function that reverses the constraining transform specified in prob_constrain(T) is the logit function,

$f^{-1}(y) = \mbox{logit}(y) = \frac{1 - y}{y}$.

Parameters
yScalar input.
Template Parameters
TType of scalar.
Exceptions
std::domain_errorif y is less than 0 or greater than 1.

Definition at line 26 of file prob_free.hpp.

§ prod() [1/2]

template<typename T >
T stan::math::prod ( const std::vector< T > &  v)
inline

Returns the product of the coefficients of the specified standard vector.

Parameters
vSpecified vector.
Returns
Product of coefficients of vector.

Definition at line 17 of file prod.hpp.

§ prod() [2/2]

template<typename T , int R, int C>
T stan::math::prod ( const Eigen::Matrix< T, R, C > &  v)
inline

Returns the product of the coefficients of the specified column vector.

Parameters
vSpecified vector.
Returns
Product of coefficients of vector.

Definition at line 32 of file prod.hpp.

§ promote_common()

template<typename T1 , typename T2 , typename F >
common_type<T1, T2>::type stan::math::promote_common ( const F &  u)
inline

Definition at line 13 of file promote_common.hpp.

§ promote_scalar()

template<typename T , typename S >
promote_scalar_type<T, S>::type stan::math::promote_scalar ( const S &  x)

This is the top-level function to call to promote the scalar types of an input of type S to type T.

Template Parameters
Tscalar type of output.
Sinput type.
Parameters
xinput vector.
Returns
input vector with scalars promoted to type T.

Definition at line 67 of file promote_scalar.hpp.

§ qr_Q() [1/2]

template<typename T >
Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> stan::math::qr_Q ( const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &  m)

Definition at line 14 of file qr_Q.hpp.

§ qr_Q() [2/2]

template<typename T >
Eigen::Matrix<fvar<T>, Eigen::Dynamic, Eigen::Dynamic> stan::math::qr_Q ( const Eigen::Matrix< fvar< T >, Eigen::Dynamic, Eigen::Dynamic > &  m)

Definition at line 15 of file qr_Q.hpp.

§ qr_R() [1/2]

template<typename T >
Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> stan::math::qr_R ( const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &  m)

Definition at line 14 of file qr_R.hpp.

§ qr_R() [2/2]

template<typename T >
Eigen::Matrix<fvar<T>, Eigen::Dynamic, Eigen::Dynamic> stan::math::qr_R ( const Eigen::Matrix< fvar< T >, Eigen::Dynamic, Eigen::Dynamic > &  m)

Definition at line 15 of file qr_R.hpp.

§ quad_form() [1/4]

template<int RA, int CA, int RB, int CB, typename T >
Eigen::Matrix<T, CB, CB> stan::math::quad_form ( const Eigen::Matrix< T, RA, CA > &  A,
const Eigen::Matrix< T, RB, CB > &  B 
)
inline

Compute B^T A B.

Definition at line 21 of file quad_form.hpp.

§ quad_form() [2/4]

template<int RA, int CA, int RB, typename T >
T stan::math::quad_form ( const Eigen::Matrix< T, RA, CA > &  A,
const Eigen::Matrix< T, RB, 1 > &  B 
)
inline

Definition at line 30 of file quad_form.hpp.

§ quad_form() [3/4]

template<typename TA , int RA, int CA, typename TB , int RB, int CB>
boost::enable_if_c< boost::is_same<TA, var>::value || boost::is_same<TB, var>::value, Eigen::Matrix<var, CB, CB> >::type stan::math::quad_form ( const Eigen::Matrix< TA, RA, CA > &  A,
const Eigen::Matrix< TB, RB, CB > &  B 
)
inline

Definition at line 123 of file quad_form.hpp.

§ quad_form() [4/4]

template<typename TA , int RA, int CA, typename TB , int RB>
boost::enable_if_c< boost::is_same<TA, var>::value || boost::is_same<TB, var>::value, var >::type stan::math::quad_form ( const Eigen::Matrix< TA, RA, CA > &  A,
const Eigen::Matrix< TB, RB, 1 > &  B 
)
inline

Definition at line 140 of file quad_form.hpp.

§ quad_form_diag()

template<typename T1 , typename T2 , int R, int C>
Eigen::Matrix< typename boost::math::tools::promote_args<T1, T2>::type, Eigen::Dynamic, Eigen::Dynamic> stan::math::quad_form_diag ( const Eigen::Matrix< T1, Eigen::Dynamic, Eigen::Dynamic > &  mat,
const Eigen::Matrix< T2, R, C > &  vec 
)
inline

Definition at line 17 of file quad_form_diag.hpp.

§ quad_form_sym() [1/8]

template<int RA, int CA, int RB, int CB, typename T >
Eigen::Matrix<fvar<T>, CB, CB> stan::math::quad_form_sym ( const Eigen::Matrix< fvar< T >, RA, CA > &  A,
const Eigen::Matrix< double, RB, CB > &  B 
)
inline

Definition at line 14 of file quad_form_sym.hpp.

§ quad_form_sym() [2/8]

template<int RA, int CA, int RB, int CB, typename T >
Eigen::Matrix<T, CB, CB> stan::math::quad_form_sym ( const Eigen::Matrix< T, RA, CA > &  A,
const Eigen::Matrix< T, RB, CB > &  B 
)
inline

Definition at line 17 of file quad_form_sym.hpp.

§ quad_form_sym() [3/8]

template<typename TA , int RA, int CA, typename TB , int RB, int CB>
boost::enable_if_c< boost::is_same<TA, var>::value || boost::is_same<TB, var>::value, Eigen::Matrix<var, CB, CB> >::type stan::math::quad_form_sym ( const Eigen::Matrix< TA, RA, CA > &  A,
const Eigen::Matrix< TB, RB, CB > &  B 
)
inline

Definition at line 25 of file quad_form_sym.hpp.

§ quad_form_sym() [4/8]

template<int RA, int CA, int RB, typename T >
T stan::math::quad_form_sym ( const Eigen::Matrix< T, RA, CA > &  A,
const Eigen::Matrix< T, RB, 1 > &  B 
)
inline

Definition at line 28 of file quad_form_sym.hpp.

§ quad_form_sym() [5/8]

template<int RA, int CA, int RB, typename T >
fvar<T> stan::math::quad_form_sym ( const Eigen::Matrix< fvar< T >, RA, CA > &  A,
const Eigen::Matrix< double, RB, 1 > &  B 
)
inline

Definition at line 28 of file quad_form_sym.hpp.

§ quad_form_sym() [6/8]

template<int RA, int CA, int RB, int CB, typename T >
Eigen::Matrix<fvar<T>, CB, CB> stan::math::quad_form_sym ( const Eigen::Matrix< double, RA, CA > &  A,
const Eigen::Matrix< fvar< T >, RB, CB > &  B 
)
inline

Definition at line 39 of file quad_form_sym.hpp.

§ quad_form_sym() [7/8]

template<typename TA , int RA, int CA, typename TB , int RB>
boost::enable_if_c< boost::is_same<TA, var>::value || boost::is_same<TB, var>::value, var >::type stan::math::quad_form_sym ( const Eigen::Matrix< TA, RA, CA > &  A,
const Eigen::Matrix< TB, RB, 1 > &  B 
)
inline

Definition at line 43 of file quad_form_sym.hpp.

§ quad_form_sym() [8/8]

template<int RA, int CA, int RB, typename T >
fvar<T> stan::math::quad_form_sym ( const Eigen::Matrix< double, RA, CA > &  A,
const Eigen::Matrix< fvar< T >, RB, 1 > &  B 
)
inline

Definition at line 53 of file quad_form_sym.hpp.

§ rank() [1/2]

template<typename T >
int stan::math::rank ( const std::vector< T > &  v,
int  s 
)
inline

Return the number of components of v less than v[s].

Template Parameters
TType of elements.
Parameters
[in]vInput vector.
[in]sPosition in vector.
Returns
Number of components of v less than v[s].
Exceptions
std::out_of_rangeif s is out of range.

Definition at line 21 of file rank.hpp.

§ rank() [2/2]

template<typename T , int R, int C>
int stan::math::rank ( const Eigen::Matrix< T, R, C > &  v,
int  s 
)
inline

Return the number of components of v less than v[s].

Template Parameters
TType of elements of the vector.
Parameters
[in]vInput vector.
sIndex for input vector.
Returns
Number of components of v less than v[s].
Exceptions
std::out_of_rangeif s is out of range.

Definition at line 43 of file rank.hpp.

§ rayleigh_ccdf_log()

template<typename T_y , typename T_scale >
return_type<T_y, T_scale>::type stan::math::rayleigh_ccdf_log ( const T_y &  y,
const T_scale &  sigma 
)

Definition at line 26 of file rayleigh_ccdf_log.hpp.

§ rayleigh_cdf()

template<typename T_y , typename T_scale >
return_type<T_y, T_scale>::type stan::math::rayleigh_cdf ( const T_y &  y,
const T_scale &  sigma 
)

Definition at line 27 of file rayleigh_cdf.hpp.

§ rayleigh_cdf_log()

template<typename T_y , typename T_scale >
return_type<T_y, T_scale>::type stan::math::rayleigh_cdf_log ( const T_y &  y,
const T_scale &  sigma 
)

Definition at line 27 of file rayleigh_cdf_log.hpp.

§ rayleigh_lccdf()

template<typename T_y , typename T_scale >
return_type<T_y, T_scale>::type stan::math::rayleigh_lccdf ( const T_y &  y,
const T_scale &  sigma 
)

Definition at line 26 of file rayleigh_lccdf.hpp.

§ rayleigh_lcdf()

template<typename T_y , typename T_scale >
return_type<T_y, T_scale>::type stan::math::rayleigh_lcdf ( const T_y &  y,
const T_scale &  sigma 
)

Definition at line 27 of file rayleigh_lcdf.hpp.

§ rayleigh_log() [1/2]

template<bool propto, typename T_y , typename T_scale >
return_type<T_y, T_scale>::type stan::math::rayleigh_log ( const T_y &  y,
const T_scale &  sigma 
)

Definition at line 28 of file rayleigh_log.hpp.

§ rayleigh_log() [2/2]

template<typename T_y , typename T_scale >
return_type<T_y, T_scale>::type stan::math::rayleigh_log ( const T_y &  y,
const T_scale &  sigma 
)
inline

Definition at line 91 of file rayleigh_log.hpp.

§ rayleigh_lpdf() [1/2]

template<bool propto, typename T_y , typename T_scale >
return_type<T_y, T_scale>::type stan::math::rayleigh_lpdf ( const T_y &  y,
const T_scale &  sigma 
)

Definition at line 28 of file rayleigh_lpdf.hpp.

§ rayleigh_lpdf() [2/2]

template<typename T_y , typename T_scale >
return_type<T_y, T_scale>::type stan::math::rayleigh_lpdf ( const T_y &  y,
const T_scale &  sigma 
)
inline

Definition at line 91 of file rayleigh_lpdf.hpp.

§ rayleigh_rng()

template<class RNG >
double stan::math::rayleigh_rng ( double  sigma,
RNG &  rng 
)
inline

Definition at line 23 of file rayleigh_rng.hpp.

§ read_corr_L() [1/2]

template<typename T >
Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> stan::math::read_corr_L ( const Eigen::Array< T, Eigen::Dynamic, 1 > &  CPCs,
size_t  K 
)

Return the Cholesky factor of the correlation matrix of the specified dimensionality corresponding to the specified canonical partial correlations.

It is generally better to work with the Cholesky factor rather than the correlation matrix itself when the determinant, inverse, etc. of the correlation matrix is needed for some statistical calculation.

See read_corr_matrix(Array, size_t, T) for more information.

Parameters
CPCsThe (K choose 2) canonical partial correlations in (-1, 1).
KDimensionality of correlation matrix.
Returns
Cholesky factor of correlation matrix for specified canonical partial correlations.
Template Parameters
TType of underlying scalar.

Definition at line 37 of file read_corr_L.hpp.

§ read_corr_L() [2/2]

template<typename T >
Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> stan::math::read_corr_L ( const Eigen::Array< T, Eigen::Dynamic, 1 > &  CPCs,
size_t  K,
T &  log_prob 
)

Return the Cholesky factor of the correlation matrix of the specified dimensionality corresponding to the specified canonical partial correlations, incrementing the specified scalar reference with the log absolute determinant of the Jacobian of the transformation.

The implementation is Ben Goodrich's Cholesky factor-based approach to the C-vine method of:

  • Daniel Lewandowski, Dorota Kurowicka, and Harry Joe, Generating random correlation matrices based on vines and extended onion method Journal of Multivariate Analysis 100 (2009) 1989–2001
Parameters
CPCsThe (K choose 2) canonical partial correlations in (-1, 1).
KDimensionality of correlation matrix.
log_probReference to variable to increment with the log Jacobian determinant.
Returns
Cholesky factor of correlation matrix for specified partial correlations.
Template Parameters
TType of underlying scalar.

Definition at line 90 of file read_corr_L.hpp.

§ read_corr_matrix() [1/2]

template<typename T >
Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> stan::math::read_corr_matrix ( const Eigen::Array< T, Eigen::Dynamic, 1 > &  CPCs,
size_t  K 
)

Return the correlation matrix of the specified dimensionality corresponding to the specified canonical partial correlations.

See read_corr_matrix(Array, size_t, T) for more information.

Parameters
CPCsThe (K choose 2) canonical partial correlations in (-1, 1).
KDimensionality of correlation matrix.
Returns
Cholesky factor of correlation matrix for specified canonical partial correlations.
Template Parameters
TType of underlying scalar.

Definition at line 26 of file read_corr_matrix.hpp.

§ read_corr_matrix() [2/2]

template<typename T >
Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> stan::math::read_corr_matrix ( const Eigen::Array< T, Eigen::Dynamic, 1 > &  CPCs,
size_t  K,
T &  log_prob 
)

Return the correlation matrix of the specified dimensionality corresponding to the specified canonical partial correlations, incrementing the specified scalar reference with the log absolute determinant of the Jacobian of the transformation.

It is usually preferable to utilize the version that returns the Cholesky factor of the correlation matrix rather than the correlation matrix itself in statistical calculations.

Parameters
CPCsThe (K choose 2) canonical partial correlations in (-1, 1).
KDimensionality of correlation matrix.
log_probReference to variable to increment with the log Jacobian determinant.
Returns
Correlation matrix for specified partial correlations.
Template Parameters
TType of underlying scalar.

Definition at line 53 of file read_corr_matrix.hpp.

§ read_cov_L()

template<typename T >
Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> stan::math::read_cov_L ( const Eigen::Array< T, Eigen::Dynamic, 1 > &  CPCs,
const Eigen::Array< T, Eigen::Dynamic, 1 > &  sds,
T &  log_prob 
)

This is the function that should be called prior to evaluating the density of any elliptical distribution.

Parameters
CPCson (-1, 1)
sdson (0, inf)
log_probthe log probability value to increment with the Jacobian
Returns
Cholesky factor of covariance matrix for specified partial correlations.

Definition at line 22 of file read_cov_L.hpp.

§ read_cov_matrix() [1/2]

template<typename T >
Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> stan::math::read_cov_matrix ( const Eigen::Array< T, Eigen::Dynamic, 1 > &  CPCs,
const Eigen::Array< T, Eigen::Dynamic, 1 > &  sds,
T &  log_prob 
)

A generally worse alternative to call prior to evaluating the density of an elliptical distribution.

Parameters
CPCson (-1, 1)
sdson (0, inf)
log_probthe log probability value to increment with the Jacobian
Returns
Covariance matrix for specified partial correlations.

Definition at line 22 of file read_cov_matrix.hpp.

§ read_cov_matrix() [2/2]

template<typename T >
Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> stan::math::read_cov_matrix ( const Eigen::Array< T, Eigen::Dynamic, 1 > &  CPCs,
const Eigen::Array< T, Eigen::Dynamic, 1 > &  sds 
)

Builds a covariance matrix from CPCs and standard deviations.

Parameters
CPCsin (-1, 1)
sdsin (0, inf)

Definition at line 39 of file read_cov_matrix.hpp.

§ recover_memory()

static void stan::math::recover_memory ( )
inlinestatic

Recover memory used for all variables for reuse.

Exceptions
std::logic_errorif empty_nested() returns false

Definition at line 18 of file recover_memory.hpp.

§ recover_memory_nested()

static void stan::math::recover_memory_nested ( )
inlinestatic

Recover only the memory used for the top nested call.

If there is nothing on the nested stack, then a std::logic_error exception is thrown.

Exceptions
std::logic_errorif empty_nested() returns true

Definition at line 20 of file recover_memory_nested.hpp.

§ rep_array() [1/3]

template<typename T >
std::vector<T> stan::math::rep_array ( const T &  x,
int  n 
)
inline

Definition at line 12 of file rep_array.hpp.

§ rep_array() [2/3]

template<typename T >
std::vector<std::vector<T> > stan::math::rep_array ( const T &  x,
int  m,
int  n 
)
inline

Definition at line 19 of file rep_array.hpp.

§ rep_array() [3/3]

template<typename T >
std::vector<std::vector<std::vector<T> > > stan::math::rep_array ( const T &  x,
int  k,
int  m,
int  n 
)
inline

Definition at line 28 of file rep_array.hpp.

§ rep_matrix() [1/3]

template<typename T >
Eigen::Matrix<typename boost::math::tools::promote_args<T>::type, Eigen::Dynamic, Eigen::Dynamic> stan::math::rep_matrix ( const T &  x,
int  m,
int  n 
)
inline

Definition at line 15 of file rep_matrix.hpp.

§ rep_matrix() [2/3]

template<typename T >
Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> stan::math::rep_matrix ( const Eigen::Matrix< T, Eigen::Dynamic, 1 > &  v,
int  n 
)
inline

Definition at line 24 of file rep_matrix.hpp.

§ rep_matrix() [3/3]

template<typename T >
Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> stan::math::rep_matrix ( const Eigen::Matrix< T, 1, Eigen::Dynamic > &  rv,
int  m 
)
inline

Definition at line 33 of file rep_matrix.hpp.

§ rep_row_vector()

template<typename T >
Eigen::Matrix<typename boost::math::tools::promote_args<T>::type, 1, Eigen::Dynamic> stan::math::rep_row_vector ( const T &  x,
int  m 
)
inline

Definition at line 14 of file rep_row_vector.hpp.

§ rep_vector()

template<typename T >
Eigen::Matrix<typename boost::math::tools::promote_args<T>::type, Eigen::Dynamic, 1> stan::math::rep_vector ( const T &  x,
int  n 
)
inline

Definition at line 15 of file rep_vector.hpp.

§ resize()

template<typename T >
void stan::math::resize ( T &  x,
std::vector< size_t >  dims 
)
inline

Recursively resize the specified vector of vectors, which must bottom out at scalar values, Eigen vectors or Eigen matrices.

Parameters
xArray-like object to resize.
dimsNew dimensions.
Template Parameters
TType of object being resized.

Definition at line 63 of file resize.hpp.

§ rising_factorial() [1/7]

template<typename T >
fvar<T> stan::math::rising_factorial ( const fvar< T > &  x,
const fvar< T > &  n 
)
inline

Definition at line 15 of file rising_factorial.hpp.

§ rising_factorial() [2/7]

template<typename T >
fvar<T> stan::math::rising_factorial ( const fvar< T > &  x,
double  n 
)
inline

Definition at line 25 of file rising_factorial.hpp.

§ rising_factorial() [3/7]

template<typename T >
fvar<T> stan::math::rising_factorial ( double  x,
const fvar< T > &  n 
)
inline

Definition at line 37 of file rising_factorial.hpp.

§ rising_factorial() [4/7]

template<typename T1 , typename T2 >
boost::math::tools::promote_args<T1, T2>::type stan::math::rising_factorial ( const T1  x,
const T2  n 
)
inline

\[ \mbox{rising\_factorial}(x, n) = \begin{cases} \textrm{error} & \mbox{if } x \leq 0\\ x^{(n)} & \mbox{if } x > 0 \textrm{ and } -\infty \leq n \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN or } n = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{rising\_factorial}(x, n)}{\partial x} = \begin{cases} \textrm{error} & \mbox{if } x \leq 0\\ \frac{\partial\, x^{(n)}}{\partial x} & \mbox{if } x > 0 \textrm{ and } -\infty \leq n \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN or } n = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{rising\_factorial}(x, n)}{\partial n} = \begin{cases} \textrm{error} & \mbox{if } x \leq 0\\ \frac{\partial\, x^{(n)}}{\partial n} & \mbox{if } x > 0 \textrm{ and } -\infty \leq n \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN or } n = \textrm{NaN} \end{cases} \]

\[ x^{(n)}=\frac{\Gamma(x+n)}{\Gamma(x)} \]

\[ \frac{\partial \, x^{(n)}}{\partial x} = x^{(n)}(\Psi(x+n)-\Psi(x)) \]

\[ \frac{\partial \, x^{(n)}}{\partial n} = (x)_n\Psi(x+n) \]

Definition at line 54 of file rising_factorial.hpp.

§ rising_factorial() [5/7]

var stan::math::rising_factorial ( const var a,
double  b 
)
inline

Definition at line 54 of file rising_factorial.hpp.

§ rising_factorial() [6/7]

var stan::math::rising_factorial ( const var a,
const var b 
)
inline

Definition at line 59 of file rising_factorial.hpp.

§ rising_factorial() [7/7]

var stan::math::rising_factorial ( double  a,
const var b 
)
inline

Definition at line 64 of file rising_factorial.hpp.

§ round() [1/5]

double stan::math::round ( double  x)
inline

Return the closest integer to the specified argument, with halfway cases rounded away from zero.

Parameters
xArgument.
Returns
The rounded value of the argument.

Definition at line 19 of file round.hpp.

§ round() [2/5]

template<typename T >
fvar<T> stan::math::round ( const fvar< T > &  x)
inline

Return the closest integer to the specified argument, with halfway cases rounded away from zero.

The derivative is always zero.

Template Parameters
TScalar type for autodiff variable.
Parameters
xArgument.
Returns
The rounded value of the argument.

Definition at line 23 of file round.hpp.

§ round() [3/5]

double stan::math::round ( int  x)
inline

Return the closest integer to the specified argument, with halfway cases rounded away from zero.

Parameters
xArgument.
Returns
The rounded value of the argument.

Definition at line 32 of file round.hpp.

§ round() [4/5]

template<typename T >
apply_scalar_unary<round_fun, T>::return_t stan::math::round ( const T &  x)
inline

Vectorized version of round.

Parameters
xContainer.
Template Parameters
TContainer type.
Returns
Rounded value of each value in x.

Definition at line 32 of file round.hpp.

§ round() [5/5]

var stan::math::round ( const var a)
inline

Returns the rounded form of the specified variable (C99).

The derivative is zero everywhere but numbers half way between whole numbers, so for convenience the derivative is defined to be everywhere zero,

$\frac{d}{dx} \mbox{round}(x) = 0$.

\[ \mbox{round}(x) = \begin{cases} \lceil x \rceil & \mbox{if } x-\lfloor x\rfloor \geq 0.5 \\ \lfloor x \rfloor & \mbox{if } x-\lfloor x\rfloor < 0.5 \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{round}(x)}{\partial x} = \begin{cases} 0 & \mbox{if } -\infty\leq x\leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

Parameters
aSpecified variable.
Returns
Rounded variable.

Definition at line 55 of file round.hpp.

§ row()

template<typename T >
Eigen::Matrix<T, 1, Eigen::Dynamic> stan::math::row ( const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &  m,
size_t  i 
)
inline

Return the specified row of the specified matrix, using start-at-1 indexing.

This is equivalent to calling m.row(i - 1) and assigning the resulting template expression to a row vector.

Template Parameters
TScalar value type for matrix.
Parameters
mMatrix.
iRow index (count from 1).
Returns
Specified row of the matrix.
Exceptions
std::out_of_rangeif i is out of range.

Definition at line 26 of file row.hpp.

§ rows()

template<typename T , int R, int C>
int stan::math::rows ( const Eigen::Matrix< T, R, C > &  m)
inline

Return the number of rows in the specified matrix, vector, or row vector.

Template Parameters
TType of matrix entries.
RRow type of matrix.
CColumn type of matrix.
Parameters
[in]mInput matrix, vector, or row vector.
Returns
Number of rows.

Definition at line 20 of file rows.hpp.

§ rows_dot_product() [1/5]

template<typename T , int R1, int C1, int R2, int C2>
Eigen::Matrix<fvar<T>, R1, 1> stan::math::rows_dot_product ( const Eigen::Matrix< fvar< T >, R1, C1 > &  v1,
const Eigen::Matrix< fvar< T >, R2, C2 > &  v2 
)
inline

Definition at line 18 of file rows_dot_product.hpp.

§ rows_dot_product() [2/5]

template<int R1, int C1, int R2, int C2>
Eigen::Matrix<double, R1, 1> stan::math::rows_dot_product ( const Eigen::Matrix< double, R1, C1 > &  v1,
const Eigen::Matrix< double, R2, C2 > &  v2 
)
inline

Returns the dot product of the specified vectors.

Parameters
v1First vector.
v2Second vector.
Returns
Dot product of the vectors.
Exceptions
std::domain_errorIf the vectors are not the same size or if they are both not vector dimensioned.

Definition at line 22 of file rows_dot_product.hpp.

§ rows_dot_product() [3/5]

template<typename T1 , int R1, int C1, typename T2 , int R2, int C2>
boost::enable_if_c<boost::is_same<T1, var>::value || boost::is_same<T2, var>::value, Eigen::Matrix<var, R1, 1> >::type stan::math::rows_dot_product ( const Eigen::Matrix< T1, R1, C1 > &  v1,
const Eigen::Matrix< T2, R2, C2 > &  v2 
)
inline

Definition at line 25 of file rows_dot_product.hpp.

§ rows_dot_product() [4/5]

template<typename T , int R1, int C1, int R2, int C2>
Eigen::Matrix<fvar<T>, R1, 1> stan::math::rows_dot_product ( const Eigen::Matrix< double, R1, C1 > &  v1,
const Eigen::Matrix< fvar< T >, R2, C2 > &  v2 
)
inline

Definition at line 33 of file rows_dot_product.hpp.

§ rows_dot_product() [5/5]

template<typename T , int R1, int C1, int R2, int C2>
Eigen::Matrix<fvar<T>, R1, 1> stan::math::rows_dot_product ( const Eigen::Matrix< fvar< T >, R1, C1 > &  v1,
const Eigen::Matrix< double, R2, C2 > &  v2 
)
inline

Definition at line 48 of file rows_dot_product.hpp.

§ rows_dot_self() [1/2]

template<typename T , int R, int C>
Eigen::Matrix<fvar<T>, R, 1> stan::math::rows_dot_self ( const Eigen::Matrix< fvar< T >, R, C > &  x)
inline

Definition at line 15 of file rows_dot_self.hpp.

§ rows_dot_self() [2/2]

template<typename T , int R, int C>
Eigen::Matrix<T, R, 1> stan::math::rows_dot_self ( const Eigen::Matrix< T, R, C > &  x)
inline

Returns the dot product of each row of a matrix with itself.

Parameters
xMatrix.
Template Parameters
Tscalar type

Definition at line 16 of file rows_dot_self.hpp.

§ scaled_add()

void stan::math::scaled_add ( std::vector< double > &  x,
const std::vector< double > &  y,
double  lambda 
)
inline

Definition at line 10 of file scaled_add.hpp.

§ scaled_inv_chi_square_ccdf_log()

template<typename T_y , typename T_dof , typename T_scale >
return_type<T_y, T_dof, T_scale>::type stan::math::scaled_inv_chi_square_ccdf_log ( const T_y &  y,
const T_dof &  nu,
const T_scale &  s 
)

Definition at line 33 of file scaled_inv_chi_square_ccdf_log.hpp.

§ scaled_inv_chi_square_cdf()

template<typename T_y , typename T_dof , typename T_scale >
return_type<T_y, T_dof, T_scale>::type stan::math::scaled_inv_chi_square_cdf ( const T_y &  y,
const T_dof &  nu,
const T_scale &  s 
)

The CDF of a scaled inverse chi-squared density for y with the specified degrees of freedom parameter and scale parameter.

Parameters
yA scalar variable.
nuDegrees of freedom.
sScale parameter.
Exceptions
std::domain_errorif nu is not greater than 0
std::domain_errorif s is not greater than 0.
std::domain_errorif y is not greater than 0.
Template Parameters
T_yType of scalar.
T_dofType of degrees of freedom.

Definition at line 46 of file scaled_inv_chi_square_cdf.hpp.

§ scaled_inv_chi_square_cdf_log()

template<typename T_y , typename T_dof , typename T_scale >
return_type<T_y, T_dof, T_scale>::type stan::math::scaled_inv_chi_square_cdf_log ( const T_y &  y,
const T_dof &  nu,
const T_scale &  s 
)

Definition at line 33 of file scaled_inv_chi_square_cdf_log.hpp.

§ scaled_inv_chi_square_lccdf()

template<typename T_y , typename T_dof , typename T_scale >
return_type<T_y, T_dof, T_scale>::type stan::math::scaled_inv_chi_square_lccdf ( const T_y &  y,
const T_dof &  nu,
const T_scale &  s 
)

Definition at line 33 of file scaled_inv_chi_square_lccdf.hpp.

§ scaled_inv_chi_square_lcdf()

template<typename T_y , typename T_dof , typename T_scale >
return_type<T_y, T_dof, T_scale>::type stan::math::scaled_inv_chi_square_lcdf ( const T_y &  y,
const T_dof &  nu,
const T_scale &  s 
)

Definition at line 33 of file scaled_inv_chi_square_lcdf.hpp.

§ scaled_inv_chi_square_log() [1/2]

template<bool propto, typename T_y , typename T_dof , typename T_scale >
return_type<T_y, T_dof, T_scale>::type stan::math::scaled_inv_chi_square_log ( const T_y &  y,
const T_dof &  nu,
const T_scale &  s 
)

The log of a scaled inverse chi-squared density for y with the specified degrees of freedom parameter and scale parameter.

\begin{eqnarray*} y &\sim& \mbox{\sf{Inv-}}\chi^2(\nu, s^2) \\ \log (p (y \, |\, \nu, s)) &=& \log \left( \frac{(\nu / 2)^{\nu / 2}}{\Gamma (\nu / 2)} s^\nu y^{- (\nu / 2 + 1)} \exp^{-\nu s^2 / (2y)} \right) \\ &=& \frac{\nu}{2} \log(\frac{\nu}{2}) - \log (\Gamma (\nu / 2)) + \nu \log(s) - (\frac{\nu}{2} + 1) \log(y) - \frac{\nu s^2}{2y} \\ & & \mathrm{ where } \; y > 0 \end{eqnarray*}

Parameters
yA scalar variable.
nuDegrees of freedom.
sScale parameter.
Exceptions
std::domain_errorif nu is not greater than 0
std::domain_errorif s is not greater than 0.
std::domain_errorif y is not greater than 0.
Template Parameters
T_yType of scalar.
T_dofType of degrees of freedom.

Definition at line 51 of file scaled_inv_chi_square_log.hpp.

§ scaled_inv_chi_square_log() [2/2]

template<typename T_y , typename T_dof , typename T_scale >
return_type<T_y, T_dof, T_scale>::type stan::math::scaled_inv_chi_square_log ( const T_y &  y,
const T_dof &  nu,
const T_scale &  s 
)
inline

Definition at line 163 of file scaled_inv_chi_square_log.hpp.

§ scaled_inv_chi_square_lpdf() [1/2]

template<bool propto, typename T_y , typename T_dof , typename T_scale >
return_type<T_y, T_dof, T_scale>::type stan::math::scaled_inv_chi_square_lpdf ( const T_y &  y,
const T_dof &  nu,
const T_scale &  s 
)

The log of a scaled inverse chi-squared density for y with the specified degrees of freedom parameter and scale parameter.

\begin{eqnarray*} y &\sim& \mbox{\sf{Inv-}}\chi^2(\nu, s^2) \\ \log (p (y \, |\, \nu, s)) &=& \log \left( \frac{(\nu / 2)^{\nu / 2}}{\Gamma (\nu / 2)} s^\nu y^{- (\nu / 2 + 1)} \exp^{-\nu s^2 / (2y)} \right) \\ &=& \frac{\nu}{2} \log(\frac{\nu}{2}) - \log (\Gamma (\nu / 2)) + \nu \log(s) - (\frac{\nu}{2} + 1) \log(y) - \frac{\nu s^2}{2y} \\ & & \mathrm{ where } \; y > 0 \end{eqnarray*}

Parameters
yA scalar variable.
nuDegrees of freedom.
sScale parameter.
Exceptions
std::domain_errorif nu is not greater than 0
std::domain_errorif s is not greater than 0.
std::domain_errorif y is not greater than 0.
Template Parameters
T_yType of scalar.
T_dofType of degrees of freedom.

Definition at line 51 of file scaled_inv_chi_square_lpdf.hpp.

§ scaled_inv_chi_square_lpdf() [2/2]

template<typename T_y , typename T_dof , typename T_scale >
return_type<T_y, T_dof, T_scale>::type stan::math::scaled_inv_chi_square_lpdf ( const T_y &  y,
const T_dof &  nu,
const T_scale &  s 
)
inline

Definition at line 164 of file scaled_inv_chi_square_lpdf.hpp.

§ scaled_inv_chi_square_rng()

template<class RNG >
double stan::math::scaled_inv_chi_square_rng ( double  nu,
double  s,
RNG &  rng 
)
inline

Definition at line 27 of file scaled_inv_chi_square_rng.hpp.

§ sd() [1/4]

template<typename T >
boost::math::tools::promote_args<T>::type stan::math::sd ( const std::vector< T > &  v)
inline

Returns the unbiased sample standard deviation of the coefficients in the specified column vector.

Parameters
vSpecified vector.
Returns
Sample variance of vector.

Definition at line 22 of file sd.hpp.

§ sd() [2/4]

template<typename T , int R, int C>
boost::math::tools::promote_args<T>::type stan::math::sd ( const Eigen::Matrix< T, R, C > &  m)
inline

Returns the unbiased sample standard deviation of the coefficients in the specified vector, row vector, or matrix.

Parameters
mSpecified vector, row vector or matrix.
Returns
Sample variance.

Definition at line 37 of file sd.hpp.

§ sd() [3/4]

var stan::math::sd ( const std::vector< var > &  v)
inline

Return the sample standard deviation of the specified standard vector.

Raise domain error if size is not greater than zero.

Parameters
[in]va vector
Returns
sample standard deviation of specified vector

Definition at line 64 of file sd.hpp.

§ sd() [4/4]

template<int R, int C>
var stan::math::sd ( const Eigen::Matrix< var, R, C > &  m)

Definition at line 81 of file sd.hpp.

§ segment() [1/3]

template<typename T >
Eigen::Matrix<T, Eigen::Dynamic, 1> stan::math::segment ( const Eigen::Matrix< T, Eigen::Dynamic, 1 > &  v,
size_t  i,
size_t  n 
)
inline

Return the specified number of elements as a vector starting from the specified element - 1 of the specified vector.

Definition at line 19 of file segment.hpp.

§ segment() [2/3]

template<typename T >
Eigen::Matrix<T, 1, Eigen::Dynamic> stan::math::segment ( const Eigen::Matrix< T, 1, Eigen::Dynamic > &  v,
size_t  i,
size_t  n 
)
inline

Definition at line 35 of file segment.hpp.

§ segment() [3/3]

template<typename T >
std::vector<T> stan::math::segment ( const std::vector< T > &  sv,
size_t  i,
size_t  n 
)

Definition at line 51 of file segment.hpp.

§ set_zero_all_adjoints()

static void stan::math::set_zero_all_adjoints ( )
static

Reset all adjoint values in the stack to zero.

Definition at line 14 of file set_zero_all_adjoints.hpp.

§ set_zero_all_adjoints_nested()

static void stan::math::set_zero_all_adjoints_nested ( )
static

Reset all adjoint values in the top nested portion of the stack to zero.

Definition at line 17 of file set_zero_all_adjoints_nested.hpp.

§ sign()

template<typename T >
int stan::math::sign ( const T &  z)
inline

Definition at line 9 of file sign.hpp.

§ simplex_constrain() [1/2]

template<typename T >
Eigen::Matrix<T, Eigen::Dynamic, 1> stan::math::simplex_constrain ( const Eigen::Matrix< T, Eigen::Dynamic, 1 > &  y)

Return the simplex corresponding to the specified free vector.

A simplex is a vector containing values greater than or equal to 0 that sum to 1. A vector with (K-1) unconstrained values will produce a simplex of size K.

The transform is based on a centered stick-breaking process.

Parameters
yFree vector input of dimensionality K - 1.
Returns
Simplex of dimensionality K.
Template Parameters
TType of scalar.

Definition at line 29 of file simplex_constrain.hpp.

§ simplex_constrain() [2/2]

template<typename T >
Eigen::Matrix<T, Eigen::Dynamic, 1> stan::math::simplex_constrain ( const Eigen::Matrix< T, Eigen::Dynamic, 1 > &  y,
T &  lp 
)

Return the simplex corresponding to the specified free vector and increment the specified log probability reference with the log absolute Jacobian determinant of the transform.

The simplex transform is defined through a centered stick-breaking process.

Parameters
yFree vector input of dimensionality K - 1.
lpLog probability reference to increment.
Returns
Simplex of dimensionality K.
Template Parameters
TType of scalar.

Definition at line 63 of file simplex_constrain.hpp.

§ simplex_free()

template<typename T >
Eigen::Matrix<T, Eigen::Dynamic, 1> stan::math::simplex_free ( const Eigen::Matrix< T, Eigen::Dynamic, 1 > &  x)

Return an unconstrained vector that when transformed produces the specified simplex.

It applies to a simplex of dimensionality K and produces an unconstrained vector of dimensionality (K-1).

The simplex transform is defined through a centered stick-breaking process.

Parameters
xSimplex of dimensionality K.
Returns
Free vector of dimensionality (K-1) that transfroms to the simplex.
Template Parameters
TType of scalar.
Exceptions
std::domain_errorif x is not a valid simplex

Definition at line 29 of file simplex_free.hpp.

§ sin() [1/3]

template<typename T >
fvar<T> stan::math::sin ( const fvar< T > &  x)
inline

Definition at line 12 of file sin.hpp.

§ sin() [2/3]

template<typename T >
apply_scalar_unary<sin_fun, T>::return_t stan::math::sin ( const T &  x)
inline

Vectorized version of sin().

Parameters
xContainer of angles in radians.
Template Parameters
TContainer type.
Returns
Sine of each value in x.

Definition at line 32 of file sin.hpp.

§ sin() [3/3]

var stan::math::sin ( const var a)
inline

Return the sine of a radian-scaled variable (cmath).

The derivative is defined by

$\frac{d}{dx} \sin x = \cos x$.

\[ \mbox{sin}(x) = \begin{cases} \sin(x) & \mbox{if } -\infty\leq x \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{sin}(x)}{\partial x} = \begin{cases} \cos(x) & \mbox{if } -\infty\leq x\leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

Parameters
aVariable for radians of angle.
Returns
Sine of variable.

Definition at line 49 of file sin.hpp.

§ singular_values()

template<typename T >
Eigen::Matrix<T, Eigen::Dynamic, 1> stan::math::singular_values ( const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &  m)

Return the vector of the singular values of the specified matrix in decreasing order of magnitude.

See the documentation for svd() for information on the signular values.

Parameters
mSpecified matrix.
Returns
Singular values of the matrix.

Definition at line 19 of file singular_values.hpp.

§ sinh() [1/3]

template<typename T >
fvar<T> stan::math::sinh ( const fvar< T > &  x)
inline

Definition at line 12 of file sinh.hpp.

§ sinh() [2/3]

template<typename T >
apply_scalar_unary<sinh_fun, T>::return_t stan::math::sinh ( const T &  x)
inline

Vectorized version of sinh().

Parameters
xContainer of variables.
Template Parameters
TContainer type.
Returns
Hyperbolic sine of each variable in x.

Definition at line 32 of file sinh.hpp.

§ sinh() [3/3]

var stan::math::sinh ( const var a)
inline

Return the hyperbolic sine of the specified variable (cmath).

The derivative is defined by

$\frac{d}{dx} \sinh x = \cosh x$.

\[ \mbox{sinh}(x) = \begin{cases} \sinh(x) & \mbox{if } -\infty\leq x \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{sinh}(x)}{\partial x} = \begin{cases} \cosh(x) & \mbox{if } -\infty\leq x\leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

Parameters
aVariable.
Returns
Hyperbolic sine of variable.

Definition at line 49 of file sinh.hpp.

§ size()

template<typename T >
int stan::math::size ( const std::vector< T > &  x)
inline

Return the size of the specified standard vector.

Template Parameters
TType of elements.
Parameters
[in]xInput vector.
Returns
Size of input vector.

Definition at line 17 of file size.hpp.

§ skew_normal_ccdf_log()

template<typename T_y , typename T_loc , typename T_scale , typename T_shape >
return_type<T_y, T_loc, T_scale, T_shape>::type stan::math::skew_normal_ccdf_log ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma,
const T_shape &  alpha 
)

Definition at line 26 of file skew_normal_ccdf_log.hpp.

§ skew_normal_cdf()

template<typename T_y , typename T_loc , typename T_scale , typename T_shape >
return_type<T_y, T_loc, T_scale, T_shape>::type stan::math::skew_normal_cdf ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma,
const T_shape &  alpha 
)

Definition at line 26 of file skew_normal_cdf.hpp.

§ skew_normal_cdf_log()

template<typename T_y , typename T_loc , typename T_scale , typename T_shape >
return_type<T_y, T_loc, T_scale, T_shape>::type stan::math::skew_normal_cdf_log ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma,
const T_shape &  alpha 
)

Definition at line 26 of file skew_normal_cdf_log.hpp.

§ skew_normal_lccdf()

template<typename T_y , typename T_loc , typename T_scale , typename T_shape >
return_type<T_y, T_loc, T_scale, T_shape>::type stan::math::skew_normal_lccdf ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma,
const T_shape &  alpha 
)

Definition at line 26 of file skew_normal_lccdf.hpp.

§ skew_normal_lcdf()

template<typename T_y , typename T_loc , typename T_scale , typename T_shape >
return_type<T_y, T_loc, T_scale, T_shape>::type stan::math::skew_normal_lcdf ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma,
const T_shape &  alpha 
)

Definition at line 26 of file skew_normal_lcdf.hpp.

§ skew_normal_log() [1/2]

template<bool propto, typename T_y , typename T_loc , typename T_scale , typename T_shape >
return_type<T_y, T_loc, T_scale, T_shape>::type stan::math::skew_normal_log ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma,
const T_shape &  alpha 
)

Definition at line 29 of file skew_normal_log.hpp.

§ skew_normal_log() [2/2]

template<typename T_y , typename T_loc , typename T_scale , typename T_shape >
return_type<T_y, T_loc, T_scale, T_shape>::type stan::math::skew_normal_log ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma,
const T_shape &  alpha 
)
inline

Definition at line 131 of file skew_normal_log.hpp.

§ skew_normal_lpdf() [1/2]

template<bool propto, typename T_y , typename T_loc , typename T_scale , typename T_shape >
return_type<T_y, T_loc, T_scale, T_shape>::type stan::math::skew_normal_lpdf ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma,
const T_shape &  alpha 
)

Definition at line 29 of file skew_normal_lpdf.hpp.

§ skew_normal_lpdf() [2/2]

template<typename T_y , typename T_loc , typename T_scale , typename T_shape >
return_type<T_y, T_loc, T_scale, T_shape>::type stan::math::skew_normal_lpdf ( const T_y &  y,
const T_loc &  mu,
const T_scale &  sigma,
const T_shape &  alpha 
)
inline

Definition at line 131 of file skew_normal_lpdf.hpp.

§ skew_normal_rng()

template<class RNG >
double stan::math::skew_normal_rng ( double  mu,
double  sigma,
double  alpha,
RNG &  rng 
)
inline

Definition at line 21 of file skew_normal_rng.hpp.

§ softmax() [1/3]

template<typename T >
Eigen::Matrix<fvar<T>, Eigen::Dynamic, 1> stan::math::softmax ( const Eigen::Matrix< fvar< T >, Eigen::Dynamic, 1 > &  alpha)
inline

Definition at line 14 of file softmax.hpp.

§ softmax() [2/3]

template<typename T >
Eigen::Matrix<T, Eigen::Dynamic, 1> stan::math::softmax ( const Eigen::Matrix< T, Eigen::Dynamic, 1 > &  v)
inline

Return the softmax of the specified vector.

$ \mbox{softmax}(y) = \frac{\exp(y)} {\sum_{k=1}^K \exp(y_k)}, $

The entries in the Jacobian of the softmax function are given by $ \begin{array}{l} \displaystyle \frac{\partial}{\partial y_m} \mbox{softmax}(y)[k] \\[8pt] \displaystyle \mbox{ } \ \ \ = \left\{ \begin{array}{ll} \mbox{softmax}(y)[k] - \mbox{softmax}(y)[k] \times \mbox{softmax}(y)[m] & \mbox{ if } m = k, \mbox{ and} \\[6pt] \mbox{softmax}(y)[k] * \mbox{softmax}(y)[m] & \mbox{ if } m \neq k. \end{array} \right. \end{array} $

Template Parameters
TScalar type of values in vector.
Parameters
[in]vVector to transform.
Returns
Unit simplex result of the softmax transform of the vector.

Definition at line 46 of file softmax.hpp.

§ softmax() [3/3]

Eigen::Matrix<var, Eigen::Dynamic, 1> stan::math::softmax ( const Eigen::Matrix< var, Eigen::Dynamic, 1 > &  alpha)
inline

Return the softmax of the specified Eigen vector.

Softmax is guaranteed to return a simplex.

The gradient calculations are unfolded.

Parameters
alphaUnconstrained input vector.
Returns
Softmax of the input.
Exceptions
std::domain_errorIf the input vector is size 0.

Definition at line 58 of file softmax.hpp.

§ sort_asc() [1/2]

template<typename T >
std::vector<T> stan::math::sort_asc ( std::vector< T >  xs)
inline

Return the specified standard vector in ascending order.

Template Parameters
TType of elements contained in vector.
Parameters
xsVector to order.
Returns
Vector in ascending order.
Exceptions
std::domain_errorIf any of the values are NaN.

Definition at line 20 of file sort_asc.hpp.

§ sort_asc() [2/2]

template<typename T , int R, int C>
Eigen::Matrix<T, R, C> stan::math::sort_asc ( Eigen::Matrix< T, R, C >  xs)
inline

Return the specified vector in ascending order.

Template Parameters
TType of elements contained in vector.
Parameters
xsVector to order.
Returns
Vector in ascending order.
Exceptions
std::domain_errorIf any of the values are NaN.

Definition at line 20 of file sort_asc.hpp.

§ sort_desc() [1/2]

template<typename T >
std::vector<T> stan::math::sort_desc ( std::vector< T >  xs)
inline

Return the specified standard vector in descending order.

Template Parameters
TType of elements contained in vector.
Parameters
xsVector to order.
Returns
Vector in descending order.
Exceptions
std::domain_errorIf any of the values are NaN.

Definition at line 21 of file sort_desc.hpp.

§ sort_desc() [2/2]

template<typename T , int R, int C>
Eigen::Matrix<T, R, C> stan::math::sort_desc ( Eigen::Matrix< T, R, C >  xs)
inline

Return the specified vector in descending order.

Template Parameters
TType of elements contained in vector.
Parameters
xsVector to order.
Returns
Vector in descending order.
Exceptions
std::domain_errorIf any of the values are NaN.

Definition at line 22 of file sort_desc.hpp.

§ sort_indices_asc()

template<typename C >
std::vector<int> stan::math::sort_indices_asc ( const C &  xs)

Return a sorted copy of the argument container in ascending order.

Template Parameters
Ctype of container
Parameters
xsContainer to sort
Returns
sorted version of container

Definition at line 22 of file sort_indices_asc.hpp.

§ sort_indices_desc()

template<typename C >
std::vector<int> stan::math::sort_indices_desc ( const C &  xs)

Return a sorted copy of the argument container in ascending order.

Template Parameters
Ctype of container
Parameters
xsContainer to sort
Returns
sorted version of container

Definition at line 22 of file sort_indices_desc.hpp.

§ sqrt() [1/3]

template<typename T >
fvar<T> stan::math::sqrt ( const fvar< T > &  x)
inline

Definition at line 14 of file sqrt.hpp.

§ sqrt() [2/3]

template<typename T >
apply_scalar_unary<sqrt_fun, T>::return_t stan::math::sqrt ( const T &  x)
inline

Vectorized version of sqrt().

Parameters
xContainer.
Template Parameters
TContainer type.
Returns
Square root of each value in x.

Definition at line 32 of file sqrt.hpp.

§ sqrt() [3/3]

var stan::math::sqrt ( const var a)
inline

Return the square root of the specified variable (cmath).

The derivative is defined by

$\frac{d}{dx} \sqrt{x} = \frac{1}{2 \sqrt{x}}$.

\[ \mbox{sqrt}(x) = \begin{cases} \textrm{NaN} & x < 0 \\ \sqrt{x} & \mbox{if } x\geq 0\\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{sqrt}(x)}{\partial x} = \begin{cases} \textrm{NaN} & x < 0 \\ \frac{1}{2\sqrt{x}} & x\geq 0\\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

Parameters
aVariable whose square root is taken.
Returns
Square root of variable.

Definition at line 50 of file sqrt.hpp.

§ sqrt2()

double stan::math::sqrt2 ( )
inline

Return the square root of two.

Returns
Square root of two.

Definition at line 103 of file constants.hpp.

§ square() [1/4]

template<typename T >
fvar<T> stan::math::square ( const fvar< T > &  x)
inline

Definition at line 14 of file square.hpp.

§ square() [2/4]

double stan::math::square ( double  x)
inline

Return the square of the specified argument.

$\mbox{square}(x) = x^2$.

The implementation of square(x) is just x * x. Given this, this method is mainly useful in cases where x is not a simple primitive type, particularly when it is an auto-dif type.

Parameters
xInput to square.
Returns
Square of input.

Definition at line 20 of file square.hpp.

§ square() [3/4]

template<typename T >
apply_scalar_unary<square_fun, T>::return_t stan::math::square ( const T &  x)
inline

Vectorized version of square().

Parameters
xContainer.
Template Parameters
TContainer type.
Returns
Each value in x squared.

Definition at line 31 of file square.hpp.

§ square() [4/4]

var stan::math::square ( const var x)
inline

Return the square of the input variable.

Using square(x) is more efficient than using x * x.

\[ \mbox{square}(x) = \begin{cases} x^2 & \mbox{if } -\infty\leq x \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{square}(x)}{\partial x} = \begin{cases} 2x & \mbox{if } -\infty\leq x\leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

Parameters
xVariable to square.
Returns
Square of variable.

Definition at line 46 of file square.hpp.

§ squared_distance() [1/15]

template<typename T1 , typename T2 >
boost::math::tools::promote_args<T1, T2>::type stan::math::squared_distance ( const T1 &  x1,
const T2 &  x2 
)
inline

Returns the squared distance.

Parameters
x1First vector.
x2Second vector.
Returns
Dot product of the vectors.
Exceptions
std::domain_errorIf the vectors are not the same size or if they are both not vector dimensioned.

Definition at line 21 of file squared_distance.hpp.

§ squared_distance() [2/15]

template<int R, int C>
double stan::math::squared_distance ( const Eigen::Matrix< double, R, C > &  v1,
const Eigen::Matrix< double, R, C > &  v2 
)
inline

Returns the squared distance between the specified vectors of the same dimensions.

Template Parameters
RRows at compile time of vector inputs
Ccolumns at compile time of vector inputs
Parameters
v1First vector.
v2Second vector.
Returns
Dot product of the vectors.
Exceptions
std::domain_errorIf the vectors are not the same size or if they are both not vector dimensioned.

Definition at line 26 of file squared_distance.hpp.

§ squared_distance() [3/15]

template<typename T , int R, int C>
fvar<T> stan::math::squared_distance ( const Eigen::Matrix< fvar< T >, R, C > &  v1,
const Eigen::Matrix< double, R, C > &  v2 
)
inline

Returns the squared distance between the specified vectors of the same dimensions.

Template Parameters
RRows at compile time of vector inputs
Ccolumns at compile time of vector inputs
TChild scalar type of fvar vector input
Parameters
v1First vector.
v2Second vector.
Returns
Dot product of the vectors.
Exceptions
std::domain_errorIf the vectors are not the same size or if they are both not vector dimensioned.

Definition at line 30 of file squared_distance.hpp.

§ squared_distance() [4/15]

var stan::math::squared_distance ( const var a,
const var b 
)
inline

Returns the log sum of exponentials.

Definition at line 46 of file squared_distance.hpp.

§ squared_distance() [5/15]

template<int R1, int C1, int R2, int C2>
double stan::math::squared_distance ( const Eigen::Matrix< double, R1, C1 > &  v1,
const Eigen::Matrix< double, R2, C2 > &  v2 
)
inline

Returns the squared distance between the specified vectors of the same dimensions.

Template Parameters
R1Rows at compile time of first vector input
C1Columns at compile time of first vector input
R2Rows at compile time of second vector input
C2Columns at compile time of second vector input
Parameters
v1First vector.
v2Second vector.
Returns
Dot product of the vectors.
Exceptions
std::domain_errorIf the vectors are not the same size or if they are both not vector dimensioned.

Definition at line 50 of file squared_distance.hpp.

§ squared_distance() [6/15]

var stan::math::squared_distance ( const var a,
double  b 
)
inline

Returns the log sum of exponentials.

Definition at line 53 of file squared_distance.hpp.

§ squared_distance() [7/15]

template<typename T , int R1, int C1, int R2, int C2>
fvar<T> stan::math::squared_distance ( const Eigen::Matrix< fvar< T >, R1, C1 > &  v1,
const Eigen::Matrix< double, R2, C2 > &  v2 
)
inline

Returns the squared distance between the specified vectors of the same dimensions.

Template Parameters
R1Rows at compile time of first vector input
C1Columns at compile time of first vector input
R2Rows at compile time of second vector input
C2Columns at compile time of second vector input
TChild scalar type of fvar vector input
Parameters
v1First vector.
v2Second vector.
Returns
Dot product of the vectors.
Exceptions
std::domain_errorIf the vectors are not the same size or if they are both not vector dimensioned.

Definition at line 56 of file squared_distance.hpp.

§ squared_distance() [8/15]

var stan::math::squared_distance ( double  a,
const var b 
)
inline

Returns the log sum of exponentials.

Definition at line 60 of file squared_distance.hpp.

§ squared_distance() [9/15]

template<typename T , int R, int C>
fvar<T> stan::math::squared_distance ( const Eigen::Matrix< double, R, C > &  v1,
const Eigen::Matrix< fvar< T >, R, C > &  v2 
)
inline

Returns the squared distance between the specified vectors of the same dimensions.

Template Parameters
RRows at compile time of vector inputs
Ccolumns at compile time of vector inputs
TChild scalar type of fvar vector input
Parameters
v1First vector.
v2Second vector.
Returns
Dot product of the vectors.
Exceptions
std::domain_errorIf the vectors are not the same size or if they are both not vector dimensioned.

Definition at line 81 of file squared_distance.hpp.

§ squared_distance() [10/15]

template<typename T , int R1, int C1, int R2, int C2>
fvar<T> stan::math::squared_distance ( const Eigen::Matrix< double, R1, C1 > &  v1,
const Eigen::Matrix< fvar< T >, R2, C2 > &  v2 
)
inline

Returns the squared distance between the specified vectors of the same dimensions.

Template Parameters
R1Rows at compile time of first vector input
C1Columns at compile time of first vector input
R2Rows at compile time of second vector input
C2Columns at compile time of second vector input
TChild scalar type of fvar vector input
Parameters
v1First vector.
v2Second vector.
Returns
Dot product of the vectors.
Exceptions
std::domain_errorIf the vectors are not the same size or if they are both not vector dimensioned.

Definition at line 107 of file squared_distance.hpp.

§ squared_distance() [11/15]

template<int R1, int C1, int R2, int C2>
var stan::math::squared_distance ( const Eigen::Matrix< var, R1, C1 > &  v1,
const Eigen::Matrix< var, R2, C2 > &  v2 
)
inline

Definition at line 109 of file squared_distance.hpp.

§ squared_distance() [12/15]

template<int R1, int C1, int R2, int C2>
var stan::math::squared_distance ( const Eigen::Matrix< var, R1, C1 > &  v1,
const Eigen::Matrix< double, R2, C2 > &  v2 
)
inline

Definition at line 119 of file squared_distance.hpp.

§ squared_distance() [13/15]

template<int R1, int C1, int R2, int C2>
var stan::math::squared_distance ( const Eigen::Matrix< double, R1, C1 > &  v1,
const Eigen::Matrix< var, R2, C2 > &  v2 
)
inline

Definition at line 129 of file squared_distance.hpp.

§ squared_distance() [14/15]

template<typename T , int R, int C>
fvar<T> stan::math::squared_distance ( const Eigen::Matrix< fvar< T >, R, C > &  v1,
const Eigen::Matrix< fvar< T >, R, C > &  v2 
)
inline

Returns the squared distance between the specified vectors of the same dimensions.

Template Parameters
RRows at compile time of vector inputs
Ccolumns at compile time of vector inputs
TChild scalar type of fvar vector input
Parameters
v1First vector.
v2Second vector.
Returns
Dot product of the vectors.
Exceptions
std::domain_errorIf the vectors are not the same size or if they are both not vector dimensioned.

Definition at line 131 of file squared_distance.hpp.

§ squared_distance() [15/15]

template<typename T , int R1, int C1, int R2, int C2>
fvar<T> stan::math::squared_distance ( const Eigen::Matrix< fvar< T >, R1, C1 > &  v1,
const Eigen::Matrix< fvar< T >, R2, C2 > &  v2 
)
inline

Returns the squared distance between the specified vectors of the same dimensions.

Template Parameters
R1Rows at compile time of first vector input
C1Columns at compile time of first vector input
R2Rows at compile time of second vector input
C2Columns at compile time of second vector input
TChild scalar type of fvar vector input
Parameters
v1First vector.
v2Second vector.
Returns
Dot product of the vectors.
Exceptions
std::domain_errorIf the vectors are not the same size or if they are both not vector dimensioned.

Definition at line 157 of file squared_distance.hpp.

§ stan_print() [1/6]

void stan::math::stan_print ( std::ostream *  o,
const var x 
)
inline

Definition at line 10 of file stan_print.hpp.

§ stan_print() [2/6]

template<typename T >
void stan::math::stan_print ( std::ostream *  o,
const T &  x 
)

Definition at line 12 of file stan_print.hpp.

§ stan_print() [3/6]

template<typename T >
void stan::math::stan_print ( std::ostream *  o,
const std::vector< T > &  x 
)

Definition at line 17 of file stan_print.hpp.

§ stan_print() [4/6]

template<typename T >
void stan::math::stan_print ( std::ostream *  o,
const Eigen::Matrix< T, Eigen::Dynamic, 1 > &  x 
)

Definition at line 27 of file stan_print.hpp.

§ stan_print() [5/6]

template<typename T >
void stan::math::stan_print ( std::ostream *  o,
const Eigen::Matrix< T, 1, Eigen::Dynamic > &  x 
)

Definition at line 38 of file stan_print.hpp.

§ stan_print() [6/6]

template<typename T >
void stan::math::stan_print ( std::ostream *  o,
const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &  x 
)

Definition at line 49 of file stan_print.hpp.

§ start_nested()

static void stan::math::start_nested ( )
inlinestatic

Record the current position so that recover_memory_nested() can find it.

Definition at line 13 of file start_nested.hpp.

§ step() [1/2]

var stan::math::step ( const var a)
inline

Return the step, or heaviside, function applied to the specified variable (stan).

See step() for the double-based version.

The derivative of the step function is zero everywhere but at 0, so for convenience, it is taken to be everywhere zero,

$\mbox{step}(x) = 0$.

Parameters
aVariable argument.
Returns
The constant variable with value 1.0 if the argument's value is greater than or equal to 0.0, and value 0.0 otherwise.

Definition at line 25 of file step.hpp.

§ step() [2/2]

template<typename T >
int stan::math::step ( const T  y)
inline

The step, or Heaviside, function.

The function is defined by

step(y) = (y < 0.0) ? 0 : 1.

\[ \mbox{step}(x) = \begin{cases} 0 & \mbox{if } x \leq 0 \\ 1 & \mbox{if } x > 0 \\[6pt] 0 & \mbox{if } x = \textrm{NaN} \end{cases} \]

Parameters
yScalar argument.
Returns
1 if the specified argument is greater than or equal to 0.0, and 0 otherwise.

Definition at line 29 of file step.hpp.

§ student_t_ccdf_log()

template<typename T_y , typename T_dof , typename T_loc , typename T_scale >
return_type<T_y, T_dof, T_loc, T_scale>::type stan::math::student_t_ccdf_log ( const T_y &  y,
const T_dof &  nu,
const T_loc &  mu,
const T_scale &  sigma 
)

Definition at line 32 of file student_t_ccdf_log.hpp.

§ student_t_cdf()

template<typename T_y , typename T_dof , typename T_loc , typename T_scale >
return_type<T_y, T_dof, T_loc, T_scale>::type stan::math::student_t_cdf ( const T_y &  y,
const T_dof &  nu,
const T_loc &  mu,
const T_scale &  sigma 
)

Definition at line 32 of file student_t_cdf.hpp.

§ student_t_cdf_log()

template<typename T_y , typename T_dof , typename T_loc , typename T_scale >
return_type<T_y, T_dof, T_loc, T_scale>::type stan::math::student_t_cdf_log ( const T_y &  y,
const T_dof &  nu,
const T_loc &  mu,
const T_scale &  sigma 
)

Definition at line 32 of file student_t_cdf_log.hpp.

§ student_t_lccdf()

template<typename T_y , typename T_dof , typename T_loc , typename T_scale >
return_type<T_y, T_dof, T_loc, T_scale>::type stan::math::student_t_lccdf ( const T_y &  y,
const T_dof &  nu,
const T_loc &  mu,
const T_scale &  sigma 
)

Definition at line 32 of file student_t_lccdf.hpp.

§ student_t_lcdf()

template<typename T_y , typename T_dof , typename T_loc , typename T_scale >
return_type<T_y, T_dof, T_loc, T_scale>::type stan::math::student_t_lcdf ( const T_y &  y,
const T_dof &  nu,
const T_loc &  mu,
const T_scale &  sigma 
)

Definition at line 32 of file student_t_lcdf.hpp.

§ student_t_log() [1/2]

template<bool propto, typename T_y , typename T_dof , typename T_loc , typename T_scale >
return_type<T_y, T_dof, T_loc, T_scale>::type stan::math::student_t_log ( const T_y &  y,
const T_dof &  nu,
const T_loc &  mu,
const T_scale &  sigma 
)

The log of the Student-t density for the given y, nu, mean, and scale parameter.

The scale parameter must be greater than 0.

\begin{eqnarray*} y &\sim& t_{\nu} (\mu, \sigma^2) \\ \log (p (y \, |\, \nu, \mu, \sigma) ) &=& \log \left( \frac{\Gamma((\nu + 1) /2)} {\Gamma(\nu/2)\sqrt{\nu \pi} \sigma} \left( 1 + \frac{1}{\nu} (\frac{y - \mu}{\sigma})^2 \right)^{-(\nu + 1)/2} \right) \\ &=& \log( \Gamma( (\nu+1)/2 )) - \log (\Gamma (\nu/2) - \frac{1}{2} \log(\nu \pi) - \log(\sigma) -\frac{\nu + 1}{2} \log (1 + \frac{1}{\nu} (\frac{y - \mu}{\sigma})^2) \end{eqnarray*}

Parameters
yA scalar variable.
nuDegrees of freedom.
muThe mean of the Student-t distribution.
sigmaThe scale parameter of the Student-t distribution.
Returns
The log of the Student-t density at y.
Exceptions
std::domain_errorif sigma is not greater than 0.
std::domain_errorif nu is not greater than 0.
Template Parameters
T_yType of scalar.
T_dofType of degrees of freedom.
T_locType of location.
T_scaleType of scale.

Definition at line 57 of file student_t_log.hpp.

§ student_t_log() [2/2]

template<typename T_y , typename T_dof , typename T_loc , typename T_scale >
return_type<T_y, T_dof, T_loc, T_scale>::type stan::math::student_t_log ( const T_y &  y,
const T_dof &  nu,
const T_loc &  mu,
const T_scale &  sigma 
)
inline

Definition at line 209 of file student_t_log.hpp.

§ student_t_lpdf() [1/2]

template<bool propto, typename T_y , typename T_dof , typename T_loc , typename T_scale >
return_type<T_y, T_dof, T_loc, T_scale>::type stan::math::student_t_lpdf ( const T_y &  y,
const T_dof &  nu,
const T_loc &  mu,
const T_scale &  sigma 
)

The log of the Student-t density for the given y, nu, mean, and scale parameter.

The scale parameter must be greater than 0.

\begin{eqnarray*} y &\sim& t_{\nu} (\mu, \sigma^2) \\ \log (p (y \, |\, \nu, \mu, \sigma) ) &=& \log \left( \frac{\Gamma((\nu + 1) /2)} {\Gamma(\nu/2)\sqrt{\nu \pi} \sigma} \left( 1 + \frac{1}{\nu} (\frac{y - \mu}{\sigma})^2 \right)^{-(\nu + 1)/2} \right) \\ &=& \log( \Gamma( (\nu+1)/2 )) - \log (\Gamma (\nu/2) - \frac{1}{2} \log(\nu \pi) - \log(\sigma) -\frac{\nu + 1}{2} \log (1 + \frac{1}{\nu} (\frac{y - \mu}{\sigma})^2) \end{eqnarray*}

Parameters
yA scalar variable.
nuDegrees of freedom.
muThe mean of the Student-t distribution.
sigmaThe scale parameter of the Student-t distribution.
Returns
The log of the Student-t density at y.
Exceptions
std::domain_errorif sigma is not greater than 0.
std::domain_errorif nu is not greater than 0.
Template Parameters
T_yType of scalar.
T_dofType of degrees of freedom.
T_locType of location.
T_scaleType of scale.

Definition at line 57 of file student_t_lpdf.hpp.

§ student_t_lpdf() [2/2]

template<typename T_y , typename T_dof , typename T_loc , typename T_scale >
return_type<T_y, T_dof, T_loc, T_scale>::type stan::math::student_t_lpdf ( const T_y &  y,
const T_dof &  nu,
const T_loc &  mu,
const T_scale &  sigma 
)
inline

Definition at line 209 of file student_t_lpdf.hpp.

§ student_t_rng()

template<class RNG >
double stan::math::student_t_rng ( double  nu,
double  mu,
double  sigma,
RNG &  rng 
)
inline

Definition at line 27 of file student_t_rng.hpp.

§ sub()

void stan::math::sub ( std::vector< double > &  x,
std::vector< double > &  y,
std::vector< double > &  result 
)
inline

Definition at line 10 of file sub.hpp.

§ sub_col()

template<typename T >
Eigen::Matrix<T, Eigen::Dynamic, 1> stan::math::sub_col ( const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &  m,
size_t  i,
size_t  j,
size_t  nrows 
)
inline

Return a nrows x 1 subcolumn starting at (i-1, j-1).

Parameters
mMatrix.
iStarting row + 1.
jStarting column + 1.
nrowsNumber of rows in block.
Exceptions
std::out_of_rangeif either index is out of range.

Definition at line 23 of file sub_col.hpp.

§ sub_row()

template<typename T >
Eigen::Matrix<T, 1, Eigen::Dynamic> stan::math::sub_row ( const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &  m,
size_t  i,
size_t  j,
size_t  ncols 
)
inline

Return a 1 x nrows subrow starting at (i-1, j-1).

Parameters
mMatrix Input matrix.
iStarting row + 1.
jStarting column + 1.
ncolsNumber of columns in block.
Exceptions
std::out_of_rangeif either index is out of range.

Definition at line 23 of file sub_row.hpp.

§ subtract() [1/3]

template<typename T1 , typename T2 , int R, int C>
Eigen::Matrix<typename boost::math::tools::promote_args<T1, T2>::type, R, C> stan::math::subtract ( const Eigen::Matrix< T1, R, C > &  m1,
const Eigen::Matrix< T2, R, C > &  m2 
)
inline

Return the result of subtracting the second specified matrix from the first specified matrix.

The return scalar type is the promotion of the input types.

Template Parameters
T1Scalar type of first matrix.
T2Scalar type of second matrix.
RRow type of matrices.
CColumn type of matrices.
Parameters
m1First matrix.
m2Second matrix.
Returns
Difference between first matrix and second matrix.

Definition at line 27 of file subtract.hpp.

§ subtract() [2/3]

template<typename T1 , typename T2 , int R, int C>
Eigen::Matrix<typename boost::math::tools::promote_args<T1, T2>::type, R, C> stan::math::subtract ( const T1 &  c,
const Eigen::Matrix< T2, R, C > &  m 
)
inline

Definition at line 41 of file subtract.hpp.

§ subtract() [3/3]

template<typename T1 , typename T2 , int R, int C>
Eigen::Matrix<typename boost::math::tools::promote_args<T1, T2>::type, R, C> stan::math::subtract ( const Eigen::Matrix< T1, R, C > &  m,
const T2 &  c 
)
inline

Definition at line 54 of file subtract.hpp.

§ sum() [1/6]

template<typename T >
T stan::math::sum ( const std::vector< T > &  xs)
inline

Return the sum of the values in the specified standard vector.

Template Parameters
TType of elements summed.
Parameters
xsStandard vector to sum.
Returns
Sum of elements.

Definition at line 18 of file sum.hpp.

§ sum() [2/6]

template<typename T >
fvar<T> stan::math::sum ( const std::vector< fvar< T > > &  m)
inline

Return the sum of the entries of the specified standard vector.

Template Parameters
TType of vector entries.
Parameters
mVector.
Returns
Sum of vector entries.

Definition at line 20 of file sum.hpp.

§ sum() [3/6]

template<typename T , int R, int C>
fvar<T> stan::math::sum ( const Eigen::Matrix< fvar< T >, R, C > &  m)
inline

Return the sum of the entries of the specified matrix.

Template Parameters
TType of matrix entries.
RRow type of matrix.
CColumn type of matrix.
Parameters
mMatrix.
Returns
Sum of matrix entries.

Definition at line 21 of file sum.hpp.

§ sum() [4/6]

template<typename T , int R, int C>
double stan::math::sum ( const Eigen::Matrix< T, R, C > &  v)
inline

Returns the sum of the coefficients of the specified column vector.

Template Parameters
TType of elements in matrix.
RRow type of matrix.
CColumn type of matrix.
Parameters
vSpecified vector.
Returns
Sum of coefficients of vector.

Definition at line 22 of file sum.hpp.

§ sum() [5/6]

template<int R, int C>
var stan::math::sum ( const Eigen::Matrix< var, R, C > &  m)
inline

Returns the sum of the coefficients of the specified matrix, column vector or row vector.

Template Parameters
RRow type for matrix.
CColumn type for matrix.
Parameters
mSpecified matrix or vector.
Returns
Sum of coefficients of matrix.

Definition at line 50 of file sum.hpp.

§ sum() [6/6]

var stan::math::sum ( const std::vector< var > &  m)
inline

Returns the sum of the entries of the specified vector.

Parameters
mVector.
Returns
Sum of vector entries.

Definition at line 53 of file sum.hpp.

§ tail() [1/3]

template<typename T >
Eigen::Matrix<T, Eigen::Dynamic, 1> stan::math::tail ( const Eigen::Matrix< T, Eigen::Dynamic, 1 > &  v,
size_t  n 
)
inline

Return the specified number of elements as a vector from the back of the specified vector.

Template Parameters
TType of value in vector.
Parameters
vVector input.
nSize of return.
Returns
The last n elements of v.
Exceptions
std::out_of_rangeif n is out of range.

Definition at line 28 of file tail.hpp.

§ tail() [2/3]

template<typename T >
Eigen::Matrix<T, 1, Eigen::Dynamic> stan::math::tail ( const Eigen::Matrix< T, 1, Eigen::Dynamic > &  rv,
size_t  n 
)
inline

Return the specified number of elements as a row vector from the back of the specified row vector.

Template Parameters
TType of value in vector.
Parameters
rvRow vector.
nSize of return row vector.
Returns
The last n elements of rv.
Exceptions
std::out_of_rangeif n is out of range.

Definition at line 48 of file tail.hpp.

§ tail() [3/3]

template<typename T >
std::vector<T> stan::math::tail ( const std::vector< T > &  sv,
size_t  n 
)

Return the specified number of elements as a standard vector from the back of the specified standard vector.

Template Parameters
TType of value in vector.
Parameters
svStandard vector.
nSize of return.
Returns
The last n elements of sv.
Exceptions
std::out_of_rangeif n is out of range.

Definition at line 66 of file tail.hpp.

§ tan() [1/3]

template<typename T >
fvar<T> stan::math::tan ( const fvar< T > &  x)
inline

Definition at line 12 of file tan.hpp.

§ tan() [2/3]

template<typename T >
apply_scalar_unary<tan_fun, T>::return_t stan::math::tan ( const T &  x)
inline

Vectorized version of tan().

Parameters
xContainer of angles in radians.
Template Parameters
TContainer type.
Returns
Tangent of each value in x.

Definition at line 32 of file tan.hpp.

§ tan() [3/3]

var stan::math::tan ( const var a)
inline

Return the tangent of a radian-scaled variable (cmath).

The derivative is defined by

$\frac{d}{dx} \tan x = \sec^2 x$.

\[ \mbox{tan}(x) = \begin{cases} \tan(x) & \mbox{if } -\infty\leq x \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{tan}(x)}{\partial x} = \begin{cases} \sec^2(x) & \mbox{if } -\infty\leq x\leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

Parameters
aVariable for radians of angle.
Returns
Tangent of variable.

Definition at line 49 of file tan.hpp.

§ tanh() [1/3]

template<typename T >
fvar<T> stan::math::tanh ( const fvar< T > &  x)
inline

Definition at line 12 of file tanh.hpp.

§ tanh() [2/3]

template<typename T >
apply_scalar_unary<tanh_fun, T>::return_t stan::math::tanh ( const T &  x)
inline

Vectorized version of tanh().

Parameters
xContainer of angles in radians.
Template Parameters
TContainer type.
Returns
Hyperbolic tangent of each value in x.

Definition at line 32 of file tanh.hpp.

§ tanh() [3/3]

var stan::math::tanh ( const var a)
inline

Return the hyperbolic tangent of the specified variable (cmath).

The derivative is defined by

$\frac{d}{dx} \tanh x = \frac{1}{\cosh^2 x}$.

\[ \mbox{tanh}(x) = \begin{cases} \tanh(x) & \mbox{if } -\infty\leq x \leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{tanh}(x)}{\partial x} = \begin{cases} \mbox{sech}^2(x) & \mbox{if } -\infty\leq x\leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

Parameters
aVariable.
Returns
Hyperbolic tangent of variable.

Definition at line 50 of file tanh.hpp.

§ tcrossprod() [1/3]

template<typename T , int R, int C>
Eigen::Matrix<fvar<T>, R, R> stan::math::tcrossprod ( const Eigen::Matrix< fvar< T >, R, C > &  m)
inline

Definition at line 17 of file tcrossprod.hpp.

§ tcrossprod() [2/3]

matrix_d stan::math::tcrossprod ( const matrix_d M)
inline

Returns the result of post-multiplying a matrix by its own transpose.

Parameters
MMatrix to multiply.
Returns
M times its transpose.

Definition at line 17 of file tcrossprod.hpp.

§ tcrossprod() [3/3]

matrix_v stan::math::tcrossprod ( const matrix_v M)
inline

Returns the result of post-multiplying a matrix by its own transpose.

Parameters
MMatrix to multiply.
Returns
M times its transpose.

Definition at line 25 of file tcrossprod.hpp.

§ tgamma() [1/4]

double stan::math::tgamma ( double  x)
inline

Return the gamma function applied to the specified argument.

Parameters
xArgument.
Returns
The gamma function applied to argument.

Definition at line 15 of file tgamma.hpp.

§ tgamma() [2/4]

template<typename T >
fvar<T> stan::math::tgamma ( const fvar< T > &  x)
inline

Return the result of applying the gamma function to the specified argument.

Template Parameters
TScalar type of autodiff variable.
Parameters
xArgument.
Returns
Gamma function applied to argument.

Definition at line 20 of file tgamma.hpp.

§ tgamma() [3/4]

template<typename T >
apply_scalar_unary<tgamma_fun, T>::return_t stan::math::tgamma ( const T &  x)
inline

Vectorized version of tgamma().

Parameters
xContainer.
Template Parameters
TContainer type.
Returns
Gamma function applied to each value in x.
Exceptions
std::domain_errorif any value is 0 or a negative integer

Definition at line 34 of file tgamma.hpp.

§ tgamma() [4/4]

var stan::math::tgamma ( const var a)
inline

Return the Gamma function applied to the specified variable (C99).

The derivative with respect to the argument is

$\frac{d}{dx} \Gamma(x) = \Gamma(x) \Psi^{(0)}(x)$

where $\Psi^{(0)}(x)$ is the digamma function.

\[ \mbox{tgamma}(x) = \begin{cases} \textrm{error} & \mbox{if } x\in \{\dots, -3, -2, -1, 0\}\\ \Gamma(x) & \mbox{if } x\not\in \{\dots, -3, -2, -1, 0\}\\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{tgamma}(x)}{\partial x} = \begin{cases} \textrm{error} & \mbox{if } x\in \{\dots, -3, -2, -1, 0\}\\ \frac{\partial\, \Gamma(x)}{\partial x} & \mbox{if } x\not\in \{\dots, -3, -2, -1, 0\}\\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \Gamma(x)=\int_0^{\infty} u^{x - 1} \exp(-u) \, du \]

\[ \frac{\partial \, \Gamma(x)}{\partial x} = \Gamma(x)\Psi(x) \]

Parameters
aArgument to function.
Returns
The Gamma function applied to the specified argument.

Definition at line 61 of file tgamma.hpp.

§ to_array_1d() [1/3]

template<typename T , int R, int C>
std::vector<T> stan::math::to_array_1d ( const Eigen::Matrix< T, R, C > &  matrix)
inline

Definition at line 15 of file to_array_1d.hpp.

§ to_array_1d() [2/3]

template<typename T >
std::vector<T> stan::math::to_array_1d ( const std::vector< T > &  x)
inline

Definition at line 29 of file to_array_1d.hpp.

§ to_array_1d() [3/3]

template<typename T >
std::vector<typename scalar_type<T>::type> stan::math::to_array_1d ( const std::vector< std::vector< T > > &  x)
inline

Definition at line 36 of file to_array_1d.hpp.

§ to_array_2d()

template<typename T >
std::vector< std::vector<T> > stan::math::to_array_2d ( const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &  matrix)
inline

Definition at line 13 of file to_array_2d.hpp.

§ to_fvar() [1/8]

template<typename T >
fvar<T> stan::math::to_fvar ( const T &  x)
inline

Definition at line 12 of file to_fvar.hpp.

§ to_fvar() [2/8]

template<typename T >
std::vector<fvar<T> > stan::math::to_fvar ( const std::vector< T > &  v)
inline

Definition at line 14 of file to_fvar.hpp.

§ to_fvar() [3/8]

template<int R, int C, typename T >
Eigen::Matrix<T, R, C> stan::math::to_fvar ( const Eigen::Matrix< T, R, C > &  m)
inline

Definition at line 15 of file to_fvar.hpp.

§ to_fvar() [4/8]

template<typename T >
fvar<T> stan::math::to_fvar ( const fvar< T > &  x)
inline

Definition at line 19 of file to_fvar.hpp.

§ to_fvar() [5/8]

template<int R, int C>
Eigen::Matrix<fvar<double>, R, C> stan::math::to_fvar ( const Eigen::Matrix< double, R, C > &  m)
inline

Definition at line 22 of file to_fvar.hpp.

§ to_fvar() [6/8]

template<typename T >
std::vector<fvar<T> > stan::math::to_fvar ( const std::vector< T > &  v,
const std::vector< T > &  d 
)
inline

Definition at line 24 of file to_fvar.hpp.

§ to_fvar() [7/8]

template<typename T , int R, int C>
Eigen::Matrix<fvar<T>, R, C> stan::math::to_fvar ( const Eigen::Matrix< T, R, C > &  val,
const Eigen::Matrix< T, R, C > &  deriv 
)
inline

Definition at line 32 of file to_fvar.hpp.

§ to_fvar() [8/8]

template<typename T >
std::vector<fvar<T> > stan::math::to_fvar ( const std::vector< fvar< T > > &  v)
inline

Definition at line 34 of file to_fvar.hpp.

§ to_matrix() [1/3]

template<typename T , int R, int C>
Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> stan::math::to_matrix ( Eigen::Matrix< T, R, C >  matrix)
inline

Definition at line 16 of file to_matrix.hpp.

§ to_matrix() [2/3]

template<typename T >
Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> stan::math::to_matrix ( const std::vector< std::vector< T > > &  vec)
inline

Definition at line 23 of file to_matrix.hpp.

§ to_matrix() [3/3]

Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic> stan::math::to_matrix ( const std::vector< std::vector< int > > &  vec)
inline

Definition at line 40 of file to_matrix.hpp.

§ to_row_vector() [1/3]

template<typename T , int R, int C>
Eigen::Matrix<T, 1, Eigen::Dynamic> stan::math::to_row_vector ( const Eigen::Matrix< T, R, C > &  matrix)
inline

Definition at line 16 of file to_row_vector.hpp.

§ to_row_vector() [2/3]

template<typename T >
Eigen::Matrix<T, 1, Eigen::Dynamic> stan::math::to_row_vector ( const std::vector< T > &  vec)
inline

Definition at line 24 of file to_row_vector.hpp.

§ to_row_vector() [3/3]

Eigen::Matrix<double, 1, Eigen::Dynamic> stan::math::to_row_vector ( const std::vector< int > &  vec)
inline

Definition at line 30 of file to_row_vector.hpp.

§ to_var() [1/10]

var stan::math::to_var ( double  x)
inline

Converts argument to an automatic differentiation variable.

Returns a var variable with the input value.

Parameters
[in]xA scalar value
Returns
An automatic differentiation variable with the input value.

Definition at line 17 of file to_var.hpp.

§ to_var() [2/10]

std::vector<var> stan::math::to_var ( const std::vector< double > &  v)
inline

Converts argument to an automatic differentiation variable.

Returns a var variable with the input value.

Parameters
[in]vA std::vector<double>
Returns
A std::vector<var> with the values set

Definition at line 20 of file to_var.hpp.

§ to_var() [3/10]

matrix_v stan::math::to_var ( const matrix_d m)
inline

Converts argument to an automatic differentiation variable.

Returns a var variable with the input value.

Parameters
[in]mA Matrix with scalars
Returns
A Matrix with automatic differentiation variables

Definition at line 21 of file to_var.hpp.

§ to_var() [4/10]

var stan::math::to_var ( const var x)
inline

Converts argument to an automatic differentiation variable.

Returns a var variable with the input value.

Parameters
[in]xAn automatic differentiation variable.
Returns
An automatic differentiation variable with the input value.

Definition at line 29 of file to_var.hpp.

§ to_var() [5/10]

std::vector<var> stan::math::to_var ( const std::vector< var > &  v)
inline

Converts argument to an automatic differentiation variable.

Returns a var variable with the input value.

Parameters
[in]vA std::vector<var>
Returns
A std::vector<var>

Definition at line 36 of file to_var.hpp.

§ to_var() [6/10]

matrix_v stan::math::to_var ( const matrix_v m)
inline

Converts argument to an automatic differentiation variable.

Returns a var variable with the input value.

Parameters
[in]mA Matrix with automatic differentiation variables.
Returns
A Matrix with automatic differentiation variables.

Definition at line 36 of file to_var.hpp.

§ to_var() [7/10]

vector_v stan::math::to_var ( const vector_d v)
inline

Converts argument to an automatic differentiation variable.

Returns a var variable with the input value.

Parameters
[in]vA Vector of scalars
Returns
A Vector of automatic differentiation variables with values of v

Definition at line 48 of file to_var.hpp.

§ to_var() [8/10]

vector_v stan::math::to_var ( const vector_v v)
inline

Converts argument to an automatic differentiation variable.

Returns a var variable with the input value.

Parameters
[in]vA Vector of automatic differentiation variables
Returns
A Vector of automatic differentiation variables with values of v

Definition at line 63 of file to_var.hpp.

§ to_var() [9/10]

row_vector_v stan::math::to_var ( const row_vector_d rv)
inline

Converts argument to an automatic differentiation variable.

Returns a var variable with the input value.

Parameters
[in]rvA row vector of scalars
Returns
A row vector of automatic differentation variables with values of rv.

Definition at line 75 of file to_var.hpp.

§ to_var() [10/10]

row_vector_v stan::math::to_var ( const row_vector_v rv)
inline

Converts argument to an automatic differentiation variable.

Returns a var variable with the input value.

Parameters
[in]rvA row vector with automatic differentiation variables
Returns
A row vector with automatic differentiation variables with values of rv.

Definition at line 90 of file to_var.hpp.

§ to_vector() [1/3]

template<typename T , int R, int C>
Eigen::Matrix<T, Eigen::Dynamic, 1> stan::math::to_vector ( const Eigen::Matrix< T, R, C > &  matrix)
inline

Definition at line 16 of file to_vector.hpp.

§ to_vector() [2/3]

template<typename T >
Eigen::Matrix<T, Eigen::Dynamic, 1> stan::math::to_vector ( const std::vector< T > &  vec)
inline

Definition at line 24 of file to_vector.hpp.

§ to_vector() [3/3]

Eigen::Matrix<double, Eigen::Dynamic, 1> stan::math::to_vector ( const std::vector< int > &  vec)
inline

Definition at line 30 of file to_vector.hpp.

§ trace() [1/2]

template<typename T >
T stan::math::trace ( const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &  m)
inline

Returns the trace of the specified matrix.

The trace is defined as the sum of the elements on the diagonal. The matrix is not required to be square. Returns 0 if matrix is empty.

Parameters
[in]mSpecified matrix.
Returns
Trace of the matrix.

Definition at line 19 of file trace.hpp.

§ trace() [2/2]

template<typename T >
T stan::math::trace ( const T &  m)
inline

Definition at line 25 of file trace.hpp.

§ trace_gen_inv_quad_form_ldlt() [1/2]

template<typename T1 , int R1, int C1, typename T2 , int R2, int C2, typename T3 , int R3, int C3>
boost::enable_if_c<stan::is_var<T1>::value || stan::is_var<T2>::value || stan::is_var<T3>::value, var>::type stan::math::trace_gen_inv_quad_form_ldlt ( const Eigen::Matrix< T1, R1, C1 > &  D,
const LDLT_factor< T2, R2, C2 > &  A,
const Eigen::Matrix< T3, R3, C3 > &  B 
)
inline

Compute the trace of an inverse quadratic form.

I.E., this computes trace(D B^T A^-1 B) where D is a square matrix and the LDLT_factor of A is provided.

Definition at line 27 of file trace_gen_inv_quad_form_ldlt.hpp.

§ trace_gen_inv_quad_form_ldlt() [2/2]

template<typename T1 , typename T2 , typename T3 , int R1, int C1, int R2, int C2, int R3, int C3>
boost::enable_if_c<!stan::is_var<T1>::value && !stan::is_var<T2>::value && !stan::is_var<T3>::value, typename boost::math::tools::promote_args<T1, T2, T3>::type>::type stan::math::trace_gen_inv_quad_form_ldlt ( const Eigen::Matrix< T1, R1, C1 > &  D,
const LDLT_factor< T2, R2, C2 > &  A,
const Eigen::Matrix< T3, R3, C3 > &  B 
)
inline

Definition at line 30 of file trace_gen_inv_quad_form_ldlt.hpp.

§ trace_gen_quad_form() [1/3]

template<int RD, int CD, int RA, int CA, int RB, int CB, typename T >
fvar<T> stan::math::trace_gen_quad_form ( const Eigen::Matrix< fvar< T >, RD, CD > &  D,
const Eigen::Matrix< fvar< T >, RA, CA > &  A,
const Eigen::Matrix< fvar< T >, RB, CB > &  B 
)
inline

Definition at line 16 of file trace_gen_quad_form.hpp.

§ trace_gen_quad_form() [2/3]

template<int RD, int CD, int RA, int CA, int RB, int CB>
double stan::math::trace_gen_quad_form ( const Eigen::Matrix< double, RD, CD > &  D,
const Eigen::Matrix< double, RA, CA > &  A,
const Eigen::Matrix< double, RB, CB > &  B 
)
inline

Compute trace(D B^T A B).

Definition at line 17 of file trace_gen_quad_form.hpp.

§ trace_gen_quad_form() [3/3]

template<typename TD , int RD, int CD, typename TA , int RA, int CA, typename TB , int RB, int CB>
boost::enable_if_c< boost::is_same<TD, var>::value || boost::is_same<TA, var>::value || boost::is_same<TB, var>::value, var >::type stan::math::trace_gen_quad_form ( const Eigen::Matrix< TD, RD, CD > &  D,
const Eigen::Matrix< TA, RA, CA > &  A,
const Eigen::Matrix< TB, RB, CB > &  B 
)
inline

Definition at line 113 of file trace_gen_quad_form.hpp.

§ trace_inv_quad_form_ldlt() [1/2]

template<typename T1 , typename T2 , int R2, int C2, int R3, int C3>
boost::enable_if_c<!stan::is_var<T1>::value && !stan::is_var<T2>::value, typename boost::math::tools::promote_args<T1, T2>::type>::type stan::math::trace_inv_quad_form_ldlt ( const LDLT_factor< T1, R2, C2 > &  A,
const Eigen::Matrix< T2, R3, C3 > &  B 
)
inline

Definition at line 27 of file trace_inv_quad_form_ldlt.hpp.

§ trace_inv_quad_form_ldlt() [2/2]

template<typename T2 , int R2, int C2, typename T3 , int R3, int C3>
boost::enable_if_c<stan::is_var<T2>::value || stan::is_var<T3>::value, var>::type stan::math::trace_inv_quad_form_ldlt ( const LDLT_factor< T2, R2, C2 > &  A,
const Eigen::Matrix< T3, R3, C3 > &  B 
)
inline

Compute the trace of an inverse quadratic form.

I.E., this computes trace(B^T A^-1 B) where the LDLT_factor of A is provided.

Definition at line 177 of file trace_inv_quad_form_ldlt.hpp.

§ trace_quad_form() [1/5]

template<int RA, int CA, int RB, int CB>
double stan::math::trace_quad_form ( const Eigen::Matrix< double, RA, CA > &  A,
const Eigen::Matrix< double, RB, CB > &  B 
)
inline

Compute trace(B^T A B).

Definition at line 15 of file trace_quad_form.hpp.

§ trace_quad_form() [2/5]

template<int RA, int CA, int RB, int CB, typename T >
fvar<T> stan::math::trace_quad_form ( const Eigen::Matrix< fvar< T >, RA, CA > &  A,
const Eigen::Matrix< fvar< T >, RB, CB > &  B 
)
inline

Definition at line 18 of file trace_quad_form.hpp.

§ trace_quad_form() [3/5]

template<int RA, int CA, int RB, int CB, typename T >
fvar<T> stan::math::trace_quad_form ( const Eigen::Matrix< fvar< T >, RA, CA > &  A,
const Eigen::Matrix< double, RB, CB > &  B 
)
inline

Definition at line 30 of file trace_quad_form.hpp.

§ trace_quad_form() [4/5]

template<int RA, int CA, int RB, int CB, typename T >
fvar<T> stan::math::trace_quad_form ( const Eigen::Matrix< double, RA, CA > &  A,
const Eigen::Matrix< fvar< T >, RB, CB > &  B 
)
inline

Definition at line 42 of file trace_quad_form.hpp.

§ trace_quad_form() [5/5]

template<typename TA , int RA, int CA, typename TB , int RB, int CB>
boost::enable_if_c< boost::is_same<TA, var>::value || boost::is_same<TB, var>::value, var >::type stan::math::trace_quad_form ( const Eigen::Matrix< TA, RA, CA > &  A,
const Eigen::Matrix< TB, RB, CB > &  B 
)
inline

Definition at line 95 of file trace_quad_form.hpp.

§ transpose()

template<typename T , int R, int C>
Eigen::Matrix<T, C, R> stan::math::transpose ( const Eigen::Matrix< T, R, C > &  m)
inline

Definition at line 12 of file transpose.hpp.

§ trigamma() [1/5]

var stan::math::trigamma ( const var u)
inline

Return the value of the trigamma function at the specified argument (i.e., the second derivative of the log Gamma function at the specified argument).

Parameters
uargument
Returns
trigamma function at argument

Definition at line 20 of file trigamma.hpp.

§ trigamma() [2/5]

template<typename T >
fvar<T> stan::math::trigamma ( const fvar< T > &  u)
inline

Return the value of the trigamma function at the specified argument (i.e., the second derivative of the log Gamma function at the specified argument).

Parameters
uargument
Returns
trigamma function at argument

Definition at line 21 of file trigamma.hpp.

§ trigamma() [3/5]

template<typename T >
apply_scalar_unary<trigamma_fun, T>::return_t stan::math::trigamma ( const T &  x)
inline

Return the elementwise application of trigamma() to specified argument container.

The return type promotes the underlying scalar argument type to double if it is an integer, and otherwise is the argument type.

Template Parameters
Tcontainer type
Parameters
xcontainer
Returns
elementwise trigamma of container elements

Definition at line 40 of file trigamma.hpp.

§ trigamma() [4/5]

double stan::math::trigamma ( double  u)
inline

Return the second derivative of the log Gamma function evaluated at the specified argument.

\[ \mbox{trigamma}(x) = \begin{cases} \textrm{error} & \mbox{if } x\in \{\dots, -3, -2, -1, 0\}\\ \Psi_1(x) & \mbox{if } x\not\in \{\dots, -3, -2, -1, 0\}\\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{trigamma}(x)}{\partial x} = \begin{cases} \textrm{error} & \mbox{if } x\in \{\dots, -3, -2, -1, 0\}\\ \frac{\partial\, \Psi_1(x)}{\partial x} & \mbox{if } x\not\in \{\dots, -3, -2, -1, 0\}\\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \Psi_1(x)=\sum_{n=0}^\infty \frac{1}{(x+n)^2} \]

\[ \frac{\partial \, \Psi_1(x)}{\partial x} = -2\sum_{n=0}^\infty \frac{1}{(x+n)^3} \]

Parameters
[in]uargument
Returns
second derivative of log Gamma function at argument

Definition at line 116 of file trigamma.hpp.

§ trigamma() [5/5]

double stan::math::trigamma ( int  u)
inline

Return the second derivative of the log Gamma function evaluated at the specified argument.

Parameters
[in]uargument
Returns
second derivative of log Gamma function at argument

Definition at line 127 of file trigamma.hpp.

§ trigamma_impl()

template<typename T >
T stan::math::trigamma_impl ( const T &  x)
inline

Return the trigamma function applied to the argument.

The trigamma function returns the second derivative of the log Gamma function evaluated at the specified argument. This base templated version is used in prim, fwd, and rev implementations.

Template Parameters
Tscalar argument type
Parameters
xargument
Returns
second derivative of log Gamma function at argument

Definition at line 30 of file trigamma.hpp.

§ trunc() [1/5]

template<typename T >
fvar<T> stan::math::trunc ( const fvar< T > &  x)
inline

Return the nearest integral value that is not larger in magnitude than the specified argument.

Template Parameters
TScalar type of autodiff variable.
Parameters
[in]xArgument.
Returns
The truncated argument.

Definition at line 19 of file trunc.hpp.

§ trunc() [2/5]

double stan::math::trunc ( double  x)
inline

Return the nearest integral value that is not larger in magnitude than the specified argument.

Parameters
[in]xArgument.
Returns
The truncated argument.

Definition at line 19 of file trunc.hpp.

§ trunc() [3/5]

double stan::math::trunc ( int  x)
inline

Return the nearest integral value that is not larger in magnitude than the specified argument.

Parameters
[in]xArgument.
Returns
The truncated argument.

Definition at line 32 of file trunc.hpp.

§ trunc() [4/5]

template<typename T >
apply_scalar_unary<trunc_fun, T>::return_t stan::math::trunc ( const T &  x)
inline

Return the elementwise application of trunc() to specified argument container.

The return type promotes the underlying scalar argument type to double if it is an integer, and otherwise is the argument type.

Template Parameters
Tcontainer type
Parameters
xcontainer
Returns
elementwise trunc of container elements

Definition at line 40 of file trunc.hpp.

§ trunc() [5/5]

var stan::math::trunc ( const var a)
inline

Returns the truncatation of the specified variable (C99).

See trunc() for the double-based version.

The derivative is zero everywhere but at integer values, so for convenience the derivative is defined to be everywhere zero,

$\frac{d}{dx} \mbox{trunc}(x) = 0$.

\[ \mbox{trunc}(x) = \begin{cases} \lfloor x \rfloor & \mbox{if } -\infty\leq x\leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

\[ \frac{\partial\, \mbox{trunc}(x)}{\partial x} = \begin{cases} 0 & \mbox{if } -\infty\leq x\leq \infty \\[6pt] \textrm{NaN} & \mbox{if } x = \textrm{NaN} \end{cases} \]

Parameters
aSpecified variable.
Returns
Truncation of the variable.

Definition at line 55 of file trunc.hpp.

§ ub_constrain() [1/2]

template<typename T , typename TU >
boost::math::tools::promote_args<T, TU>::type stan::math::ub_constrain ( const T  x,
const TU  ub 
)
inline

Return the upper-bounded value for the specified unconstrained scalar and upper bound.

The transform is

$f(x) = U - \exp(x)$

where $U$ is the upper bound.

If the upper bound is positive infinity, this function reduces to identity_constrain(x).

Parameters
xFree scalar.
ubUpper bound.
Returns
Transformed scalar with specified upper bound.
Template Parameters
TType of scalar.
TUType of upper bound.

Definition at line 34 of file ub_constrain.hpp.

§ ub_constrain() [2/2]

template<typename T , typename TU >
boost::math::tools::promote_args<T, TU>::type stan::math::ub_constrain ( const T  x,
const TU  ub,
T &  lp 
)
inline

Return the upper-bounded value for the specified unconstrained scalar and upper bound and increment the specified log probability reference with the log absolute Jacobian determinant of the transform.

The transform is as specified for ub_constrain(T, double). The log absolute Jacobian determinant is

$ \log | \frac{d}{dx} -\mbox{exp}(x) + U | = \log | -\mbox{exp}(x) + 0 | = x$.

If the upper bound is positive infinity, this function reduces to identity_constrain(x, lp).

Parameters
xFree scalar.
ubUpper bound.
lpLog probability reference.
Returns
Transformed scalar with specified upper bound.
Template Parameters
TType of scalar.
TUType of upper bound.

Definition at line 67 of file ub_constrain.hpp.

§ ub_free()

template<typename T , typename TU >
boost::math::tools::promote_args<T, TU>::type stan::math::ub_free ( const T  y,
const TU  ub 
)
inline

Return the free scalar that corresponds to the specified upper-bounded value with respect to the specified upper bound.

The transform is the reverse of the ub_constrain(T, double) transform,

$f^{-1}(y) = \log -(y - U)$

where $U$ is the upper bound.

If the upper bound is positive infinity, this function reduces to identity_free(y).

Parameters
yUpper-bounded scalar.
ubUpper bound.
Returns
Free scalar corresponding to upper-bounded scalar.
Template Parameters
TType of scalar.
TUType of upper bound.
Exceptions
std::invalid_argumentif y is greater than the upper bound.

Definition at line 38 of file ub_free.hpp.

§ uniform_ccdf_log()

template<typename T_y , typename T_low , typename T_high >
return_type<T_y, T_low, T_high>::type stan::math::uniform_ccdf_log ( const T_y &  y,
const T_low &  alpha,
const T_high &  beta 
)

Definition at line 24 of file uniform_ccdf_log.hpp.

§ uniform_cdf()

template<typename T_y , typename T_low , typename T_high >
return_type<T_y, T_low, T_high>::type stan::math::uniform_cdf ( const T_y &  y,
const T_low &  alpha,
const T_high &  beta 
)

Definition at line 23 of file uniform_cdf.hpp.

§ uniform_cdf_log()

template<typename T_y , typename T_low , typename T_high >
return_type<T_y, T_low, T_high>::type stan::math::uniform_cdf_log ( const T_y &  y,
const T_low &  alpha,
const T_high &  beta 
)

Definition at line 24 of file uniform_cdf_log.hpp.

§ uniform_lccdf()

template<typename T_y , typename T_low , typename T_high >
return_type<T_y, T_low, T_high>::type stan::math::uniform_lccdf ( const T_y &  y,
const T_low &  alpha,
const T_high &  beta 
)

Definition at line 24 of file uniform_lccdf.hpp.

§ uniform_lcdf()

template<typename T_y , typename T_low , typename T_high >
return_type<T_y, T_low, T_high>::type stan::math::uniform_lcdf ( const T_y &  y,
const T_low &  alpha,
const T_high &  beta 
)

Definition at line 24 of file uniform_lcdf.hpp.

§ uniform_log() [1/2]

template<bool propto, typename T_y , typename T_low , typename T_high >
return_type<T_y, T_low, T_high>::type stan::math::uniform_log ( const T_y &  y,
const T_low &  alpha,
const T_high &  beta 
)

The log of a uniform density for the given y, lower, and upper bound.

\begin{eqnarray*} y &\sim& \mbox{\sf{U}}(\alpha, \beta) \\ \log (p (y \, |\, \alpha, \beta)) &=& \log \left( \frac{1}{\beta-\alpha} \right) \\ &=& \log (1) - \log (\beta - \alpha) \\ &=& -\log (\beta - \alpha) \\ & & \mathrm{ where } \; y \in [\alpha, \beta], \log(0) \; \mathrm{otherwise} \end{eqnarray*}

Parameters
yA scalar variable.
alphaLower bound.
betaUpper bound.
Exceptions
std::invalid_argumentif the lower bound is greater than or equal to the lower bound
Template Parameters
T_yType of scalar.
T_lowType of lower bound.
T_highType of upper bound.

Definition at line 46 of file uniform_log.hpp.

§ uniform_log() [2/2]

template<typename T_y , typename T_low , typename T_high >
return_type<T_y, T_low, T_high>::type stan::math::uniform_log ( const T_y &  y,
const T_low &  alpha,
const T_high &  beta 
)
inline

Definition at line 116 of file uniform_log.hpp.

§ uniform_lpdf() [1/2]

template<bool propto, typename T_y , typename T_low , typename T_high >
return_type<T_y, T_low, T_high>::type stan::math::uniform_lpdf ( const T_y &  y,
const T_low &  alpha,
const T_high &  beta 
)

The log of a uniform density for the given y, lower, and upper bound.

\begin{eqnarray*} y &\sim& \mbox{\sf{U}}(\alpha, \beta) \\ \log (p (y \, |\, \alpha, \beta)) &=& \log \left( \frac{1}{\beta-\alpha} \right) \\ &=& \log (1) - \log (\beta - \alpha) \\ &=& -\log (\beta - \alpha) \\ & & \mathrm{ where } \; y \in [\alpha, \beta], \log(0) \; \mathrm{otherwise} \end{eqnarray*}

Parameters
yA scalar variable.
alphaLower bound.
betaUpper bound.
Exceptions
std::invalid_argumentif the lower bound is greater than or equal to the lower bound
Template Parameters
T_yType of scalar.
T_lowType of lower bound.
T_highType of upper bound.

Definition at line 46 of file uniform_lpdf.hpp.

§ uniform_lpdf() [2/2]

template<typename T_y , typename T_low , typename T_high >
return_type<T_y, T_low, T_high>::type stan::math::uniform_lpdf ( const T_y &  y,
const T_low &  alpha,
const T_high &  beta 
)
inline

Definition at line 116 of file uniform_lpdf.hpp.

§ uniform_rng()

template<class RNG >
double stan::math::uniform_rng ( double  alpha,
double  beta,
RNG &  rng 
)
inline

Definition at line 20 of file uniform_rng.hpp.

§ unit_vector_constrain() [1/6]

template<typename T , int R, int C>
Eigen::Matrix<fvar<T>, R, C> stan::math::unit_vector_constrain ( const Eigen::Matrix< fvar< T >, R, C > &  y)
inline

Definition at line 20 of file unit_vector_constrain.hpp.

§ unit_vector_constrain() [2/6]

template<typename T , int R, int C>
Eigen::Matrix<T, R, C> stan::math::unit_vector_constrain ( const Eigen::Matrix< T, R, C > &  y)

Return the unit length vector corresponding to the free vector y.

See https://en.wikipedia.org/wiki/N-sphere#Generating_random_points

Parameters
yvector of K unrestricted variables
Returns
Unit length vector of dimension K
Template Parameters
TScalar type.

Definition at line 25 of file unit_vector_constrain.hpp.

§ unit_vector_constrain() [3/6]

template<typename T , int R, int C>
Eigen::Matrix<T, R, C> stan::math::unit_vector_constrain ( const Eigen::Matrix< T, R, C > &  y,
T &  lp 
)

Return the unit length vector corresponding to the free vector y.

See https://en.wikipedia.org/wiki/N-sphere#Generating_random_points

Parameters
yvector of K unrestricted variables
Returns
Unit length vector of dimension K
Parameters
lpLog probability reference to increment.
Template Parameters
TScalar type.

Definition at line 45 of file unit_vector_constrain.hpp.

§ unit_vector_constrain() [4/6]

template<typename T , int R, int C>
Eigen::Matrix<fvar<T>, R, C> stan::math::unit_vector_constrain ( const Eigen::Matrix< fvar< T >, R, C > &  y,
fvar< T > &  lp 
)
inline

Definition at line 51 of file unit_vector_constrain.hpp.

§ unit_vector_constrain() [5/6]

template<int R, int C>
Eigen::Matrix<var, R, C> stan::math::unit_vector_constrain ( const Eigen::Matrix< var, R, C > &  y)

Return the unit length vector corresponding to the free vector y.

See https://en.wikipedia.org/wiki/N-sphere#Generating_random_points

Parameters
yvector of K unrestricted variables
Returns
Unit length vector of dimension K
Template Parameters
TScalar type.

Definition at line 61 of file unit_vector_constrain.hpp.

§ unit_vector_constrain() [6/6]

template<int R, int C>
Eigen::Matrix<var, R, C> stan::math::unit_vector_constrain ( const Eigen::Matrix< var, R, C > &  y,
var lp 
)

Return the unit length vector corresponding to the free vector y.

See https://en.wikipedia.org/wiki/N-sphere#Generating_random_points

Parameters
yvector of K unrestricted variables
Returns
Unit length vector of dimension K
Parameters
lpLog probability reference to increment.
Template Parameters
TScalar type.

Definition at line 108 of file unit_vector_constrain.hpp.

§ unit_vector_free()

template<typename T >
Eigen::Matrix<T, Eigen::Dynamic, 1> stan::math::unit_vector_free ( const Eigen::Matrix< T, Eigen::Dynamic, 1 > &  x)

Transformation of a unit length vector to a "free" vector However, we are just fixing the unidentified radius to 1.

Thus, the transformation is just the identity

Parameters
xunit vector of dimension K
Returns
Unit vector of dimension K considered "free"
Template Parameters
TScalar type.

Definition at line 23 of file unit_vector_free.hpp.

§ validate_non_negative_index()

void stan::math::validate_non_negative_index ( const char *  var_name,
const char *  expr,
int  val 
)
inline

Definition at line 12 of file validate_non_negative_index.hpp.

§ value_of() [1/7]

template<typename T >
T stan::math::value_of ( const fvar< T > &  v)
inline

Return the value of the specified variable.

Parameters
vVariable.
Returns
Value of variable.

Definition at line 16 of file value_of.hpp.

§ value_of() [2/7]

template<typename T >
std::vector<typename child_type<T>::type> stan::math::value_of ( const std::vector< T > &  x)
inline

Convert a std::vector of type T to a std::vector of child_type<T>::type.

Template Parameters
TScalar type in std::vector
Parameters
[in]xstd::vector to be converted
Returns
std::vector of values

Definition at line 22 of file value_of.hpp.

§ value_of() [3/7]

double stan::math::value_of ( const var v)
inline

Return the value of the specified variable.

This function is used internally by auto-dif functions along with value_of(T x) to extract the double value of either a scalar or an auto-dif variable. This function will be called when the argument is a var even if the function is not referred to by namespace because of argument-dependent lookup.

Parameters
vVariable.
Returns
Value of variable.

Definition at line 22 of file value_of.hpp.

§ value_of() [4/7]

template<typename T >
double stan::math::value_of ( const T  x)
inline

Return the value of the specified scalar argument converted to a double value.

See the primitive_value function to extract values without casting to double.

This function is meant to cover the primitive types. For types requiring pass-by-reference, this template function should be specialized.

Template Parameters
TType of scalar.
Parameters
xScalar to convert to double.
Returns
Value of scalar cast to a double.

Definition at line 23 of file value_of.hpp.

§ value_of() [5/7]

template<typename T , int R, int C>
Eigen::Matrix<typename child_type<T>::type, R, C> stan::math::value_of ( const Eigen::Matrix< T, R, C > &  M)
inline

Convert a matrix of type T to a matrix of doubles.

T must implement value_of. See test/math/fwd/mat/fun/value_of.cpp for fvar and var usage.

Template Parameters
TScalar type in matrix
RRows of matrix
CColumns of matrix
Parameters
[in]MMatrix to be converted
Returns
Matrix of values

Definition at line 25 of file value_of.hpp.

§ value_of() [6/7]

template<>
std::vector<double> stan::math::value_of ( const std::vector< double > &  x)
inline

Return the specified argument.

See value_of(T) for a polymorphic implementation using static casts.

This inline pass-through no-op should be compiled away.

Parameters
xSpecified std::vector.
Returns
Specified std::vector.

Definition at line 42 of file value_of.hpp.

§ value_of() [7/7]

template<int R, int C>
Eigen::Matrix<double, R, C> stan::math::value_of ( const Eigen::Matrix< double, R, C > &  x)
inline

Return the specified argument.

See value_of(T) for a polymorphic implementation using static casts.

This inline pass-through no-op should be compiled away.

Parameters
xSpecified matrix.
Returns
Specified matrix.

Definition at line 46 of file value_of.hpp.

§ value_of< double >()

template<>
double stan::math::value_of< double > ( double  x)
inline

Return the specified argument.

See value_of(T) for a polymorphic implementation using static casts.

This inline pass-through no-op should be compiled away.

Parameters
xSpecified value.
Returns
Specified value.

Definition at line 39 of file value_of.hpp.

§ value_of_rec() [1/7]

double stan::math::value_of_rec ( const var v)
inline

Return the value of the specified variable.

Parameters
vVariable.
Returns
Value of variable.

Definition at line 16 of file value_of_rec.hpp.

§ value_of_rec() [2/7]

template<typename T >
double stan::math::value_of_rec ( const fvar< T > &  v)
inline

Return the value of the specified variable.

T must implement value_of_rec.

Template Parameters
TScalar type
Parameters
vVariable.
Returns
Value of variable.

Definition at line 21 of file value_of_rec.hpp.

§ value_of_rec() [3/7]

template<typename T >
std::vector<double> stan::math::value_of_rec ( const std::vector< T > &  x)
inline

Convert a std::vector of type T to a std::vector of doubles.

T must implement value_of_rec. See test/math/fwd/mat/fun/value_of_rec.cpp for fvar and var usage.

Template Parameters
TScalar type in std::vector
Parameters
[in]xstd::vector to be converted
Returns
std::vector of values

Definition at line 23 of file value_of_rec.hpp.

§ value_of_rec() [4/7]

template<typename T >
double stan::math::value_of_rec ( const T  x)
inline

Return the value of the specified scalar argument converted to a double value.

See the primitive_value function to extract values without casting to double.

This function is meant to cover the primitive types. For types requiring pass-by-reference, this template function should be specialized.

Template Parameters
TType of scalar.
Parameters
xScalar to convert to double.
Returns
Value of scalar cast to a double.

Definition at line 23 of file value_of_rec.hpp.

§ value_of_rec() [5/7]

template<typename T , int R, int C>
Eigen::Matrix<double, R, C> stan::math::value_of_rec ( const Eigen::Matrix< T, R, C > &  M)
inline

Convert a matrix of type T to a matrix of doubles.

T must implement value_of_rec. See test/unit/math/fwd/mat/fun/value_of_test.cpp for fvar and var usage.

Template Parameters
TScalar type in matrix
RRows of matrix
CColumns of matrix
Parameters
[in]MMatrix to be converted
Returns
Matrix of values

Definition at line 24 of file value_of_rec.hpp.

§ value_of_rec() [6/7]

template<>
std::vector<double> stan::math::value_of_rec ( const std::vector< double > &  x)
inline

Return the specified argument.

See value_of_rec(T) for a polymorphic implementation using static casts.

This inline pass-through no-op should be compiled away.

Parameters
xSpecified std::vector.
Returns
Specified std::vector.

Definition at line 43 of file value_of_rec.hpp.

§ value_of_rec() [7/7]

template<int R, int C>
Eigen::Matrix<double, R, C> stan::math::value_of_rec ( const Eigen::Matrix< double, R, C > &  x)
inline

Return the specified argument.

See value_of_rec(T) for a polymorphic implementation using static casts.

This inline pass-through no-op should be compiled away.

Parameters
xSpecified matrix.
Returns
Specified matrix.

Definition at line 45 of file value_of_rec.hpp.

§ value_of_rec< double >()

template<>
double stan::math::value_of_rec< double > ( double  x)
inline

Return the specified argument.

See value_of(T) for a polymorphic implementation using static casts.

This inline pass-through no-op should be compiled away.

Parameters
xSpecified value.
Returns
Specified value.

Definition at line 39 of file value_of_rec.hpp.

§ variance() [1/4]

template<typename T >
boost::math::tools::promote_args<T>::type stan::math::variance ( const std::vector< T > &  v)
inline

Returns the sample variance (divide by length - 1) of the coefficients in the specified standard vector.

Parameters
vSpecified vector.
Returns
Sample variance of vector.
Exceptions
std::domain_errorif the size of the vector is less than 1.

Definition at line 24 of file variance.hpp.

§ variance() [2/4]

template<typename T , int R, int C>
boost::math::tools::promote_args<T>::type stan::math::variance ( const Eigen::Matrix< T, R, C > &  m)
inline

Returns the sample variance (divide by length - 1) of the coefficients in the specified column vector.

Parameters
mSpecified vector.
Returns
Sample variance of vector.

Definition at line 46 of file variance.hpp.

§ variance() [3/4]

var stan::math::variance ( const std::vector< var > &  v)
inline

Return the sample variance of the specified standard vector.

Raise domain error if size is not greater than zero.

Parameters
[in]va vector
Returns
sample variance of specified vector

Definition at line 51 of file variance.hpp.

§ variance() [4/4]

template<int R, int C>
var stan::math::variance ( const Eigen::Matrix< var, R, C > &  m)

Definition at line 68 of file variance.hpp.

§ von_mises_log() [1/2]

template<bool propto, typename T_y , typename T_loc , typename T_scale >
return_type<T_y, T_loc, T_scale>::type stan::math::von_mises_log ( T_y const &  y,
T_loc const &  mu,
T_scale const &  kappa 
)

Definition at line 26 of file von_mises_log.hpp.

§ von_mises_log() [2/2]

template<typename T_y , typename T_loc , typename T_scale >
return_type<T_y, T_loc, T_scale>::type stan::math::von_mises_log ( T_y const &  y,
T_loc const &  mu,
T_scale const &  kappa 
)
inline

Definition at line 114 of file von_mises_log.hpp.

§ von_mises_lpdf() [1/2]

template<bool propto, typename T_y , typename T_loc , typename T_scale >
return_type<T_y, T_loc, T_scale>::type stan::math::von_mises_lpdf ( T_y const &  y,
T_loc const &  mu,
T_scale const &  kappa 
)

Definition at line 26 of file von_mises_lpdf.hpp.

§ von_mises_lpdf() [2/2]

template<typename T_y , typename T_loc , typename T_scale >
return_type<T_y, T_loc, T_scale>::type stan::math::von_mises_lpdf ( T_y const &  y,
T_loc const &  mu,
T_scale const &  kappa 
)
inline

Definition at line 114 of file von_mises_lpdf.hpp.

§ von_mises_rng()

template<class RNG >
double stan::math::von_mises_rng ( double  mu,
double  kappa,
RNG &  rng 
)
inline

Definition at line 30 of file von_mises_rng.hpp.

§ weibull_ccdf_log()

template<typename T_y , typename T_shape , typename T_scale >
return_type<T_y, T_shape, T_scale>::type stan::math::weibull_ccdf_log ( const T_y &  y,
const T_shape &  alpha,
const T_scale &  sigma 
)

Definition at line 28 of file weibull_ccdf_log.hpp.

§ weibull_cdf()

template<typename T_y , typename T_shape , typename T_scale >
return_type<T_y, T_shape, T_scale>::type stan::math::weibull_cdf ( const T_y &  y,
const T_shape &  alpha,
const T_scale &  sigma 
)

Definition at line 28 of file weibull_cdf.hpp.

§ weibull_cdf_log()

template<typename T_y , typename T_shape , typename T_scale >
return_type<T_y, T_shape, T_scale>::type stan::math::weibull_cdf_log ( const T_y &  y,
const T_shape &  alpha,
const T_scale &  sigma 
)

Definition at line 28 of file weibull_cdf_log.hpp.

§ weibull_lccdf()

template<typename T_y , typename T_shape , typename T_scale >
return_type<T_y, T_shape, T_scale>::type stan::math::weibull_lccdf ( const T_y &  y,
const T_shape &  alpha,
const T_scale &  sigma 
)

Definition at line 28 of file weibull_lccdf.hpp.

§ weibull_lcdf()

template<typename T_y , typename T_shape , typename T_scale >
return_type<T_y, T_shape, T_scale>::type stan::math::weibull_lcdf ( const T_y &  y,
const T_shape &  alpha,
const T_scale &  sigma 
)

Definition at line 28 of file weibull_lcdf.hpp.

§ weibull_log() [1/2]

template<bool propto, typename T_y , typename T_shape , typename T_scale >
return_type<T_y, T_shape, T_scale>::type stan::math::weibull_log ( const T_y &  y,
const T_shape &  alpha,
const T_scale &  sigma 
)

Definition at line 30 of file weibull_log.hpp.

§ weibull_log() [2/2]

template<typename T_y , typename T_shape , typename T_scale >
return_type<T_y, T_shape, T_scale>::type stan::math::weibull_log ( const T_y &  y,
const T_shape &  alpha,
const T_scale &  sigma 
)
inline

Definition at line 132 of file weibull_log.hpp.

§ weibull_lpdf() [1/2]

template<bool propto, typename T_y , typename T_shape , typename T_scale >
return_type<T_y, T_shape, T_scale>::type stan::math::weibull_lpdf ( const T_y &  y,
const T_shape &  alpha,
const T_scale &  sigma 
)

Definition at line 30 of file weibull_lpdf.hpp.

§ weibull_lpdf() [2/2]

template<typename T_y , typename T_shape , typename T_scale >
return_type<T_y, T_shape, T_scale>::type stan::math::weibull_lpdf ( const T_y &  y,
const T_shape &  alpha,
const T_scale &  sigma 
)
inline

Definition at line 132 of file weibull_lpdf.hpp.

§ weibull_rng()

template<class RNG >
double stan::math::weibull_rng ( double  alpha,
double  sigma,
RNG &  rng 
)
inline

Definition at line 22 of file weibull_rng.hpp.

§ wiener_log() [1/2]

template<bool propto, typename T_y , typename T_alpha , typename T_tau , typename T_beta , typename T_delta >
return_type<T_y, T_alpha, T_tau, T_beta, T_delta>::type stan::math::wiener_log ( const T_y &  y,
const T_alpha &  alpha,
const T_tau &  tau,
const T_beta &  beta,
const T_delta &  delta 
)

The log of the first passage time density function for a (Wiener) drift diffusion model for the given $y$, boundary separation $\alpha$, nondecision time $\tau$, relative bias $\beta$, and drift rate $\delta$.

$\alpha$ and $\tau$ must be greater than 0, and $\beta$ must be between 0 and 1. $y$ should contain reaction times in seconds (strictly positive) with upper-boundary responses.

Parameters
yA scalar variate.
alphaThe boundary separation.
tauThe nondecision time.
betaThe relative bias.
deltaThe drift rate.
Returns
The log of the Wiener first passage time density of the specified arguments.

Definition at line 73 of file wiener_log.hpp.

§ wiener_log() [2/2]

template<typename T_y , typename T_alpha , typename T_tau , typename T_beta , typename T_delta >
return_type<T_y, T_alpha, T_tau, T_beta, T_delta>::type stan::math::wiener_log ( const T_y &  y,
const T_alpha &  alpha,
const T_tau &  tau,
const T_beta &  beta,
const T_delta &  delta 
)
inline

Definition at line 206 of file wiener_log.hpp.

§ wiener_lpdf() [1/2]

template<bool propto, typename T_y , typename T_alpha , typename T_tau , typename T_beta , typename T_delta >
return_type<T_y, T_alpha, T_tau, T_beta, T_delta>::type stan::math::wiener_lpdf ( const T_y &  y,
const T_alpha &  alpha,
const T_tau &  tau,
const T_beta &  beta,
const T_delta &  delta 
)

The log of the first passage time density function for a (Wiener) drift diffusion model for the given $y$, boundary separation $\alpha$, nondecision time $\tau$, relative bias $\beta$, and drift rate $\delta$.

$\alpha$ and $\tau$ must be greater than 0, and $\beta$ must be between 0 and 1. $y$ should contain reaction times in seconds (strictly positive) with upper-boundary responses.

Parameters
yA scalar variate.
alphaThe boundary separation.
tauThe nondecision time.
betaThe relative bias.
deltaThe drift rate.
Returns
The log of the Wiener first passage time density of the specified arguments.

Definition at line 73 of file wiener_lpdf.hpp.

§ wiener_lpdf() [2/2]

template<typename T_y , typename T_alpha , typename T_tau , typename T_beta , typename T_delta >
return_type<T_y, T_alpha, T_tau, T_beta, T_delta>::type stan::math::wiener_lpdf ( const T_y &  y,
const T_alpha &  alpha,
const T_tau &  tau,
const T_beta &  beta,
const T_delta &  delta 
)
inline

Definition at line 206 of file wiener_lpdf.hpp.

§ wishart_log() [1/2]

template<bool propto, typename T_y , typename T_dof , typename T_scale >
boost::math::tools::promote_args<T_y, T_dof, T_scale>::type stan::math::wishart_log ( const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &  W,
const T_dof &  nu,
const Eigen::Matrix< T_scale, Eigen::Dynamic, Eigen::Dynamic > &  S 
)

The log of the Wishart density for the given W, degrees of freedom, and scale matrix.

The scale matrix, S, must be k x k, symmetric, and semi-positive definite. Dimension, k, is implicit. nu must be greater than k-1

\begin{eqnarray*} W &\sim& \mbox{\sf{Wishart}}_{\nu} (S) \\ \log (p (W \, |\, \nu, S) ) &=& \log \left( \left(2^{\nu k/2} \pi^{k (k-1) /4} \prod_{i=1}^k{\Gamma (\frac{\nu + 1 - i}{2})} \right)^{-1} \times \left| S \right|^{-\nu/2} \left| W \right|^{(\nu - k - 1) / 2} \times \exp (-\frac{1}{2} \mbox{tr} (S^{-1} W)) \right) \\ &=& -\frac{\nu k}{2}\log(2) - \frac{k (k-1)}{4} \log(\pi) - \sum_{i=1}^{k}{\log (\Gamma (\frac{\nu+1-i}{2}))} -\frac{\nu}{2} \log(\det(S)) + \frac{\nu-k-1}{2}\log (\det(W)) - \frac{1}{2} \mbox{tr} (S^{-1}W) \end{eqnarray*}

Parameters
WA scalar matrix
nuDegrees of freedom
SThe scale matrix
Returns
The log of the Wishart density at W given nu and S.
Exceptions
std::domain_errorif nu is not greater than k-1
std::domain_errorif S is not square, not symmetric, or not semi-positive definite.
Template Parameters
T_yType of scalar.
T_dofType of degrees of freedom.
T_scaleType of scale.

Definition at line 54 of file wishart_log.hpp.

§ wishart_log() [2/2]

template<typename T_y , typename T_dof , typename T_scale >
boost::math::tools::promote_args<T_y, T_dof, T_scale>::type stan::math::wishart_log ( const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &  W,
const T_dof &  nu,
const Eigen::Matrix< T_scale, Eigen::Dynamic, Eigen::Dynamic > &  S 
)
inline

Definition at line 109 of file wishart_log.hpp.

§ wishart_lpdf() [1/2]

template<bool propto, typename T_y , typename T_dof , typename T_scale >
boost::math::tools::promote_args<T_y, T_dof, T_scale>::type stan::math::wishart_lpdf ( const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &  W,
const T_dof &  nu,
const Eigen::Matrix< T_scale, Eigen::Dynamic, Eigen::Dynamic > &  S 
)

The log of the Wishart density for the given W, degrees of freedom, and scale matrix.

The scale matrix, S, must be k x k, symmetric, and semi-positive definite. Dimension, k, is implicit. nu must be greater than k-1

\begin{eqnarray*} W &\sim& \mbox{\sf{Wishart}}_{\nu} (S) \\ \log (p (W \, |\, \nu, S) ) &=& \log \left( \left(2^{\nu k/2} \pi^{k (k-1) /4} \prod_{i=1}^k{\Gamma (\frac{\nu + 1 - i}{2})} \right)^{-1} \times \left| S \right|^{-\nu/2} \left| W \right|^{(\nu - k - 1) / 2} \times \exp (-\frac{1}{2} \mbox{tr} (S^{-1} W)) \right) \\ &=& -\frac{\nu k}{2}\log(2) - \frac{k (k-1)}{4} \log(\pi) - \sum_{i=1}^{k}{\log (\Gamma (\frac{\nu+1-i}{2}))} -\frac{\nu}{2} \log(\det(S)) + \frac{\nu-k-1}{2}\log (\det(W)) - \frac{1}{2} \mbox{tr} (S^{-1}W) \end{eqnarray*}

Parameters
WA scalar matrix
nuDegrees of freedom
SThe scale matrix
Returns
The log of the Wishart density at W given nu and S.
Exceptions
std::domain_errorif nu is not greater than k-1
std::domain_errorif S is not square, not symmetric, or not semi-positive definite.
Template Parameters
T_yType of scalar.
T_dofType of degrees of freedom.
T_scaleType of scale.

Definition at line 54 of file wishart_lpdf.hpp.

§ wishart_lpdf() [2/2]

template<typename T_y , typename T_dof , typename T_scale >
boost::math::tools::promote_args<T_y, T_dof, T_scale>::type stan::math::wishart_lpdf ( const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &  W,
const T_dof &  nu,
const Eigen::Matrix< T_scale, Eigen::Dynamic, Eigen::Dynamic > &  S 
)
inline

Definition at line 109 of file wishart_lpdf.hpp.

§ wishart_rng()

template<class RNG >
Eigen::MatrixXd stan::math::wishart_rng ( double  nu,
const Eigen::MatrixXd &  S,
RNG &  rng 
)
inline

Definition at line 17 of file wishart_rng.hpp.

Variable Documentation

§ CONSTRAINT_TOLERANCE

const double stan::math::CONSTRAINT_TOLERANCE = 1E-8

The tolerance for checking arithmetic bounds In rank and in simplexes.

The default value is 1E-8.

Definition at line 11 of file constraint_tolerance.hpp.

§ E

const double stan::math::E = boost::math::constants::e<double>()

The base of the natural logarithm, $ e $.

Definition at line 14 of file constants.hpp.

§ EPSILON

const double stan::math::EPSILON = std::numeric_limits<double>::epsilon()

Smallest positive value.

Definition at line 60 of file constants.hpp.

§ INFTY

const double stan::math::INFTY = std::numeric_limits<double>::infinity()

Positive infinity.

Definition at line 43 of file constants.hpp.

§ INV_SQRT_2

const double stan::math::INV_SQRT_2 = 1.0 / SQRT_2

The value of 1 over the square root of 2, $ 1 / \sqrt{2} $.

Definition at line 26 of file constants.hpp.

§ INV_SQRT_TWO_PI

const double stan::math::INV_SQRT_TWO_PI = 1.0 / std::sqrt(2.0 * boost::math::constants::pi<double>())

Definition at line 164 of file constants.hpp.

§ LOG_10

const double stan::math::LOG_10 = std::log(10.0)

The natural logarithm of 10, $ \log 10 $.

Definition at line 38 of file constants.hpp.

§ LOG_2

const double stan::math::LOG_2 = std::log(2.0)

The natural logarithm of 2, $ \log 2 $.

Definition at line 32 of file constants.hpp.

§ LOG_HALF

const double stan::math::LOG_HALF = std::log(0.5)

Definition at line 176 of file constants.hpp.

§ LOG_PI

const double stan::math::LOG_PI = std::log(boost::math::constants::pi<double>())

Definition at line 167 of file constants.hpp.

§ LOG_PI_OVER_FOUR

const double stan::math::LOG_PI_OVER_FOUR = std::log(boost::math::constants::pi<double>()) / 4.0

Log pi divided by 4 $ \log \pi / 4 $.

Definition at line 78 of file constants.hpp.

§ LOG_SQRT_PI

const double stan::math::LOG_SQRT_PI = std::log(SQRT_PI)

Definition at line 170 of file constants.hpp.

§ LOG_TWO

const double stan::math::LOG_TWO = std::log(2.0)

Definition at line 174 of file constants.hpp.

§ LOG_TWO_PI

const double stan::math::LOG_TWO_PI = LOG_TWO + LOG_PI

Definition at line 190 of file constants.hpp.

§ LOG_ZERO

const double stan::math::LOG_ZERO = std::log(0.0)

Definition at line 172 of file constants.hpp.

§ MAJOR_VERSION

const std::string stan::math::MAJOR_VERSION = STAN_STRING(STAN_MATH_MAJOR)

Major version number for Stan math library.

Definition at line 22 of file version.hpp.

§ MINOR_VERSION

const std::string stan::math::MINOR_VERSION = STAN_STRING(STAN_MATH_MINOR)

Minor version number for Stan math library.

Definition at line 25 of file version.hpp.

§ NEG_LOG_PI

const double stan::math::NEG_LOG_PI = - LOG_PI

Definition at line 183 of file constants.hpp.

§ NEG_LOG_SQRT_PI

const double stan::math::NEG_LOG_SQRT_PI = -std::log(std::sqrt(boost::math::constants::pi<double>()))

Definition at line 186 of file constants.hpp.

§ NEG_LOG_SQRT_TWO_PI

const double stan::math::NEG_LOG_SQRT_TWO_PI = - std::log(std::sqrt(2.0 * boost::math::constants::pi<double>()))

Definition at line 181 of file constants.hpp.

§ NEG_LOG_TWO

const double stan::math::NEG_LOG_TWO = - LOG_TWO

Definition at line 178 of file constants.hpp.

§ NEG_LOG_TWO_OVER_TWO

const double stan::math::NEG_LOG_TWO_OVER_TWO = - LOG_TWO / 2.0

Definition at line 188 of file constants.hpp.

§ NEG_LOG_TWO_PI

const double stan::math::NEG_LOG_TWO_PI = - LOG_TWO_PI

Definition at line 192 of file constants.hpp.

§ NEG_TWO_OVER_SQRT_PI

const double stan::math::NEG_TWO_OVER_SQRT_PI = -TWO_OVER_SQRT_PI

Definition at line 161 of file constants.hpp.

§ NEGATIVE_EPSILON

const double stan::math::NEGATIVE_EPSILON = - std::numeric_limits<double>::epsilon()

Largest negative value (i.e., smallest absolute value).

Definition at line 66 of file constants.hpp.

§ NEGATIVE_INFTY

const double stan::math::NEGATIVE_INFTY = - std::numeric_limits<double>::infinity()

Negative infinity.

Definition at line 49 of file constants.hpp.

§ NOT_A_NUMBER

const double stan::math::NOT_A_NUMBER = std::numeric_limits<double>::quiet_NaN()

(Quiet) not-a-number value.

Definition at line 55 of file constants.hpp.

§ PATCH_VERSION

const std::string stan::math::PATCH_VERSION = STAN_STRING(STAN_MATH_PATCH)

Patch version for Stan math library.

Definition at line 28 of file version.hpp.

§ POISSON_MAX_RATE

const double stan::math::POISSON_MAX_RATE = std::pow(2.0, 30)

Largest rate parameter allowed in Poisson RNG.

Definition at line 71 of file constants.hpp.

§ SQRT_2

const double stan::math::SQRT_2 = std::sqrt(2.0)

The value of the square root of 2, $ \sqrt{2} $.

Definition at line 20 of file constants.hpp.

§ SQRT_2_TIMES_SQRT_PI

const double stan::math::SQRT_2_TIMES_SQRT_PI = SQRT_2 * SQRT_PI

Definition at line 156 of file constants.hpp.

§ SQRT_PI

const double stan::math::SQRT_PI = std::sqrt(boost::math::constants::pi<double>())

Definition at line 154 of file constants.hpp.

§ TWO_OVER_SQRT_PI

const double stan::math::TWO_OVER_SQRT_PI = 2.0 / SQRT_PI

Definition at line 159 of file constants.hpp.


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