Stan Math Library  2.15.0
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 
15 #include <boost/random/normal_distribution.hpp>
16 #include <boost/random/variate_generator.hpp>
17 #include <cmath>
18 
19 namespace stan {
20  namespace math {
21 
22  template <bool propto,
23  typename T_y, typename T_loc, typename T_scale,
24  typename T_inv_scale>
26  exp_mod_normal_lpdf(const T_y& y, const T_loc& mu, const T_scale& sigma,
27  const T_inv_scale& lambda) {
28  static const char* function("exp_mod_normal_lpdf");
29  typedef typename stan::partials_return_type<T_y, T_loc, T_scale,
30  T_inv_scale>::type
31  T_partials_return;
32 
34  using std::log;
35 
36  if (!(stan::length(y)
37  && stan::length(mu)
38  && stan::length(sigma)
39  && stan::length(lambda)))
40  return 0.0;
41 
42  T_partials_return logp(0.0);
43 
44  check_not_nan(function, "Random variable", y);
45  check_finite(function, "Location parameter", mu);
46  check_positive_finite(function, "Inv_scale parameter", lambda);
47  check_positive_finite(function, "Scale parameter", sigma);
48  check_consistent_sizes(function,
49  "Random variable", y,
50  "Location parameter", mu,
51  "Scale parameter", sigma,
52  "Inv_scale paramter", lambda);
53 
55  return 0.0;
56 
57  using boost::math::erfc;
58  using std::sqrt;
59  using std::log;
60  using std::exp;
61 
63  operands_and_partials(y, mu, sigma, lambda);
64 
67  scalar_seq_view<const T_scale> sigma_vec(sigma);
68  scalar_seq_view<const T_inv_scale> lambda_vec(lambda);
69  size_t N = max_size(y, mu, sigma, lambda);
70 
71  for (size_t n = 0; n < N; n++) {
72  const T_partials_return y_dbl = value_of(y_vec[n]);
73  const T_partials_return mu_dbl = value_of(mu_vec[n]);
74  const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
75  const T_partials_return lambda_dbl = value_of(lambda_vec[n]);
76 
77  const T_partials_return pi_dbl = boost::math::constants::pi<double>();
78 
80  logp -= log(2.0);
82  logp += log(lambda_dbl);
84  logp += lambda_dbl
85  * (mu_dbl + 0.5 * lambda_dbl * sigma_dbl * sigma_dbl - y_dbl)
86  + log(erfc((mu_dbl + lambda_dbl * sigma_dbl
87  * sigma_dbl - y_dbl)
88  / (sqrt(2.0) * sigma_dbl)));
89 
90  const T_partials_return deriv_logerfc
91  = -2.0 / sqrt(pi_dbl)
92  * exp(-(mu_dbl + lambda_dbl * sigma_dbl * sigma_dbl - y_dbl)
93  / (std::sqrt(2.0) * sigma_dbl)
94  * (mu_dbl + lambda_dbl * sigma_dbl * sigma_dbl - y_dbl)
95  / (sigma_dbl * std::sqrt(2.0)))
96  / erfc((mu_dbl + lambda_dbl * sigma_dbl * sigma_dbl
97  - y_dbl) / (sigma_dbl * std::sqrt(2.0)));
98 
100  operands_and_partials.d_x1[n]
101  += -lambda_dbl
102  + deriv_logerfc * -1.0 / (sigma_dbl * std::sqrt(2.0));
104  operands_and_partials.d_x2[n]
105  += lambda_dbl
106  + deriv_logerfc / (sigma_dbl * std::sqrt(2.0));
108  operands_and_partials.d_x3[n]
109  += sigma_dbl * lambda_dbl * lambda_dbl
110  + deriv_logerfc
111  * (-mu_dbl / (sigma_dbl * sigma_dbl * std::sqrt(2.0))
112  + lambda_dbl / std::sqrt(2.0)
113  + y_dbl / (sigma_dbl * sigma_dbl * std::sqrt(2.0)));
115  operands_and_partials.d_x4[n]
116  += 1 / lambda_dbl + lambda_dbl * sigma_dbl * sigma_dbl
117  + mu_dbl - y_dbl + deriv_logerfc * sigma_dbl / std::sqrt(2.0);
118  }
119  return operands_and_partials.value(logp);
120  }
121 
122  template <typename T_y, typename T_loc, typename T_scale,
123  typename T_inv_scale>
124  inline
126  exp_mod_normal_lpdf(const T_y& y, const T_loc& mu, const T_scale& sigma,
127  const T_inv_scale& lambda) {
128  return exp_mod_normal_lpdf<false>(y, mu, sigma, lambda);
129  }
130 
131  }
132 }
133 #endif
134 
VectorView< T_return_type, false, true > d_x2
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
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:14
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
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) prob...
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
Metaprogram to determine if a type has a base scalar type that can be assigned to type double...
void check_positive_finite(const char *function, const char *name, const T_y &y)
Check if y is positive and finite.
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_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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