Stan Math Library  2.10.0
reverse mode automatic differentiation
lognormal_cdf_log.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_LOGNORMAL_CDF_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_LOGNORMAL_CDF_LOG_HPP
3 
16 #include <boost/random/lognormal_distribution.hpp>
17 #include <boost/random/variate_generator.hpp>
18 #include <cmath>
19 
20 namespace stan {
21  namespace math {
22 
23  template <typename T_y, typename T_loc, typename T_scale>
24  typename return_type<T_y, T_loc, T_scale>::type
25  lognormal_cdf_log(const T_y& y, const T_loc& mu, const T_scale& sigma) {
26  static const char* function("stan::math::lognormal_cdf_log");
28  T_partials_return;
29 
30  T_partials_return cdf_log = 0.0;
31 
36  using boost::math::tools::promote_args;
38  using std::log;
39  using std::exp;
40 
41  // check if any vectors are zero length
42  if (!(stan::length(y)
43  && stan::length(mu)
44  && stan::length(sigma)))
45  return cdf_log;
46 
47  check_not_nan(function, "Random variable", y);
48  check_nonnegative(function, "Random variable", y);
49  check_finite(function, "Location parameter", mu);
50  check_positive_finite(function, "Scale parameter", sigma);
51 
53  operands_and_partials(y, mu, sigma);
54 
55  VectorView<const T_y> y_vec(y);
56  VectorView<const T_loc> mu_vec(mu);
57  VectorView<const T_scale> sigma_vec(sigma);
58  size_t N = max_size(y, mu, sigma);
59 
60  const double sqrt_pi = std::sqrt(stan::math::pi());
61 
62  for (size_t i = 0; i < stan::length(y); i++) {
63  if (value_of(y_vec[i]) == 0.0)
64  return operands_and_partials.value(stan::math::negative_infinity());
65  }
66 
67  const double log_half = std::log(0.5);
68 
69  for (size_t n = 0; n < N; n++) {
70  const T_partials_return y_dbl = value_of(y_vec[n]);
71  const T_partials_return mu_dbl = value_of(mu_vec[n]);
72  const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
73  const T_partials_return scaled_diff = (log(y_dbl) - mu_dbl)
74  / (sigma_dbl * SQRT_2);
75  const T_partials_return rep_deriv = SQRT_2 / sqrt_pi
76  * exp(-scaled_diff * scaled_diff) / sigma_dbl;
77 
78  // cdf_log
79  const T_partials_return erfc_calc = erfc(-scaled_diff);
80  cdf_log += log_half + log(erfc_calc);
81 
82  // gradients
84  operands_and_partials.d_x1[n] += rep_deriv / erfc_calc / y_dbl;
86  operands_and_partials.d_x2[n] -= rep_deriv / erfc_calc;
88  operands_and_partials.d_x3[n] -= rep_deriv * scaled_diff * SQRT_2
89  / erfc_calc;
90  }
91 
92  return operands_and_partials.value(cdf_log);
93  }
94  }
95 }
96 #endif
VectorView< T_return_type, false, true > d_x2
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
return_type< T_y, T_loc, T_scale >::type lognormal_cdf_log(const T_y &y, const T_loc &mu, const T_scale &sigma)
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:15
T_return_type value(double value)
Returns a T_return_type with the value specified with the partial derivatves.
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
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
This class builds partial derivatives with respect to a set of operands.
VectorView< T_return_type, false, true > d_x3
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.
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 expression that is constructed with a container or scalar, which it then allows to be used as an array using operator[].
Definition: VectorView.hpp:48
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.
VectorView< T_return_type, false, true > d_x1
double negative_infinity()
Return negative infinity.
Definition: constants.hpp:132

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