1 #ifndef STAN_MATH_PRIM_SCAL_PROB_INV_GAMMA_CDF_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_INV_GAMMA_CDF_LOG_HPP
4 #include <boost/random/gamma_distribution.hpp>
5 #include <boost/random/variate_generator.hpp>
33 template <
typename T_y,
typename T_shape,
typename T_scale>
34 typename return_type<T_y, T_shape, T_scale>::type
36 const T_scale& beta) {
45 static const char*
function(
"stan::math::inv_gamma_cdf_log");
54 using boost::math::tools::promote_args;
57 T_partials_return P(0.0);
65 "Shape parameter", alpha,
66 "Scale Parameter", beta);
75 operands_and_partials(y, alpha, beta);
96 T_partials_return, T_shape> gamma_vec(stan::length(alpha));
98 T_partials_return, T_shape>
99 digamma_vec(stan::length(alpha));
103 const T_partials_return alpha_dbl =
value_of(alpha_vec[i]);
104 gamma_vec[i] =
tgamma(alpha_dbl);
105 digamma_vec[i] =
digamma(alpha_dbl);
110 for (
size_t n = 0; n < N; n++) {
113 if (
value_of(y_vec[n]) == std::numeric_limits<double>::infinity())
117 const T_partials_return y_dbl =
value_of(y_vec[n]);
118 const T_partials_return y_inv_dbl = 1.0 / y_dbl;
119 const T_partials_return alpha_dbl =
value_of(alpha_vec[n]);
120 const T_partials_return beta_dbl =
value_of(beta_vec[n]);
123 const T_partials_return Pn =
gamma_q(alpha_dbl, beta_dbl * y_inv_dbl);
128 operands_and_partials.
d_x1[n] += beta_dbl * y_inv_dbl * y_inv_dbl
129 *
exp(-beta_dbl * y_inv_dbl) *
pow(beta_dbl * y_inv_dbl,
133 operands_and_partials.
d_x2[n]
135 * y_inv_dbl, gamma_vec[n],
136 digamma_vec[n]) / Pn;
138 operands_and_partials.
d_x3[n] += - y_inv_dbl
139 *
exp(-beta_dbl * y_inv_dbl)
140 *
pow(beta_dbl * y_inv_dbl, alpha_dbl-1)
144 return operands_and_partials.
to_var(P, y, alpha, beta);
bool check_greater_or_equal(const char *function, const char *name, const T_y &y, const T_low &low)
Return true if y is greater or equal than low.
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)
T grad_reg_inc_gamma(T a, T z, T g, T dig, T precision=1e-6)
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...
fvar< T > exp(const fvar< T > &x)
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)
return_type< T_y, T_shape, T_scale >::type inv_gamma_cdf_log(const T_y &y, const T_shape &alpha, const T_scale &beta)
bool check_less_or_equal(const char *function, const char *name, const T_y &y, const T_high &high)
Return true if y is less or equal to high.
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
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 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
fvar< T > gamma_q(const fvar< T > &x1, const fvar< T > &x2)
bool check_positive_finite(const char *function, const char *name, const T_y &y)
Return true if y is positive and finite.
double negative_infinity()
Return negative infinity.
fvar< T > digamma(const fvar< T > &x)