1 #ifndef STAN_MATH_PRIM_SCAL_PROB_GAMMA_LPDF_HPP 2 #define STAN_MATH_PRIM_SCAL_PROB_GAMMA_LPDF_HPP 41 template <
bool propto,
typename T_y,
typename T_shape,
typename T_inv_scale>
43 const T_y& y,
const T_shape& alpha,
const T_inv_scale&
beta) {
44 static const char*
function =
"gamma_lpdf";
51 T_partials_return logp(0.0);
57 alpha,
"Inverse scale parameter", beta);
66 for (
size_t n = 0; n <
length(y); n++) {
67 const T_partials_return y_dbl =
value_of(y_vec[n]);
81 for (
size_t n = 0; n <
length(y); n++) {
89 lgamma_alpha(
length(alpha));
91 digamma_alpha(
length(alpha));
92 for (
size_t n = 0; n <
length(alpha); n++) {
100 T_partials_return, T_inv_scale>
103 for (
size_t n = 0; n <
length(beta); n++)
107 for (
size_t n = 0; n < N; n++) {
108 const T_partials_return y_dbl =
value_of(y_vec[n]);
109 const T_partials_return alpha_dbl =
value_of(alpha_vec[n]);
110 const T_partials_return beta_dbl =
value_of(beta_vec[n]);
113 logp -= lgamma_alpha[n];
115 logp += alpha_dbl * log_beta[n];
117 logp += (alpha_dbl - 1.0) * log_y[n];
119 logp -= beta_dbl * y_dbl;
122 ops_partials.
edge1_.partials_[n] += (alpha_dbl - 1) / y_dbl - beta_dbl;
124 ops_partials.
edge2_.partials_[n]
125 += -digamma_alpha[n] + log_beta[n] + log_y[n];
127 ops_partials.
edge3_.partials_[n] += alpha_dbl / beta_dbl - y_dbl;
129 return ops_partials.
build(logp);
132 template <
typename T_y,
typename T_shape,
typename T_inv_scale>
134 const T_y& y,
const T_shape& alpha,
const T_inv_scale&
beta) {
135 return gamma_lpdf<false>(y, alpha,
beta);
boost::math::tools::promote_args< double, typename partials_type< typename scalar_type< T >::type >::type, typename partials_return_type< T_pack... >::type >::type type
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.
Extends std::true_type when instantiated with zero or more template parameters, all of which extend t...
fvar< T > log(const fvar< T > &x)
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.
size_t length(const std::vector< T > &x)
Returns the length of the provided std::vector.
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...
fvar< T > beta(const fvar< T > &x1, const fvar< T > &x2)
Return fvar with the beta function applied to the specified arguments and its gradient.
void check_positive_finite(const char *function, const char *name, const T_y &y)
Check if y is positive and finite.
boost::math::tools::promote_args< double, typename scalar_type< T >::type, typename return_type< Types_pack... >::type >::type type
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.
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.
internal::ops_partials_edge< double, Op2 > edge2_
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_
fvar< T > digamma(const fvar< T > &x)
Return the derivative of the log gamma function at the specified argument.