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lognormal_ccdf_log.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_LOGNORMAL_CCDF_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_LOGNORMAL_CCDF_LOG_HPP
3 
4 #include <boost/random/lognormal_distribution.hpp>
5 #include <boost/random/variate_generator.hpp>
16 #include <cmath>
17 
18 namespace stan {
19  namespace math {
20 
21  template <typename T_y, typename T_loc, typename T_scale>
22  typename return_type<T_y, T_loc, T_scale>::type
23  lognormal_ccdf_log(const T_y& y, const T_loc& mu, const T_scale& sigma) {
24  static const char* function("stan::math::lognormal_ccdf_log");
26  T_partials_return;
27 
28  T_partials_return ccdf_log = 0.0;
29 
34  using boost::math::tools::promote_args;
36  using std::log;
37  using std::exp;
38 
39  // check if any vectors are zero length
40  if (!(stan::length(y)
41  && stan::length(mu)
42  && stan::length(sigma)))
43  return ccdf_log;
44 
45  check_not_nan(function, "Random variable", y);
46  check_nonnegative(function, "Random variable", y);
47  check_finite(function, "Location parameter", mu);
48  check_positive_finite(function, "Scale parameter", sigma);
49 
51  operands_and_partials(y, mu, sigma);
52 
53  VectorView<const T_y> y_vec(y);
54  VectorView<const T_loc> mu_vec(mu);
55  VectorView<const T_scale> sigma_vec(sigma);
56  size_t N = max_size(y, mu, sigma);
57 
58  const double sqrt_pi = std::sqrt(stan::math::pi());
59 
60  for (size_t i = 0; i < stan::length(y); i++) {
61  if (value_of(y_vec[i]) == 0.0)
62  return operands_and_partials.to_var(0.0, y, mu, sigma);
63  }
64 
65  const double log_half = std::log(0.5);
66 
67  for (size_t n = 0; n < N; n++) {
68  const T_partials_return y_dbl = value_of(y_vec[n]);
69  const T_partials_return mu_dbl = value_of(mu_vec[n]);
70  const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
71  const T_partials_return scaled_diff = (log(y_dbl) - mu_dbl)
72  / (sigma_dbl * SQRT_2);
73  const T_partials_return rep_deriv = SQRT_2 / sqrt_pi
74  * exp(-scaled_diff * scaled_diff) / sigma_dbl;
75 
76  // ccdf_log
77  const T_partials_return erfc_calc = erfc(scaled_diff);
78  ccdf_log += log_half + log(erfc_calc);
79 
80  // gradients
82  operands_and_partials.d_x1[n] -= rep_deriv / erfc_calc / y_dbl;
84  operands_and_partials.d_x2[n] += rep_deriv / erfc_calc;
86  operands_and_partials.d_x3[n] += rep_deriv * scaled_diff * SQRT_2
87  / erfc_calc;
88  }
89 
90  return operands_and_partials.to_var(ccdf_log, y, mu, sigma);
91  }
92  }
93 }
94 #endif
return_type< T_y, T_loc, T_scale >::type lognormal_ccdf_log(const T_y &y, const T_loc &mu, const T_scale &sigma)
fvar< T > sqrt(const fvar< T > &x)
Definition: sqrt.hpp:15
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)
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...
const double SQRT_2
The value of the square root of 2, .
Definition: constants.hpp:21
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:10
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
bool check_finite(const char *function, const char *name, const T_y &y)
Return true if y is finite.
VectorView< T_partials_return, is_vector< T2 >::value, is_constant_struct< T2 >::value > d_x2
fvar< T > erfc(const fvar< T > &x)
Definition: erfc.hpp:14
double pi()
Return the value of pi.
Definition: constants.hpp:86
bool check_nonnegative(const char *function, const char *name, const T_y &y)
Return true if y is non-negative.
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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