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gamma_log.hpp
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#ifndef STAN_MATH_PRIM_SCAL_PROB_GAMMA_LOG_HPP
#define STAN_MATH_PRIM_SCAL_PROB_GAMMA_LOG_HPP
#include <boost/random/gamma_distribution.hpp>
#include <boost/random/variate_generator.hpp>
#include <stan/math/prim/scal/meta/OperandsAndPartials.hpp>
#include <stan/math/prim/scal/err/check_consistent_sizes.hpp>
#include <stan/math/prim/scal/err/check_greater_or_equal.hpp>
#include <stan/math/prim/scal/err/check_less_or_equal.hpp>
#include <stan/math/prim/scal/err/check_nonnegative.hpp>
#include <stan/math/prim/scal/err/check_not_nan.hpp>
#include <stan/math/prim/scal/err/check_positive_finite.hpp>
#include <stan/math/prim/scal/fun/constants.hpp>
#include <stan/math/prim/scal/fun/multiply_log.hpp>
#include <stan/math/prim/scal/fun/value_of.hpp>
#include <stan/math/prim/scal/fun/gamma_p.hpp>
#include <stan/math/prim/scal/fun/digamma.hpp>
#include <stan/math/prim/scal/meta/VectorBuilder.hpp>
#include <stan/math/prim/scal/meta/include_summand.hpp>
#include <stan/math/prim/scal/fun/grad_reg_inc_gamma.hpp>
#include <cmath>
namespace stan {
namespace math {
template <bool propto,
typename T_y, typename T_shape, typename T_inv_scale>
typename return_type<T_y, T_shape, T_inv_scale>::type
gamma_log(const T_y& y, const T_shape& alpha, const T_inv_scale& beta) {
static const char* function("stan::math::gamma_log");
typedef typename stan::partials_return_type<T_y, T_shape,
T_inv_scale>::type
T_partials_return;
using stan::is_constant_struct;
using stan::math::check_not_nan;
using stan::math::check_positive_finite;
using stan::math::check_nonnegative;
using stan::math::check_consistent_sizes;
using stan::math::value_of;
// check if any vectors are zero length
if (!(stan::length(y)
&& stan::length(alpha)
&& stan::length(beta)))
return 0.0;
// set up return value accumulator
T_partials_return logp(0.0);
// validate args (here done over var, which should be OK)
check_not_nan(function, "Random variable", y);
check_positive_finite(function, "Shape parameter", alpha);
check_positive_finite(function, "Inverse scale parameter", beta);
check_consistent_sizes(function,
"Random variable", y,
"Shape parameter", alpha,
"Inverse scale parameter", beta);
// check if no variables are involved and prop-to
if (!include_summand<propto, T_y, T_shape, T_inv_scale>::value)
return 0.0;
// set up template expressions wrapping scalars into vector views
VectorView<const T_y> y_vec(y);
VectorView<const T_shape> alpha_vec(alpha);
VectorView<const T_inv_scale> beta_vec(beta);
for (size_t n = 0; n < length(y); n++) {
const T_partials_return y_dbl = value_of(y_vec[n]);
if (y_dbl < 0)
return LOG_ZERO;
}
size_t N = max_size(y, alpha, beta);
OperandsAndPartials<T_y, T_shape, T_inv_scale>
operands_and_partials(y, alpha, beta);
using boost::math::lgamma;
using stan::math::multiply_log;
using boost::math::digamma;
using std::log;
VectorBuilder<include_summand<propto, T_y, T_shape>::value,
T_partials_return, T_y> log_y(length(y));
if (include_summand<propto, T_y, T_shape>::value) {
for (size_t n = 0; n < length(y); n++) {
if (value_of(y_vec[n]) > 0)
log_y[n] = log(value_of(y_vec[n]));
}
}
VectorBuilder<include_summand<propto, T_shape>::value,
T_partials_return, T_shape> lgamma_alpha(length(alpha));
VectorBuilder<!is_constant_struct<T_shape>::value,
T_partials_return, T_shape> digamma_alpha(length(alpha));
for (size_t n = 0; n < length(alpha); n++) {
if (include_summand<propto, T_shape>::value)
lgamma_alpha[n] = lgamma(value_of(alpha_vec[n]));
if (!is_constant_struct<T_shape>::value)
digamma_alpha[n] = digamma(value_of(alpha_vec[n]));
}
VectorBuilder<include_summand<propto, T_shape, T_inv_scale>::value,
T_partials_return, T_inv_scale> log_beta(length(beta));
if (include_summand<propto, T_shape, T_inv_scale>::value) {
for (size_t n = 0; n < length(beta); n++)
log_beta[n] = log(value_of(beta_vec[n]));
}
for (size_t n = 0; n < N; n++) {
// pull out values of arguments
const T_partials_return y_dbl = value_of(y_vec[n]);
const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
const T_partials_return beta_dbl = value_of(beta_vec[n]);
if (include_summand<propto, T_shape>::value)
logp -= lgamma_alpha[n];
if (include_summand<propto, T_shape, T_inv_scale>::value)
logp += alpha_dbl * log_beta[n];
if (include_summand<propto, T_y, T_shape>::value)
logp += (alpha_dbl-1.0) * log_y[n];
if (include_summand<propto, T_y, T_inv_scale>::value)
logp -= beta_dbl * y_dbl;
// gradients
if (!is_constant_struct<T_y>::value)
operands_and_partials.d_x1[n] += (alpha_dbl-1)/y_dbl - beta_dbl;
if (!is_constant_struct<T_shape>::value)
operands_and_partials.d_x2[n] += -digamma_alpha[n] + log_beta[n]
+ log_y[n];
if (!is_constant_struct<T_inv_scale>::value)
operands_and_partials.d_x3[n] += alpha_dbl / beta_dbl - y_dbl;
}
return operands_and_partials.to_var(logp, y, alpha, beta);
}
template <typename T_y, typename T_shape, typename T_inv_scale>
inline
typename return_type<T_y, T_shape, T_inv_scale>::type
gamma_log(const T_y& y, const T_shape& alpha, const T_inv_scale& beta) {
return gamma_log<false>(y, alpha, beta);
}
}
}
#endif
check_not_nan.hpp
stan::math::lgamma
fvar< T > lgamma(const fvar< T > &x)
Definition: lgamma.hpp:15
stan::math::check_not_nan
bool check_not_nan(const char *function, const char *name, const T_y &y)
Return true if y is not NaN.
Definition: check_not_nan.hpp:63
check_positive_finite.hpp
stan::math::value_of
T value_of(const fvar< T > &v)
Return the value of the specified variable.
Definition: value_of.hpp:16
digamma.hpp
stan::math::log
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:15
stan::length
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
stan::math::OperandsAndPartials::to_var
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)
Definition: OperandsAndPartials.hpp:322
stan::math::LOG_ZERO
const double LOG_ZERO
Definition: constants.hpp:175
stan::math::include_summand
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) prob...
Definition: include_summand.hpp:36
stan::return_type::type
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
include_summand.hpp
multiply_log.hpp
stan::math::OperandsAndPartials::d_x1
VectorView< T_partials_return, is_vector< T1 >::value, is_constant_struct< T1 >::value > d_x1
Definition: OperandsAndPartials.hpp:253
check_nonnegative.hpp
stan::is_constant_struct
Metaprogram to determine if a type has a base scalar type that can be assigned to type double...
Definition: is_constant_struct.hpp:16
stan::partials_return_type
Definition: partials_return_type.hpp:16
check_less_or_equal.hpp
stan::math::OperandsAndPartials::d_x3
VectorView< T_partials_return, is_vector< T3 >::value, is_constant_struct< T3 >::value > d_x3
Definition: OperandsAndPartials.hpp:259
stan::math::OperandsAndPartials
A variable implementation that stores operands and derivatives with respect to the variable...
Definition: OperandsAndPartials.hpp:238
OperandsAndPartials.hpp
stan::max_size
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
VectorBuilder.hpp
gamma_p.hpp
stan::math::multiply_log
fvar< T > multiply_log(const fvar< T > &x1, const fvar< T > &x2)
Definition: multiply_log.hpp:15
grad_reg_inc_gamma.hpp
stan::VectorBuilder
Definition: VectorBuilder.hpp:61
constants.hpp
stan::math::check_consistent_sizes
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.
Definition: check_consistent_sizes.hpp:31
stan::math::OperandsAndPartials::d_x2
VectorView< T_partials_return, is_vector< T2 >::value, is_constant_struct< T2 >::value > d_x2
Definition: OperandsAndPartials.hpp:256
stan::math::check_nonnegative
bool check_nonnegative(const char *function, const char *name, const T_y &y)
Return true if y is non-negative.
Definition: check_nonnegative.hpp:66
check_greater_or_equal.hpp
value_of.hpp
stan::VectorView
VectorView is a template metaprogram that takes its argument and allows it to be used like a vector...
Definition: VectorView.hpp:41
check_consistent_sizes.hpp
stan::math::check_positive_finite
bool check_positive_finite(const char *function, const char *name, const T_y &y)
Return true if y is positive and finite.
Definition: check_positive_finite.hpp:28
stan::math::gamma_log
return_type< T_y, T_shape, T_inv_scale >::type gamma_log(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.
Definition: gamma_log.hpp:52
stan::math::digamma
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:16

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