Stan Math Library  2.20.0
reverse mode automatic differentiation
exp_mod_normal_lpdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_EXP_MOD_NORMAL_LPDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_EXP_MOD_NORMAL_LPDF_HPP
3 
13 #include <cmath>
14 
15 namespace stan {
16 namespace math {
17 
18 template <bool propto, typename T_y, typename T_loc, typename T_scale,
19  typename T_inv_scale>
21 exp_mod_normal_lpdf(const T_y& y, const T_loc& mu, const T_scale& sigma,
22  const T_inv_scale& lambda) {
23  static const char* function = "exp_mod_normal_lpdf";
24  typedef
25  typename stan::partials_return_type<T_y, T_loc, T_scale,
26  T_inv_scale>::type T_partials_return;
27 
28  if (size_zero(y, mu, sigma, lambda))
29  return 0.0;
30 
31  T_partials_return logp(0.0);
32 
33  check_not_nan(function, "Random variable", y);
34  check_finite(function, "Location parameter", mu);
35  check_positive_finite(function, "Inv_scale parameter", lambda);
36  check_positive_finite(function, "Scale parameter", sigma);
37  check_consistent_sizes(function, "Random variable", y, "Location parameter",
38  mu, "Scale parameter", sigma, "Inv_scale paramter",
39  lambda);
40 
42  return 0.0;
43 
44  using std::exp;
45  using std::log;
46  using std::sqrt;
47 
49  y, mu, sigma, lambda);
50 
51  scalar_seq_view<T_y> y_vec(y);
52  scalar_seq_view<T_loc> mu_vec(mu);
53  scalar_seq_view<T_scale> sigma_vec(sigma);
54  scalar_seq_view<T_inv_scale> lambda_vec(lambda);
55  size_t N = max_size(y, mu, sigma, lambda);
56 
57  for (size_t n = 0; n < N; n++) {
58  const T_partials_return y_dbl = value_of(y_vec[n]);
59  const T_partials_return mu_dbl = value_of(mu_vec[n]);
60  const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
61  const T_partials_return lambda_dbl = value_of(lambda_vec[n]);
62 
63  const T_partials_return pi_dbl = boost::math::constants::pi<double>();
64 
66  logp -= log(2.0);
68  logp += log(lambda_dbl);
70  logp += lambda_dbl
71  * (mu_dbl + 0.5 * lambda_dbl * sigma_dbl * sigma_dbl - y_dbl)
72  + log(erfc((mu_dbl + lambda_dbl * sigma_dbl * sigma_dbl - y_dbl)
73  / (sqrt(2.0) * sigma_dbl)));
74 
75  const T_partials_return deriv_logerfc
76  = -2.0 / sqrt(pi_dbl)
77  * exp(-(mu_dbl + lambda_dbl * sigma_dbl * sigma_dbl - y_dbl)
78  / (std::sqrt(2.0) * sigma_dbl)
79  * (mu_dbl + lambda_dbl * sigma_dbl * sigma_dbl - y_dbl)
80  / (sigma_dbl * std::sqrt(2.0)))
81  / erfc((mu_dbl + lambda_dbl * sigma_dbl * sigma_dbl - y_dbl)
82  / (sigma_dbl * std::sqrt(2.0)));
83 
85  ops_partials.edge1_.partials_[n]
86  += -lambda_dbl + deriv_logerfc * -1.0 / (sigma_dbl * std::sqrt(2.0));
88  ops_partials.edge2_.partials_[n]
89  += lambda_dbl + deriv_logerfc / (sigma_dbl * std::sqrt(2.0));
91  ops_partials.edge3_.partials_[n]
92  += sigma_dbl * lambda_dbl * lambda_dbl
93  + deriv_logerfc
94  * (-mu_dbl / (sigma_dbl * sigma_dbl * std::sqrt(2.0))
95  + lambda_dbl / std::sqrt(2.0)
96  + y_dbl / (sigma_dbl * sigma_dbl * std::sqrt(2.0)));
98  ops_partials.edge4_.partials_[n]
99  += 1 / lambda_dbl + lambda_dbl * sigma_dbl * sigma_dbl + mu_dbl
100  - y_dbl + deriv_logerfc * sigma_dbl / std::sqrt(2.0);
101  }
102  return ops_partials.build(logp);
103 }
104 
105 template <typename T_y, typename T_loc, typename T_scale, typename T_inv_scale>
107 exp_mod_normal_lpdf(const T_y& y, const T_loc& mu, const T_scale& sigma,
108  const T_inv_scale& lambda) {
109  return exp_mod_normal_lpdf<false>(y, mu, sigma, lambda);
110 }
111 
112 } // namespace math
113 } // namespace stan
114 #endif
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: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
return_type< T_y, T_loc, T_scale, T_inv_scale >::type exp_mod_normal_lpdf(const T_y &y, const T_loc &mu, const T_scale &sigma, const T_inv_scale &lambda)
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.
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...
void check_positive_finite(const char *function, const char *name, const T_y &y)
Check if y is positive and finite.
Template metaprogram to calculate the partial derivative type resulting from promoting all the scalar...
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_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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