Stan Math Library  2.20.0
reverse mode automatic differentiation
skew_normal_lpdf.hpp
Go to the documentation of this file.
1 #ifndef STAN_MATH_PRIM_SCAL_PROB_SKEW_NORMAL_LPDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_SKEW_NORMAL_LPDF_HPP
3 
14 #include <cmath>
15 
16 namespace stan {
17 namespace math {
18 
19 template <bool propto, typename T_y, typename T_loc, typename T_scale,
20  typename T_shape>
22  const T_y& y, const T_loc& mu, const T_scale& sigma, const T_shape& alpha) {
23  static const char* function = "skew_normal_lpdf";
24  typedef
26  T_partials_return;
27 
28  using std::exp;
29  using std::log;
30 
31  if (size_zero(y, mu, sigma, alpha))
32  return 0.0;
33 
34  T_partials_return logp(0.0);
35 
36  check_not_nan(function, "Random variable", y);
37  check_finite(function, "Location parameter", mu);
38  check_finite(function, "Shape parameter", alpha);
39  check_positive(function, "Scale parameter", sigma);
40  check_consistent_sizes(function, "Random variable", y, "Location parameter",
41  mu, "Scale parameter", sigma, "Shape paramter", alpha);
42 
44  return 0.0;
45 
47  alpha);
48 
49  scalar_seq_view<T_y> y_vec(y);
50  scalar_seq_view<T_loc> mu_vec(mu);
51  scalar_seq_view<T_scale> sigma_vec(sigma);
52  scalar_seq_view<T_shape> alpha_vec(alpha);
53  size_t N = max_size(y, mu, sigma, alpha);
54 
57  T_scale>
58  log_sigma(length(sigma));
59  for (size_t i = 0; i < length(sigma); i++) {
60  inv_sigma[i] = 1.0 / value_of(sigma_vec[i]);
62  log_sigma[i] = log(value_of(sigma_vec[i]));
63  }
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 
71  const T_partials_return y_minus_mu_over_sigma
72  = (y_dbl - mu_dbl) * inv_sigma[n];
73  const double pi_dbl = pi();
74 
76  logp -= 0.5 * log(2.0 * pi_dbl);
78  logp -= log(sigma_dbl);
80  logp -= y_minus_mu_over_sigma * y_minus_mu_over_sigma / 2.0;
82  logp += log(erfc(-alpha_dbl * y_minus_mu_over_sigma / std::sqrt(2.0)));
83 
84  T_partials_return deriv_logerf
85  = 2.0 / std::sqrt(pi_dbl)
86  * exp(-alpha_dbl * y_minus_mu_over_sigma / std::sqrt(2.0) * alpha_dbl
87  * y_minus_mu_over_sigma / std::sqrt(2.0))
88  / (1 + erf(alpha_dbl * y_minus_mu_over_sigma / std::sqrt(2.0)));
90  ops_partials.edge1_.partials_[n]
91  += -y_minus_mu_over_sigma / sigma_dbl
92  + deriv_logerf * alpha_dbl / (sigma_dbl * std::sqrt(2.0));
94  ops_partials.edge2_.partials_[n]
95  += y_minus_mu_over_sigma / sigma_dbl
96  + deriv_logerf * -alpha_dbl / (sigma_dbl * std::sqrt(2.0));
98  ops_partials.edge3_.partials_[n]
99  += -1.0 / sigma_dbl
100  + y_minus_mu_over_sigma * y_minus_mu_over_sigma / sigma_dbl
101  - deriv_logerf * y_minus_mu_over_sigma * alpha_dbl
102  / (sigma_dbl * std::sqrt(2.0));
104  ops_partials.edge4_.partials_[n]
105  += deriv_logerf * y_minus_mu_over_sigma / std::sqrt(2.0);
106  }
107  return ops_partials.build(logp);
108 }
109 
110 template <typename T_y, typename T_loc, typename T_scale, typename T_shape>
112 skew_normal_lpdf(const T_y& y, const T_loc& mu, const T_scale& sigma,
113  const T_shape& alpha) {
114  return skew_normal_lpdf<false>(y, mu, sigma, alpha);
115 }
116 
117 } // namespace math
118 } // namespace stan
119 #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.
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
return_type< T_y, T_loc, T_scale, T_shape >::type skew_normal_lpdf(const T_y &y, const T_loc &mu, const T_scale &sigma, const T_shape &alpha)
bool size_zero(T &x)
Returns 1 if input is of length 0, returns 0 otherwise.
Definition: size_zero.hpp:18
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) prob...
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.
VectorBuilder allocates type T1 values to be used as intermediate values.
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_

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