Stan Math Library  2.20.0
reverse mode automatic differentiation
normal_lcdf.hpp
Go to the documentation of this file.
1 #ifndef STAN_MATH_PRIM_SCAL_PROB_NORMAL_LCDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_NORMAL_LCDF_HPP
3 
12 #include <cmath>
13 #include <limits>
14 
15 namespace stan {
16 namespace math {
17 
18 template <typename T_y, typename T_loc, typename T_scale>
20  const T_y& y, const T_loc& mu, const T_scale& sigma) {
21  static const char* function = "normal_lcdf";
23  T_partials_return;
24 
25  using std::exp;
26  using std::log;
27 
28  T_partials_return cdf_log(0.0);
29  if (size_zero(y, mu, sigma))
30  return cdf_log;
31 
32  check_not_nan(function, "Random variable", y);
33  check_finite(function, "Location parameter", mu);
34  check_not_nan(function, "Scale parameter", sigma);
35  check_positive(function, "Scale parameter", sigma);
36  check_consistent_sizes(function, "Random variable", y, "Location parameter",
37  mu, "Scale parameter", sigma);
38 
39  operands_and_partials<T_y, T_loc, T_scale> ops_partials(y, mu, sigma);
40 
41  scalar_seq_view<T_y> y_vec(y);
42  scalar_seq_view<T_loc> mu_vec(mu);
43  scalar_seq_view<T_scale> sigma_vec(sigma);
44  size_t N = max_size(y, mu, sigma);
45 
46  const double SQRT_TWO_OVER_PI = std::sqrt(2.0 / pi());
47  for (size_t n = 0; n < N; n++) {
48  const T_partials_return y_dbl = value_of(y_vec[n]);
49  const T_partials_return mu_dbl = value_of(mu_vec[n]);
50  const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
51 
52  const T_partials_return scaled_diff
53  = (y_dbl - mu_dbl) / (sigma_dbl * SQRT_2);
54 
55  T_partials_return one_p_erf;
56  if (scaled_diff < -37.5 * INV_SQRT_2)
57  one_p_erf = 0.0;
58  else if (scaled_diff < -5.0 * INV_SQRT_2)
59  one_p_erf = erfc(-scaled_diff);
60  else if (scaled_diff > 8.25 * INV_SQRT_2)
61  one_p_erf = 2.0;
62  else
63  one_p_erf = 1.0 + erf(scaled_diff);
64 
65  cdf_log += LOG_HALF + log(one_p_erf);
66 
68  const T_partials_return rep_deriv_div_sigma
69  = scaled_diff < -37.5 * INV_SQRT_2
70  ? std::numeric_limits<double>::infinity()
71  : SQRT_TWO_OVER_PI * exp(-scaled_diff * scaled_diff) / sigma_dbl
72  / one_p_erf;
74  ops_partials.edge1_.partials_[n] += rep_deriv_div_sigma;
76  ops_partials.edge2_.partials_[n] -= rep_deriv_div_sigma;
78  ops_partials.edge3_.partials_[n]
79  -= rep_deriv_div_sigma * scaled_diff * SQRT_2;
80  }
81  }
82  return ops_partials.build(cdf_log);
83 }
84 
85 } // namespace math
86 } // namespace stan
87 #endif
const double LOG_HALF
Definition: constants.hpp:152
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
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:12
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.
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_
return_type< T_y, T_loc, T_scale >::type normal_lcdf(const T_y &y, const T_loc &mu, const T_scale &sigma)
Definition: normal_lcdf.hpp:19
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.
internal::ops_partials_edge< double, Op3 > edge3_
internal::ops_partials_edge< double, Op1 > edge1_

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