1 #ifndef STAN_MATH_PRIM_SCAL_PROB_GAMMA_CDF_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_GAMMA_CDF_LOG_HPP
4 #include <boost/random/gamma_distribution.hpp>
5 #include <boost/random/variate_generator.hpp>
32 template <
typename T_y,
typename T_shape,
typename T_inv_scale>
33 typename return_type<T_y, T_shape, T_inv_scale>::type
34 gamma_cdf_log(
const T_y& y,
const T_shape& alpha,
const T_inv_scale& beta) {
41 static const char*
function(
"gamma_cdf_log");
43 using boost::math::tools::promote_args;
46 T_partials_return P(0.0);
54 "Shape parameter", alpha,
55 "Scale Parameter", beta);
63 operands_and_partials(y, alpha, beta);
78 T_partials_return, T_shape> gamma_vec(stan::length(alpha));
80 T_partials_return, T_shape>
81 digamma_vec(stan::length(alpha));
85 const T_partials_return alpha_dbl =
value_of(alpha_vec[i]);
86 gamma_vec[i] =
tgamma(alpha_dbl);
87 digamma_vec[i] =
digamma(alpha_dbl);
91 for (
size_t n = 0; n < N; n++) {
94 if (
value_of(y_vec[n]) == std::numeric_limits<double>::infinity())
95 return operands_and_partials.
value(0.0);
97 const T_partials_return y_dbl =
value_of(y_vec[n]);
98 const T_partials_return alpha_dbl =
value_of(alpha_vec[n]);
99 const T_partials_return beta_dbl =
value_of(beta_vec[n]);
101 const T_partials_return Pn =
gamma_p(alpha_dbl, beta_dbl * y_dbl);
106 operands_and_partials.
d_x1[n] += beta_dbl *
exp(-beta_dbl * y_dbl)
107 *
pow(beta_dbl * y_dbl, alpha_dbl-1) /
tgamma(alpha_dbl) / Pn;
109 operands_and_partials.
d_x2[n]
111 * y_dbl, gamma_vec[n],
112 digamma_vec[n]) / Pn;
114 operands_and_partials.
d_x3[n] += y_dbl *
exp(-beta_dbl * y_dbl)
115 *
pow(beta_dbl * y_dbl, alpha_dbl-1) /
tgamma(alpha_dbl) / Pn;
117 return operands_and_partials.
value(P);
VectorView< T_return_type, false, true > d_x2
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.
return_type< T_y, T_shape, T_inv_scale >::type gamma_cdf_log(const T_y &y, const T_shape &alpha, const T_inv_scale &beta)
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.
size_t length(const std::vector< T > &x)
Metaprogram to determine if a type has a base scalar type that can be assigned to type double...
fvar< T > exp(const fvar< T > &x)
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)
fvar< T > gamma_p(const fvar< T > &x1, const fvar< T > &x2)
VectorBuilder allocates type T1 values to be used as intermediate values.
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.
T grad_reg_inc_gamma(T a, T z, T g, T dig, double precision=1e-6)
Gradient of the regularized incomplete gamma functions igamma(a, z)
fvar< T > pow(const fvar< T > &x1, const fvar< T > &x2)
bool check_nonnegative(const char *function, const char *name, const T_y &y)
Return true if y is non-negative.
fvar< T > tgamma(const fvar< T > &x)
VectorView is a template expression that is constructed with a container or scalar, which it then allows to be used as an array using operator[].
bool check_positive_finite(const char *function, const char *name, const T_y &y)
Return true if y is positive and finite.
VectorView< T_return_type, false, true > d_x1
double negative_infinity()
Return negative infinity.
fvar< T > digamma(const fvar< T > &x)