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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 
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_cdf(const T_y& y, const T_loc& mu, const T_scale& sigma) {
24  static const char* function("stan::math::lognormal_cdf");
25 
27  T_partials_return;
28 
29  T_partials_return cdf = 1.0;
30 
35  using boost::math::tools::promote_args;
37  using std::exp;
38  using std::log;
39 
40  // check if any vectors are zero length
41  if (!(stan::length(y)
42  && stan::length(mu)
43  && stan::length(sigma)))
44  return cdf;
45 
46  check_not_nan(function, "Random variable", y);
47  check_nonnegative(function, "Random variable", y);
48  check_finite(function, "Location parameter", mu);
49  check_positive_finite(function, "Scale parameter", sigma);
50 
52  operands_and_partials(y, mu, sigma);
53 
54  VectorView<const T_y> y_vec(y);
55  VectorView<const T_loc> mu_vec(mu);
56  VectorView<const T_scale> sigma_vec(sigma);
57  size_t N = max_size(y, mu, sigma);
58 
59  const double sqrt_pi = std::sqrt(stan::math::pi());
60 
61  for (size_t i = 0; i < stan::length(y); i++) {
62  if (value_of(y_vec[i]) == 0.0)
63  return operands_and_partials.to_var(0.0, y, mu, sigma);
64  }
65 
66  for (size_t n = 0; n < N; n++) {
67  const T_partials_return y_dbl = value_of(y_vec[n]);
68  const T_partials_return mu_dbl = value_of(mu_vec[n]);
69  const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
70  const T_partials_return scaled_diff = (log(y_dbl) - mu_dbl)
71  / (sigma_dbl * SQRT_2);
72  const T_partials_return rep_deriv = SQRT_2 * 0.5 / sqrt_pi
73  * exp(-scaled_diff * scaled_diff) / sigma_dbl;
74 
75  // cdf
76  const T_partials_return cdf_ = 0.5 * erfc(-scaled_diff);
77  cdf *= cdf_;
78 
79  // gradients
81  operands_and_partials.d_x1[n] += rep_deriv / cdf_ / y_dbl;
83  operands_and_partials.d_x2[n] -= rep_deriv / cdf_;
85  operands_and_partials.d_x3[n] -= rep_deriv * scaled_diff * SQRT_2
86  / cdf_;
87  }
88 
90  for (size_t n = 0; n < stan::length(y); ++n)
91  operands_and_partials.d_x1[n] *= cdf;
92  }
94  for (size_t n = 0; n < stan::length(mu); ++n)
95  operands_and_partials.d_x2[n] *= cdf;
96  }
98  for (size_t n = 0; n < stan::length(sigma); ++n)
99  operands_and_partials.d_x3[n] *= cdf;
100  }
101 
102  return operands_and_partials.to_var(cdf, y, mu, sigma);
103  }
104  }
105 }
106 #endif
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.
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 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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