Stan Math Library  2.20.0
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 
12 #include <cmath>
13 
14 namespace stan {
15 namespace math {
16 
31 template <typename T_y, typename T_loc, typename T_scale>
33  const T_y& y, const T_loc& mu, const T_scale& sigma) {
34  static const char* function = "normal_cdf";
36  T_partials_return;
37 
38  using std::exp;
39 
40  T_partials_return cdf(1.0);
41 
42  if (size_zero(y, mu, sigma))
43  return cdf;
44 
45  check_not_nan(function, "Random variable", y);
46  check_finite(function, "Location parameter", mu);
47  check_not_nan(function, "Scale parameter", sigma);
48  check_positive(function, "Scale parameter", sigma);
49  check_consistent_sizes(function, "Random variable", y, "Location parameter",
50  mu, "Scale parameter", sigma);
51 
52  operands_and_partials<T_y, T_loc, T_scale> ops_partials(y, mu, sigma);
53 
54  scalar_seq_view<T_y> y_vec(y);
55  scalar_seq_view<T_loc> mu_vec(mu);
56  scalar_seq_view<T_scale> sigma_vec(sigma);
57  size_t N = max_size(y, mu, sigma);
58  const double SQRT_TWO_OVER_PI = std::sqrt(2.0 / pi());
59 
60  for (size_t n = 0; n < N; n++) {
61  const T_partials_return y_dbl = value_of(y_vec[n]);
62  const T_partials_return mu_dbl = value_of(mu_vec[n]);
63  const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
64  const T_partials_return scaled_diff
65  = (y_dbl - mu_dbl) / (sigma_dbl * SQRT_2);
66  T_partials_return cdf_;
67  if (scaled_diff < -37.5 * INV_SQRT_2)
68  cdf_ = 0.0;
69  else if (scaled_diff < -5.0 * INV_SQRT_2)
70  cdf_ = 0.5 * erfc(-scaled_diff);
71  else if (scaled_diff > 8.25 * INV_SQRT_2)
72  cdf_ = 1;
73  else
74  cdf_ = 0.5 * (1.0 + erf(scaled_diff));
75 
76  cdf *= cdf_;
77 
79  const T_partials_return rep_deriv
80  = (scaled_diff < -37.5 * INV_SQRT_2)
81  ? 0.0
82  : SQRT_TWO_OVER_PI * 0.5 * exp(-scaled_diff * scaled_diff)
83  / cdf_ / sigma_dbl;
85  ops_partials.edge1_.partials_[n] += rep_deriv;
87  ops_partials.edge2_.partials_[n] -= rep_deriv;
89  ops_partials.edge3_.partials_[n] -= rep_deriv * scaled_diff * SQRT_2;
90  }
91  }
92 
94  for (size_t n = 0; n < stan::length(y); ++n)
95  ops_partials.edge1_.partials_[n] *= cdf;
96  }
98  for (size_t n = 0; n < stan::length(mu); ++n)
99  ops_partials.edge2_.partials_[n] *= cdf;
100  }
102  for (size_t n = 0; n < stan::length(sigma); ++n)
103  ops_partials.edge3_.partials_[n] *= cdf;
104  }
105  return ops_partials.build(cdf);
106 }
107 
108 } // namespace math
109 } // namespace stan
110 #endif
void check_finite(const char *function, const char *name, const T_y &y)
Check if y is finite.
boost::math::tools::promote_args< double, typename partials_type< typename scalar_type< T >::type >::type, typename partials_return_type< T_pack... >::type >::type type
fvar< T > sqrt(const fvar< T > &x)
Definition: sqrt.hpp:13
T value_of(const fvar< T > &v)
Return the value of the specified variable.
Definition: value_of.hpp:17
Extends std::true_type when instantiated with zero or more template parameters, all of which extend t...
Definition: conjunction.hpp:14
scalar_seq_view provides a uniform sequence-like wrapper around either a scalar or a sequence of scal...
This template builds partial derivatives with respect to a set of operands.
size_t length(const std::vector< T > &x)
Returns the length of the provided std::vector.
Definition: length.hpp:16
fvar< T > erf(const fvar< T > &x)
Definition: erf.hpp:15
bool size_zero(T &x)
Returns 1 if input is of length 0, returns 0 otherwise.
Definition: size_zero.hpp:18
const double SQRT_2
The value of the square root of 2, .
Definition: constants.hpp:25
const double INV_SQRT_2
The value of 1 over the square root of 2, .
Definition: constants.hpp:31
boost::math::tools::promote_args< double, typename scalar_type< T >::type, typename return_type< Types_pack... >::type >::type type
Definition: return_type.hpp:36
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:11
void check_not_nan(const char *function, const char *name, const T_y &y)
Check if y is not NaN.
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
T_return_type build(double value)
Build the node to be stored on the autodiff graph.
internal::ops_partials_edge< double, Op2 > edge2_
fvar< T > erfc(const fvar< T > &x)
Definition: erfc.hpp:15
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:80
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.
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:32
internal::ops_partials_edge< double, Op3 > edge3_
internal::ops_partials_edge< double, Op1 > edge1_

     [ Stan Home Page ] © 2011–2018, Stan Development Team.