Stan Math Library  2.15.0
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 
16 #include <boost/random/normal_distribution.hpp>
17 #include <boost/random/variate_generator.hpp>
18 #include <cmath>
19 
20 namespace stan {
21  namespace math {
22 
37  template <typename T_y, typename T_loc, typename T_scale>
39  normal_cdf(const T_y& y, const T_loc& mu, const T_scale& sigma) {
40  static const char* function("normal_cdf");
42  T_partials_return;
43 
44  using std::exp;
45 
46  T_partials_return cdf(1.0);
47 
48  if (!(stan::length(y)
49  && stan::length(mu)
50  && stan::length(sigma)))
51  return cdf;
52 
53  check_not_nan(function, "Random variable", y);
54  check_finite(function, "Location parameter", mu);
55  check_not_nan(function, "Scale parameter", sigma);
56  check_positive(function, "Scale parameter", sigma);
57  check_consistent_sizes(function,
58  "Random variable", y,
59  "Location parameter", mu,
60  "Scale parameter", sigma);
61 
63  operands_and_partials(y, mu, sigma);
64 
67  scalar_seq_view<const T_scale> sigma_vec(sigma);
68  size_t N = max_size(y, mu, sigma);
69  const double SQRT_TWO_OVER_PI = std::sqrt(2.0 / pi());
70 
71  for (size_t n = 0; n < N; n++) {
72  const T_partials_return y_dbl = value_of(y_vec[n]);
73  const T_partials_return mu_dbl = value_of(mu_vec[n]);
74  const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
75  const T_partials_return scaled_diff = (y_dbl - mu_dbl)
76  / (sigma_dbl * SQRT_2);
77  T_partials_return cdf_;
78  if (scaled_diff < -37.5 * INV_SQRT_2)
79  cdf_ = 0.0;
80  else if (scaled_diff < -5.0 * INV_SQRT_2)
81  cdf_ = 0.5 * erfc(-scaled_diff);
82  else if (scaled_diff > 8.25 * INV_SQRT_2)
83  cdf_ = 1;
84  else
85  cdf_ = 0.5 * (1.0 + erf(scaled_diff));
86 
87  cdf *= cdf_;
88 
90  const T_partials_return rep_deriv
91  = (scaled_diff < -37.5 * INV_SQRT_2)
92  ? 0.0
93  : SQRT_TWO_OVER_PI * 0.5
94  * exp(-scaled_diff * scaled_diff) / cdf_ / sigma_dbl;
96  operands_and_partials.d_x1[n] += rep_deriv;
98  operands_and_partials.d_x2[n] -= rep_deriv;
100  operands_and_partials.d_x3[n] -= rep_deriv * scaled_diff * SQRT_2;
101  }
102  }
103 
105  for (size_t n = 0; n < stan::length(y); ++n)
106  operands_and_partials.d_x1[n] *= cdf;
107  }
109  for (size_t n = 0; n < stan::length(mu); ++n)
110  operands_and_partials.d_x2[n] *= cdf;
111  }
113  for (size_t n = 0; n < stan::length(sigma); ++n)
114  operands_and_partials.d_x3[n] *= cdf;
115  }
116  return operands_and_partials.value(cdf);
117  }
118 
119  }
120 }
121 #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
T_return_type value(double value)
Returns a T_return_type with the value specified with the partial derivatves.
scalar_seq_view provides a uniform sequence-like wrapper around either a scalar or a sequence of scal...
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
fvar< T > erf(const fvar< T > &x)
Definition: erf.hpp:14
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
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
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
void check_positive(const char *function, const char *name, const T_y &y)
Check if y is positive.
double pi()
Return the value of pi.
Definition: constants.hpp:85
void check_consistent_sizes(const char *function, const char *name1, const T1 &x1, const char *name2, const T2 &x2)
Check if the dimension of x1 is consistent with x2.
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:39
VectorView< T_return_type, false, true > d_x1

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