Stan Math Library  2.10.0
reverse mode automatic differentiation
lognormal_cdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_LOGNORMAL_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_LOGNORMAL_CDF_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(const T_y& y, const T_loc& mu, const T_scale& sigma) {
26  static const char* function("stan::math::lognormal_cdf");
27 
29  T_partials_return;
30 
31  T_partials_return cdf = 1.0;
32 
37  using boost::math::tools::promote_args;
39  using std::exp;
40  using std::log;
41 
42  // check if any vectors are zero length
43  if (!(stan::length(y)
44  && stan::length(mu)
45  && stan::length(sigma)))
46  return cdf;
47 
48  check_not_nan(function, "Random variable", y);
49  check_nonnegative(function, "Random variable", y);
50  check_finite(function, "Location parameter", mu);
51  check_positive_finite(function, "Scale parameter", sigma);
52 
54  operands_and_partials(y, mu, sigma);
55 
56  VectorView<const T_y> y_vec(y);
57  VectorView<const T_loc> mu_vec(mu);
58  VectorView<const T_scale> sigma_vec(sigma);
59  size_t N = max_size(y, mu, sigma);
60 
61  const double sqrt_pi = std::sqrt(stan::math::pi());
62 
63  for (size_t i = 0; i < stan::length(y); i++) {
64  if (value_of(y_vec[i]) == 0.0)
65  return operands_and_partials.value(0.0);
66  }
67 
68  for (size_t n = 0; n < N; n++) {
69  const T_partials_return y_dbl = value_of(y_vec[n]);
70  const T_partials_return mu_dbl = value_of(mu_vec[n]);
71  const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
72  const T_partials_return scaled_diff = (log(y_dbl) - mu_dbl)
73  / (sigma_dbl * SQRT_2);
74  const T_partials_return rep_deriv = SQRT_2 * 0.5 / sqrt_pi
75  * exp(-scaled_diff * scaled_diff) / sigma_dbl;
76 
77  // cdf
78  const T_partials_return cdf_ = 0.5 * erfc(-scaled_diff);
79  cdf *= cdf_;
80 
81  // gradients
83  operands_and_partials.d_x1[n] += rep_deriv / cdf_ / y_dbl;
85  operands_and_partials.d_x2[n] -= rep_deriv / cdf_;
87  operands_and_partials.d_x3[n] -= rep_deriv * scaled_diff * SQRT_2
88  / cdf_;
89  }
90 
92  for (size_t n = 0; n < stan::length(y); ++n)
93  operands_and_partials.d_x1[n] *= cdf;
94  }
96  for (size_t n = 0; n < stan::length(mu); ++n)
97  operands_and_partials.d_x2[n] *= cdf;
98  }
100  for (size_t n = 0; n < stan::length(sigma); ++n)
101  operands_and_partials.d_x3[n] *= cdf;
102  }
103 
104  return operands_and_partials.value(cdf);
105  }
106  }
107 }
108 #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
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.
return_type< T_y, T_loc, T_scale >::type lognormal_cdf(const T_y &y, const T_loc &mu, const T_scale &sigma)
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

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