1 #ifndef STAN_MATH_PRIM_SCAL_PROB_GAMMA_LPDF_HPP 2 #define STAN_MATH_PRIM_SCAL_PROB_GAMMA_LPDF_HPP 22 #include <boost/random/gamma_distribution.hpp> 23 #include <boost/random/variate_generator.hpp> 51 template <
bool propto,
52 typename T_y,
typename T_shape,
typename T_inv_scale>
54 gamma_lpdf(
const T_y& y,
const T_shape& alpha,
const T_inv_scale& beta) {
55 static const char*
function(
"gamma_lpdf");
67 T_partials_return logp(0.0);
74 "Shape parameter", alpha,
75 "Inverse scale parameter", beta);
84 for (
size_t n = 0; n <
length(y); n++) {
85 const T_partials_return y_dbl =
value_of(y_vec[n]);
92 operands_and_partials(y, alpha, beta);
99 T_partials_return, T_y> log_y(
length(y));
101 for (
size_t n = 0; n <
length(y); n++) {
108 T_partials_return, T_shape> lgamma_alpha(
length(alpha));
110 T_partials_return, T_shape> digamma_alpha(
length(alpha));
111 for (
size_t n = 0; n <
length(alpha); n++) {
119 T_partials_return, T_inv_scale> log_beta(
length(beta));
121 for (
size_t n = 0; n <
length(beta); n++)
125 for (
size_t n = 0; n < N; n++) {
126 const T_partials_return y_dbl =
value_of(y_vec[n]);
127 const T_partials_return alpha_dbl =
value_of(alpha_vec[n]);
128 const T_partials_return beta_dbl =
value_of(beta_vec[n]);
131 logp -= lgamma_alpha[n];
133 logp += alpha_dbl * log_beta[n];
135 logp += (alpha_dbl-1.0) * log_y[n];
137 logp -= beta_dbl * y_dbl;
140 operands_and_partials.
d_x1[n] += (alpha_dbl-1)/y_dbl - beta_dbl;
142 operands_and_partials.
d_x2[n] += -digamma_alpha[n] + log_beta[n]
145 operands_and_partials.
d_x3[n] += alpha_dbl / beta_dbl - y_dbl;
147 return operands_and_partials.
value(logp);
150 template <
typename T_y,
typename T_shape,
typename T_inv_scale>
153 gamma_lpdf(
const T_y& y,
const T_shape& alpha,
const T_inv_scale& beta) {
154 return gamma_lpdf<false>(y, alpha, beta);
VectorView< T_return_type, false, true > d_x2
fvar< T > lgamma(const fvar< T > &x)
Return the natural logarithm of the gamma function applied to the specified argument.
T value_of(const fvar< T > &v)
Return the value of the specified variable.
fvar< T > log(const fvar< T > &x)
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)
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
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.
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)
return_type< T_y, T_shape, T_inv_scale >::type gamma_lpdf(const T_y &y, const T_shape &alpha, const T_inv_scale &beta)
The log of a gamma density for y with the specified shape and inverse scale parameters.
VectorBuilder allocates type T1 values to be used as intermediate values.
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
fvar< T > digamma(const fvar< T > &x)
Return the derivative of the log gamma function at the specified argument.