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cauchy_log.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_CAUCHY_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_CAUCHY_LOG_HPP
3 
4 #include <boost/random/cauchy_distribution.hpp>
5 #include <boost/random/variate_generator.hpp>
17 #include <cmath>
18 
19 namespace stan {
20 
21  namespace math {
22 
40  template <bool propto,
41  typename T_y, typename T_loc, typename T_scale>
42  typename return_type<T_y, T_loc, T_scale>::type
43  cauchy_log(const T_y& y, const T_loc& mu, const T_scale& sigma) {
44  static const char* function("stan::math::cauchy_log");
46  T_partials_return;
47 
54 
55  // check if any vectors are zero length
56  if (!(stan::length(y)
57  && stan::length(mu)
58  && stan::length(sigma)))
59  return 0.0;
60 
61  // set up return value accumulator
62  T_partials_return logp(0.0);
63 
64  // validate args (here done over var, which should be OK)
65  check_not_nan(function, "Random variable", y);
66  check_finite(function, "Location parameter", mu);
67  check_positive_finite(function, "Scale parameter", sigma);
68  check_consistent_sizes(function,
69  "Random variable", y,
70  "Location parameter", mu,
71  "Scale parameter", sigma);
72 
73  // check if no variables are involved and prop-to
75  return 0.0;
76 
77  using stan::math::log1p;
78  using stan::math::square;
79  using std::log;
80 
81  // set up template expressions wrapping scalars into vector views
82  VectorView<const T_y> y_vec(y);
83  VectorView<const T_loc> mu_vec(mu);
84  VectorView<const T_scale> sigma_vec(sigma);
85  size_t N = max_size(y, mu, sigma);
86 
88  VectorBuilder<true, T_partials_return,
89  T_scale> sigma_squared(length(sigma));
91  T_partials_return, T_scale> log_sigma(length(sigma));
92  for (size_t i = 0; i < length(sigma); i++) {
93  const T_partials_return sigma_dbl = value_of(sigma_vec[i]);
94  inv_sigma[i] = 1.0 / sigma_dbl;
95  sigma_squared[i] = sigma_dbl * sigma_dbl;
97  log_sigma[i] = log(sigma_dbl);
98  }
99  }
100 
102  operands_and_partials(y, mu, sigma);
103 
104  for (size_t n = 0; n < N; n++) {
105  // pull out values of arguments
106  const T_partials_return y_dbl = value_of(y_vec[n]);
107  const T_partials_return mu_dbl = value_of(mu_vec[n]);
108 
109  // reusable subexpression values
110  const T_partials_return y_minus_mu
111  = y_dbl - mu_dbl;
112  const T_partials_return y_minus_mu_squared
113  = y_minus_mu * y_minus_mu;
114  const T_partials_return y_minus_mu_over_sigma
115  = y_minus_mu * inv_sigma[n];
116  const T_partials_return y_minus_mu_over_sigma_squared
117  = y_minus_mu_over_sigma * y_minus_mu_over_sigma;
118 
119  // log probability
121  logp += NEG_LOG_PI;
123  logp -= log_sigma[n];
125  logp -= log1p(y_minus_mu_over_sigma_squared);
126 
127  // gradients
129  operands_and_partials.d_x1[n] -= 2 * y_minus_mu
130  / (sigma_squared[n] + y_minus_mu_squared);
132  operands_and_partials.d_x2[n] += 2 * y_minus_mu
133  / (sigma_squared[n] + y_minus_mu_squared);
135  operands_and_partials.d_x3[n]
136  += (y_minus_mu_squared - sigma_squared[n])
137  * inv_sigma[n] / (sigma_squared[n] + y_minus_mu_squared);
138  }
139  return operands_and_partials.to_var(logp, y, mu, sigma);
140  }
141 
142  template <typename T_y, typename T_loc, typename T_scale>
143  inline
145  cauchy_log(const T_y& y, const T_loc& mu, const T_scale& sigma) {
146  return cauchy_log<false>(y, mu, sigma);
147  }
148 
149 
150  }
151 }
152 #endif
const double NEG_LOG_PI
Definition: constants.hpp:186
bool check_not_nan(const char *function, const char *name, const T_y &y)
Return true if y is not NaN.
T value_of(const fvar< T > &v)
Return the value of the specified variable.
Definition: value_of.hpp:16
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:15
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
T_return_type to_var(T_partials_return logp, const T1 &x1=0, const T2 &x2=0, const T3 &x3=0, const T4 &x4=0, const T5 &x5=0, const T6 &x6=0)
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) prob...
boost::math::tools::promote_args< typename scalar_type< T1 >::type, typename scalar_type< T2 >::type, typename scalar_type< T3 >::type, typename scalar_type< T4 >::type, typename scalar_type< T5 >::type, typename scalar_type< T6 >::type >::type type
Definition: return_type.hpp:27
fvar< T > square(const fvar< T > &x)
Definition: square.hpp:15
VectorView< T_partials_return, is_vector< T1 >::value, is_constant_struct< T1 >::value > d_x1
Metaprogram to determine if a type has a base scalar type that can be assigned to type double...
VectorView< T_partials_return, is_vector< T3 >::value, is_constant_struct< T3 >::value > d_x3
A variable implementation that stores operands and derivatives with respect to the variable...
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
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) a...
Definition: cauchy_log.hpp:43
bool check_finite(const char *function, const char *name, const T_y &y)
Return true if y is finite.
bool check_consistent_sizes(const char *function, const char *name1, const T1 &x1, const char *name2, const T2 &x2)
Return true if the dimension of x1 is consistent with x2.
VectorView< T_partials_return, is_vector< T2 >::value, is_constant_struct< T2 >::value > d_x2
fvar< T > log1p(const fvar< T > &x)
Definition: log1p.hpp:16
VectorView is a template metaprogram that takes its argument and allows it to be used like a vector...
Definition: VectorView.hpp:41
boost::math::tools::promote_args< typename partials_type< typename scalar_type< T1 >::type >::type, typename partials_type< typename scalar_type< T2 >::type >::type, typename partials_type< typename scalar_type< T3 >::type >::type, typename partials_type< typename scalar_type< T4 >::type >::type, typename partials_type< typename scalar_type< T5 >::type >::type, typename partials_type< typename scalar_type< T6 >::type >::type >::type type
bool check_positive_finite(const char *function, const char *name, const T_y &y)
Return true if y is positive and finite.

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