Stan Math Library  2.14.0
reverse mode automatic differentiation
lognormal_cdf.hpp
Go to the documentation of this file.
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>
25  lognormal_cdf(const T_y& y, const T_loc& mu, const T_scale& sigma) {
26  static const char* function("lognormal_cdf");
27 
29  T_partials_return;
30 
31  T_partials_return cdf = 1.0;
32 
33  using boost::math::tools::promote_args;
34  using std::exp;
35  using std::log;
36 
37  if (!(stan::length(y)
38  && stan::length(mu)
39  && stan::length(sigma)))
40  return cdf;
41 
42  check_not_nan(function, "Random variable", y);
43  check_nonnegative(function, "Random variable", y);
44  check_finite(function, "Location parameter", mu);
45  check_positive_finite(function, "Scale parameter", sigma);
46 
48  operands_and_partials(y, mu, sigma);
49 
50  VectorView<const T_y> y_vec(y);
51  VectorView<const T_loc> mu_vec(mu);
52  VectorView<const T_scale> sigma_vec(sigma);
53  size_t N = max_size(y, mu, sigma);
54 
55  const double sqrt_pi = std::sqrt(pi());
56 
57  for (size_t i = 0; i < stan::length(y); i++) {
58  if (value_of(y_vec[i]) == 0.0)
59  return operands_and_partials.value(0.0);
60  }
61 
62  for (size_t n = 0; n < N; n++) {
63  const T_partials_return y_dbl = value_of(y_vec[n]);
64  const T_partials_return mu_dbl = value_of(mu_vec[n]);
65  const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
66  const T_partials_return scaled_diff = (log(y_dbl) - mu_dbl)
67  / (sigma_dbl * SQRT_2);
68  const T_partials_return rep_deriv = SQRT_2 * 0.5 / sqrt_pi
69  * exp(-scaled_diff * scaled_diff) / sigma_dbl;
70 
71  const T_partials_return cdf_ = 0.5 * erfc(-scaled_diff);
72  cdf *= cdf_;
73 
75  operands_and_partials.d_x1[n] += rep_deriv / cdf_ / y_dbl;
77  operands_and_partials.d_x2[n] -= rep_deriv / cdf_;
79  operands_and_partials.d_x3[n] -= rep_deriv * scaled_diff * SQRT_2
80  / cdf_;
81  }
82 
84  for (size_t n = 0; n < stan::length(y); ++n)
85  operands_and_partials.d_x1[n] *= cdf;
86  }
88  for (size_t n = 0; n < stan::length(mu); ++n)
89  operands_and_partials.d_x2[n] *= cdf;
90  }
92  for (size_t n = 0; n < stan::length(sigma); ++n)
93  operands_and_partials.d_x3[n] *= cdf;
94  }
95  return operands_and_partials.value(cdf);
96  }
97 
98  }
99 }
100 #endif
VectorView< T_return_type, false, true > d_x2
void check_finite(const char *function, const char *name, const T_y &y)
Check if y is finite.
fvar< T > sqrt(const fvar< T > &x)
Definition: sqrt.hpp:14
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:14
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
void check_nonnegative(const char *function, const char *name, const T_y &y)
Check if y is non-negative.
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
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:20
void check_positive_finite(const char *function, const char *name, const T_y &y)
Check if y is positive and finite.
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:10
void check_not_nan(const char *function, const char *name, const T_y &y)
Check if y is not NaN.
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
fvar< T > erfc(const fvar< T > &x)
Definition: erfc.hpp:14
double pi()
Return the value of pi.
Definition: constants.hpp:85
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
VectorView< T_return_type, false, true > d_x1

     [ Stan Home Page ] © 2011–2016, Stan Development Team.