Stan Math Library  2.12.0
reverse mode automatic differentiation
normal_cdf.hpp
Go to the documentation of this file.
1 #ifndef STAN_MATH_PRIM_SCAL_PROB_NORMAL_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_NORMAL_CDF_HPP
3 
15 #include <boost/random/normal_distribution.hpp>
16 #include <boost/random/variate_generator.hpp>
17 #include <cmath>
18 
19 namespace stan {
20  namespace math {
21 
36  template <typename T_y, typename T_loc, typename T_scale>
37  typename return_type<T_y, T_loc, T_scale>::type
38  normal_cdf(const T_y& y, const T_loc& mu, const T_scale& sigma) {
39  static const char* function("normal_cdf");
41  T_partials_return;
42 
43  using std::exp;
44 
45  T_partials_return cdf(1.0);
46 
47  if (!(stan::length(y)
48  && stan::length(mu)
49  && stan::length(sigma)))
50  return cdf;
51 
52  check_not_nan(function, "Random variable", y);
53  check_finite(function, "Location parameter", mu);
54  check_not_nan(function, "Scale parameter", sigma);
55  check_positive(function, "Scale parameter", sigma);
56  check_consistent_sizes(function,
57  "Random variable", y,
58  "Location parameter", mu,
59  "Scale parameter", sigma);
60 
62  operands_and_partials(y, mu, sigma);
63 
64  VectorView<const T_y> y_vec(y);
65  VectorView<const T_loc> mu_vec(mu);
66  VectorView<const T_scale> sigma_vec(sigma);
67  size_t N = max_size(y, mu, sigma);
68  const double SQRT_TWO_OVER_PI = std::sqrt(2.0 / pi());
69 
70  for (size_t n = 0; n < N; n++) {
71  const T_partials_return y_dbl = value_of(y_vec[n]);
72  const T_partials_return mu_dbl = value_of(mu_vec[n]);
73  const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
74  const T_partials_return scaled_diff = (y_dbl - mu_dbl)
75  / (sigma_dbl * SQRT_2);
76  T_partials_return cdf_;
77  if (scaled_diff < -37.5 * INV_SQRT_2)
78  cdf_ = 0.0;
79  else if (scaled_diff < -5.0 * INV_SQRT_2)
80  cdf_ = 0.5 * erfc(-scaled_diff);
81  else if (scaled_diff > 8.25 * INV_SQRT_2)
82  cdf_ = 1;
83  else
84  cdf_ = 0.5 * (1.0 + erf(scaled_diff));
85 
86  cdf *= cdf_;
87 
89  const T_partials_return rep_deriv
90  = (scaled_diff < -37.5 * INV_SQRT_2)
91  ? 0.0
92  : SQRT_TWO_OVER_PI * 0.5
93  * exp(-scaled_diff * scaled_diff) / cdf_ / sigma_dbl;
95  operands_and_partials.d_x1[n] += rep_deriv;
97  operands_and_partials.d_x2[n] -= rep_deriv;
99  operands_and_partials.d_x3[n] -= rep_deriv * scaled_diff * SQRT_2;
100  }
101  }
102 
104  for (size_t n = 0; n < stan::length(y); ++n)
105  operands_and_partials.d_x1[n] *= cdf;
106  }
108  for (size_t n = 0; n < stan::length(mu); ++n)
109  operands_and_partials.d_x2[n] *= cdf;
110  }
112  for (size_t n = 0; n < stan::length(sigma); ++n)
113  operands_and_partials.d_x3[n] *= cdf;
114  }
115  return operands_and_partials.value(cdf);
116  }
117 
118  }
119 }
120 #endif
VectorView< T_return_type, false, true > d_x2
fvar< T > sqrt(const fvar< T > &x)
Definition: sqrt.hpp:14
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
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:20
const double INV_SQRT_2
The value of 1 over the square root of 2, .
Definition: constants.hpp:26
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.
fvar< T > erfc(const fvar< T > &x)
Definition: erfc.hpp:14
double pi()
Return the value of pi.
Definition: constants.hpp:85
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
return_type< T_y, T_loc, T_scale >::type normal_cdf(const T_y &y, const T_loc &mu, const T_scale &sigma)
Calculates the normal cumulative distribution function for the given variate, location, and scale.
Definition: normal_cdf.hpp:38
VectorView< T_return_type, false, true > d_x1

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