1 #ifndef STAN_MATH_PRIM_SCAL_PROB_EXP_MOD_NORMAL_LPDF_HPP 2 #define STAN_MATH_PRIM_SCAL_PROB_EXP_MOD_NORMAL_LPDF_HPP 18 template <
bool propto,
typename T_y,
typename T_loc,
typename T_scale,
22 const T_inv_scale& lambda) {
23 static const char*
function =
"exp_mod_normal_lpdf";
26 T_inv_scale>::type T_partials_return;
31 T_partials_return logp(0.0);
38 mu,
"Scale parameter", sigma,
"Inv_scale paramter",
49 y, mu, sigma, lambda);
55 size_t N =
max_size(y, mu, sigma, lambda);
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]);
63 const T_partials_return pi_dbl = boost::math::constants::pi<double>();
68 logp +=
log(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)));
75 const T_partials_return deriv_logerfc
77 *
exp(-(mu_dbl + lambda_dbl * sigma_dbl * sigma_dbl - y_dbl)
79 * (mu_dbl + lambda_dbl * sigma_dbl * sigma_dbl - y_dbl)
81 /
erfc((mu_dbl + lambda_dbl * sigma_dbl * sigma_dbl - y_dbl)
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
94 * (-mu_dbl / (sigma_dbl * sigma_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);
102 return ops_partials.
build(logp);
105 template <
typename T_y,
typename T_loc,
typename T_scale,
typename T_inv_scale>
108 const T_inv_scale& lambda) {
109 return exp_mod_normal_lpdf<false>(y, mu, sigma, lambda);
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)
T value_of(const fvar< T > &v)
Return the value of the specified variable.
Extends std::true_type when instantiated with zero or more template parameters, all of which extend t...
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)
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.
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
fvar< T > exp(const fvar< T > &x)
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)
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)
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_