Stan Math Library  2.15.0
reverse mode automatic differentiation
skew_normal_cdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_SKEW_NORMAL_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_SKEW_NORMAL_CDF_HPP
3 
17 #include <boost/random/variate_generator.hpp>
18 #include <boost/math/distributions.hpp>
19 #include <cmath>
20 
21 namespace stan {
22  namespace math {
23 
24  template <typename T_y, typename T_loc, typename T_scale, typename T_shape>
26  skew_normal_cdf(const T_y& y, const T_loc& mu, const T_scale& sigma,
27  const T_shape& alpha) {
28  static const char* function("skew_normal_cdf");
29  typedef typename stan::partials_return_type<T_y, T_loc, T_scale,
30  T_shape>::type
31  T_partials_return;
32 
33  T_partials_return cdf(1.0);
34 
35  if (!(stan::length(y)
36  && stan::length(mu)
37  && stan::length(sigma)
38  && stan::length(alpha)))
39  return cdf;
40 
41  check_not_nan(function, "Random variable", y);
42  check_finite(function, "Location parameter", mu);
43  check_not_nan(function, "Scale parameter", sigma);
44  check_positive(function, "Scale parameter", sigma);
45  check_finite(function, "Shape parameter", alpha);
46  check_not_nan(function, "Shape parameter", alpha);
47  check_consistent_sizes(function,
48  "Random variable", y,
49  "Location parameter", mu,
50  "Scale parameter", sigma,
51  "Shape paramter", alpha);
52 
54  operands_and_partials(y, mu, sigma, alpha);
55 
56  using std::exp;
57 
60  scalar_seq_view<const T_scale> sigma_vec(sigma);
61  scalar_seq_view<const T_shape> alpha_vec(alpha);
62  size_t N = max_size(y, mu, sigma, alpha);
63  const double SQRT_TWO_OVER_PI = std::sqrt(2.0 / pi());
64 
65  for (size_t n = 0; n < N; n++) {
66  const T_partials_return y_dbl = value_of(y_vec[n]);
67  const T_partials_return mu_dbl = value_of(mu_vec[n]);
68  const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
69  const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
70  const T_partials_return alpha_dbl_sq = alpha_dbl * alpha_dbl;
71  const T_partials_return diff = (y_dbl - mu_dbl) / sigma_dbl;
72  const T_partials_return diff_sq = diff * diff;
73  const T_partials_return scaled_diff = diff / SQRT_2;
74  const T_partials_return scaled_diff_sq = diff_sq * 0.5;
75  const T_partials_return cdf_ = 0.5 * erfc(-scaled_diff) - 2
76  * owens_t(diff, alpha_dbl);
77 
78  cdf *= cdf_;
79 
80  const T_partials_return deriv_erfc = SQRT_TWO_OVER_PI * 0.5
81  * exp(-scaled_diff_sq)
82  / sigma_dbl;
83  const T_partials_return deriv_owens = erf(alpha_dbl * scaled_diff)
84  * exp(-scaled_diff_sq) / SQRT_TWO_OVER_PI / (-2.0 * pi()) / sigma_dbl;
85  const T_partials_return rep_deriv = (-2.0 * deriv_owens + deriv_erfc)
86  / cdf_;
87 
89  operands_and_partials.d_x1[n] += rep_deriv;
91  operands_and_partials.d_x2[n] -= rep_deriv;
93  operands_and_partials.d_x3[n] -= rep_deriv * diff;
95  operands_and_partials.d_x4[n] += -2.0 * exp(-0.5 * diff_sq
96  * (1.0 + alpha_dbl_sq))
97  / ((1 + alpha_dbl_sq) * 2.0 * pi()) / cdf_;
98  }
99 
101  for (size_t n = 0; n < stan::length(y); ++n)
102  operands_and_partials.d_x1[n] *= cdf;
103  }
105  for (size_t n = 0; n < stan::length(mu); ++n)
106  operands_and_partials.d_x2[n] *= cdf;
107  }
109  for (size_t n = 0; n < stan::length(sigma); ++n)
110  operands_and_partials.d_x3[n] *= cdf;
111  }
113  for (size_t n = 0; n < stan::length(alpha); ++n)
114  operands_and_partials.d_x4[n] *= cdf;
115  }
116  return operands_and_partials.value(cdf);
117  }
118 
119  }
120 }
121 #endif
122 
VectorView< T_return_type, false, true > d_x2
return_type< T_y, T_loc, T_scale, T_shape >::type skew_normal_cdf(const T_y &y, const T_loc &mu, const T_scale &sigma, const T_shape &alpha)
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
fvar< T > owens_t(const fvar< T > &x1, const fvar< T > &x2)
Return Owen&#39;s T function applied to the specified arguments.
Definition: owens_t.hpp:23
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
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.
VectorView< T_return_type, false, true > d_x1
VectorView< T_return_type, false, true > d_x4

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