Stan Math Library  2.11.0
reverse mode automatic differentiation
normal_cdf.hpp
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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 
20 namespace stan {
21 
22  namespace math {
23 
38  template <typename T_y, typename T_loc, typename T_scale>
39  typename return_type<T_y, T_loc, T_scale>::type
40  normal_cdf(const T_y& y, const T_loc& mu, const T_scale& sigma) {
41  static const char* function("stan::math::normal_cdf");
43  T_partials_return;
44 
51  using std::exp;
52 
53  T_partials_return cdf(1.0);
54 
55  // check if any vectors are zero length
56  if (!(stan::length(y)
57  && stan::length(mu)
58  && stan::length(sigma)))
59  return cdf;
60 
61  check_not_nan(function, "Random variable", y);
62  check_finite(function, "Location parameter", mu);
63  check_not_nan(function, "Scale parameter", sigma);
64  check_positive(function, "Scale parameter", sigma);
65  check_consistent_sizes(function,
66  "Random variable", y,
67  "Location parameter", mu,
68  "Scale parameter", sigma);
69 
70 
72  operands_and_partials(y, mu, sigma);
73 
74  VectorView<const T_y> y_vec(y);
75  VectorView<const T_loc> mu_vec(mu);
76  VectorView<const T_scale> sigma_vec(sigma);
77  size_t N = max_size(y, mu, sigma);
78  const double SQRT_TWO_OVER_PI = std::sqrt(2.0 / stan::math::pi());
79 
80  for (size_t n = 0; n < N; n++) {
81  const T_partials_return y_dbl = value_of(y_vec[n]);
82  const T_partials_return mu_dbl = value_of(mu_vec[n]);
83  const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
84  const T_partials_return scaled_diff = (y_dbl - mu_dbl)
85  / (sigma_dbl * SQRT_2);
86  T_partials_return cdf_;
87  if (scaled_diff < -37.5 * INV_SQRT_2)
88  cdf_ = 0.0;
89  else if (scaled_diff < -5.0 * INV_SQRT_2)
90  cdf_ = 0.5 * erfc(-scaled_diff);
91  else if (scaled_diff > 8.25 * INV_SQRT_2)
92  cdf_ = 1;
93  else
94  cdf_ = 0.5 * (1.0 + erf(scaled_diff));
95 
96  // cdf
97  cdf *= cdf_;
98 
99  // gradients
101  const T_partials_return rep_deriv
102  = scaled_diff < -37.5 * INV_SQRT_2
103  ? 0.0
104  : SQRT_TWO_OVER_PI * 0.5
105  * exp(-scaled_diff * scaled_diff) / cdf_ / sigma_dbl;
107  operands_and_partials.d_x1[n] += rep_deriv;
109  operands_and_partials.d_x2[n] -= rep_deriv;
111  operands_and_partials.d_x3[n] -= rep_deriv * scaled_diff * SQRT_2;
112  }
113  }
114 
116  for (size_t n = 0; n < stan::length(y); ++n)
117  operands_and_partials.d_x1[n] *= cdf;
118  }
120  for (size_t n = 0; n < stan::length(mu); ++n)
121  operands_and_partials.d_x2[n] *= cdf;
122  }
124  for (size_t n = 0; n < stan::length(sigma); ++n)
125  operands_and_partials.d_x3[n] *= cdf;
126  }
127 
128  return operands_and_partials.value(cdf);
129  }
130  }
131 }
132 #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
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.
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
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:40
VectorView< T_return_type, false, true > d_x1

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