Stan Math Library  2.20.0
reverse mode automatic differentiation
skew_normal_lccdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_SKEW_NORMAL_LCCDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_SKEW_NORMAL_LCCDF_HPP
3 
13 #include <cmath>
14 
15 namespace stan {
16 namespace math {
17 
18 template <typename T_y, typename T_loc, typename T_scale, typename T_shape>
20  const T_y& y, const T_loc& mu, const T_scale& sigma, const T_shape& alpha) {
21  static const char* function = "skew_normal_lccdf";
22  typedef
24  T_partials_return;
25 
26  T_partials_return ccdf_log(0.0);
27 
28  if (size_zero(y, mu, sigma, alpha))
29  return ccdf_log;
30 
31  check_not_nan(function, "Random variable", y);
32  check_finite(function, "Location parameter", mu);
33  check_not_nan(function, "Scale parameter", sigma);
34  check_positive(function, "Scale parameter", sigma);
35  check_finite(function, "Shape parameter", alpha);
36  check_not_nan(function, "Shape parameter", alpha);
37  check_consistent_sizes(function, "Random variable", y, "Location parameter",
38  mu, "Scale parameter", sigma, "Shape paramter", alpha);
39 
41  alpha);
42 
43  using std::exp;
44  using std::log;
45 
46  scalar_seq_view<T_y> y_vec(y);
47  scalar_seq_view<T_loc> mu_vec(mu);
48  scalar_seq_view<T_scale> sigma_vec(sigma);
49  scalar_seq_view<T_shape> alpha_vec(alpha);
50  size_t N = max_size(y, mu, sigma, alpha);
51  const double SQRT_TWO_OVER_PI = std::sqrt(2.0 / pi());
52 
53  for (size_t n = 0; n < N; n++) {
54  const T_partials_return y_dbl = value_of(y_vec[n]);
55  const T_partials_return mu_dbl = value_of(mu_vec[n]);
56  const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
57  const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
58  const T_partials_return alpha_dbl_sq = alpha_dbl * alpha_dbl;
59  const T_partials_return diff = (y_dbl - mu_dbl) / sigma_dbl;
60  const T_partials_return diff_sq = diff * diff;
61  const T_partials_return scaled_diff = diff / SQRT_2;
62  const T_partials_return scaled_diff_sq = diff_sq * 0.5;
63  const T_partials_return ccdf_log_
64  = 1.0 - 0.5 * erfc(-scaled_diff) + 2 * owens_t(diff, alpha_dbl);
65 
66  ccdf_log += log(ccdf_log_);
67 
68  const T_partials_return deriv_erfc
69  = SQRT_TWO_OVER_PI * 0.5 * exp(-scaled_diff_sq) / sigma_dbl;
70  const T_partials_return deriv_owens
71  = erf(alpha_dbl * scaled_diff) * exp(-scaled_diff_sq) / SQRT_TWO_OVER_PI
72  / (-2.0 * pi()) / sigma_dbl;
73  const T_partials_return rep_deriv
74  = (-2.0 * deriv_owens + deriv_erfc) / ccdf_log_;
75 
77  ops_partials.edge1_.partials_[n] -= rep_deriv;
79  ops_partials.edge2_.partials_[n] += rep_deriv;
81  ops_partials.edge3_.partials_[n] += rep_deriv * diff;
83  ops_partials.edge4_.partials_[n]
84  -= -2.0 * exp(-0.5 * diff_sq * (1.0 + alpha_dbl_sq))
85  / ((1 + alpha_dbl_sq) * 2.0 * pi()) / ccdf_log_;
86  }
87  return ops_partials.build(ccdf_log);
88 }
89 
90 } // namespace math
91 } // namespace stan
92 #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
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:12
internal::ops_partials_edge< double, Op4 > edge4_
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
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:24
return_type< T_y, T_loc, T_scale, T_shape >::type skew_normal_lccdf(const T_y &y, const T_loc &mu, const T_scale &sigma, const T_shape &alpha)
const double SQRT_2
The value of the square root of 2, .
Definition: constants.hpp:25
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.
internal::ops_partials_edge< double, Op3 > edge3_
internal::ops_partials_edge< double, Op1 > edge1_

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