1 #ifndef STAN_MATH_PRIM_SCAL_PROB_INV_GAMMA_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_INV_GAMMA_LOG_HPP
4 #include <boost/random/gamma_distribution.hpp>
5 #include <boost/random/variate_generator.hpp>
48 template <
bool propto,
49 typename T_y,
typename T_shape,
typename T_scale>
50 typename return_type<T_y, T_shape, T_scale>::type
51 inv_gamma_log(
const T_y& y,
const T_shape& alpha,
const T_scale& beta) {
52 static const char*
function(
"stan::math::inv_gamma_log");
59 using boost::math::tools::promote_args;
70 T_partials_return logp(0.0);
77 "Shape parameter", alpha,
78 "Scale parameter", beta);
89 for (
size_t n = 0; n <
length(y); n++) {
90 const T_partials_return y_dbl =
value_of(y_vec[n]);
97 operands_and_partials(y, alpha, beta);
104 T_partials_return, T_y> log_y(
length(y));
106 T_partials_return, T_y> inv_y(
length(y));
107 for (
size_t n = 0; n <
length(y); n++) {
112 inv_y[n] = 1.0 /
value_of(y_vec[n]);
116 T_partials_return, T_shape> lgamma_alpha(
length(alpha));
118 T_partials_return, T_shape> digamma_alpha(
length(alpha));
119 for (
size_t n = 0; n <
length(alpha); n++) {
127 T_partials_return, T_scale> log_beta(
length(beta));
129 for (
size_t n = 0; n <
length(beta); n++)
133 for (
size_t n = 0; n < N; n++) {
135 const T_partials_return alpha_dbl =
value_of(alpha_vec[n]);
136 const T_partials_return beta_dbl =
value_of(beta_vec[n]);
139 logp -= lgamma_alpha[n];
141 logp += alpha_dbl * log_beta[n];
143 logp -= (alpha_dbl+1.0) * log_y[n];
145 logp -= beta_dbl * inv_y[n];
149 operands_and_partials.
d_x1[n]
150 += -(alpha_dbl+1) * inv_y[n] + beta_dbl * inv_y[n] * inv_y[n];
152 operands_and_partials.
d_x2[n]
153 += -digamma_alpha[n] + log_beta[n] - log_y[n];
155 operands_and_partials.
d_x3[n] += alpha_dbl / beta_dbl - inv_y[n];
157 return operands_and_partials.
to_var(logp, y, alpha, beta);
160 template <
typename T_y,
typename T_shape,
typename T_scale>
164 return inv_gamma_log<false>(y, alpha, beta);
Metaprogramming struct to detect whether a given type is constant in the mathematical sense (not the ...
return_type< T_y, T_shape, T_scale >::type inv_gamma_log(const T_y &y, const T_shape &alpha, const T_scale &beta)
The log of an inverse gamma density for y with the specified shape and scale parameters.
fvar< T > lgamma(const fvar< T > &x)
bool check_not_nan(const char *function, const char *name, const T_y &y)
Return true if y is not NaN.
T value_of(const fvar< T > &v)
Return the value of the specified variable.
fvar< T > log(const fvar< T > &x)
size_t length(const std::vector< T > &x)
T_return_type to_var(T_partials_return logp, const T1 &x1=0, const T2 &x2=0, const T3 &x3=0, const T4 &x4=0, const T5 &x5=0, const T6 &x6=0)
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
VectorView< T_partials_return, is_vector< T1 >::value, is_constant_struct< T1 >::value > d_x1
Metaprogram to determine if a type has a base scalar type that can be assigned to type double...
VectorView< T_partials_return, is_vector< T3 >::value, is_constant_struct< T3 >::value > d_x3
A variable implementation that stores operands and derivatives with respect to the variable...
size_t max_size(const T1 &x1, const T2 &x2)
bool check_consistent_sizes(const char *function, const char *name1, const T1 &x1, const char *name2, const T2 &x2)
Return true if the dimension of x1 is consistent with x2.
VectorView< T_partials_return, is_vector< T2 >::value, is_constant_struct< T2 >::value > d_x2
VectorView is a template metaprogram that takes its argument and allows it to be used like a vector...
boost::math::tools::promote_args< typename partials_type< typename scalar_type< T1 >::type >::type, typename partials_type< typename scalar_type< T2 >::type >::type, typename partials_type< typename scalar_type< T3 >::type >::type, typename partials_type< typename scalar_type< T4 >::type >::type, typename partials_type< typename scalar_type< T5 >::type >::type, typename partials_type< typename scalar_type< T6 >::type >::type >::type type
bool check_positive_finite(const char *function, const char *name, const T_y &y)
Return true if y is positive and finite.
fvar< T > digamma(const fvar< T > &x)