Stan Math Library  2.11.0
reverse mode automatic differentiation
normal_cdf_log.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_NORMAL_CDF_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_NORMAL_CDF_LOG_HPP
3 
15 #include <boost/random/normal_distribution.hpp>
16 #include <boost/random/variate_generator.hpp>
17 #include <cmath>
18 #include <limits>
19 
20 namespace stan {
21 
22  namespace math {
23 
24  template <typename T_y, typename T_loc, typename T_scale>
25  typename return_type<T_y, T_loc, T_scale>::type
26  normal_cdf_log(const T_y& y, const T_loc& mu, const T_scale& sigma) {
27  static const char* function("stan::math::normal_cdf_log");
29  T_partials_return;
30 
37  using std::log;
38  using std::exp;
39 
40  T_partials_return cdf_log(0.0);
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_finite(function, "Location parameter", mu);
49  check_not_nan(function, "Scale parameter", sigma);
50  check_positive(function, "Scale parameter", sigma);
51  check_consistent_sizes(function,
52  "Random variable", y,
53  "Location parameter", mu,
54  "Scale parameter", sigma);
55 
57  operands_and_partials(y, mu, sigma);
58 
59  VectorView<const T_y> y_vec(y);
60  VectorView<const T_loc> mu_vec(mu);
61  VectorView<const T_scale> sigma_vec(sigma);
62  size_t N = max_size(y, mu, sigma);
63 
64  const double SQRT_TWO_OVER_PI = std::sqrt(2.0 / stan::math::pi());
65  for (size_t n = 0; n < N; n++) {
66  const T_partials_return y_dbl = value_of(y_vec[n]);
67  const T_partials_return mu_dbl = value_of(mu_vec[n]);
68  const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
69 
70  const T_partials_return scaled_diff = (y_dbl - mu_dbl)
71  / (sigma_dbl * SQRT_2);
72 
73  T_partials_return one_p_erf;
74  if (scaled_diff < -37.5 * INV_SQRT_2)
75  one_p_erf = 0.0;
76  else if (scaled_diff < -5.0 * INV_SQRT_2)
77  one_p_erf = erfc(-scaled_diff);
78  else if (scaled_diff > 8.25 * INV_SQRT_2)
79  one_p_erf = 2.0;
80  else
81  one_p_erf = 1.0 + erf(scaled_diff);
82 
83  // log cdf
84  cdf_log += LOG_HALF + log(one_p_erf);
85 
86  // gradients
88  const T_partials_return rep_deriv_div_sigma
89  = scaled_diff < -37.5 * INV_SQRT_2
90  ? std::numeric_limits<double>::infinity()
91  : SQRT_TWO_OVER_PI * exp(-scaled_diff * scaled_diff)
92  / sigma_dbl / one_p_erf;
94  operands_and_partials.d_x1[n] += rep_deriv_div_sigma;
96  operands_and_partials.d_x2[n] -= rep_deriv_div_sigma;
98  operands_and_partials.d_x3[n] -= rep_deriv_div_sigma
99  * scaled_diff * stan::math::SQRT_2;
100  }
101  }
102  return operands_and_partials.value(cdf_log);
103  }
104  }
105 }
106 #endif
VectorView< T_return_type, false, true > d_x2
const double LOG_HALF
Definition: constants.hpp:179
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
fvar< T > erf(const fvar< T > &x)
Definition: erf.hpp:14
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
const double INV_SQRT_2
The value of 1 over the square root of 2, .
Definition: constants.hpp:27
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
bool check_positive(const char *function, const char *name, const T_y &y)
Return true if y is positive.
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.
bool check_consistent_sizes(const char *function, const char *name1, const T1 &x1, const char *name2, const T2 &x2)
Return true if the dimension of x1 is consistent with x2.
return_type< T_y, T_loc, T_scale >::type normal_cdf_log(const T_y &y, const T_loc &mu, const T_scale &sigma)
fvar< T > erfc(const fvar< T > &x)
Definition: erfc.hpp:14
double pi()
Return the value of pi.
Definition: constants.hpp:86
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

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