1 #ifndef STAN_MATH_PRIM_SCAL_PROB_INV_GAMMA_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_INV_GAMMA_CDF_HPP
4 #include <boost/random/gamma_distribution.hpp>
5 #include <boost/random/variate_generator.hpp>
49 template <
typename T_y,
typename T_shape,
typename T_scale>
50 typename return_type<T_y, T_shape, T_scale>::type
51 inv_gamma_cdf(
const T_y& y,
const T_shape& alpha,
const T_scale& beta) {
60 static const char*
function(
"stan::math::inv_gamma_cdf");
69 using boost::math::tools::promote_args;
72 T_partials_return P(1.0);
80 "Shape parameter", alpha,
81 "Scale Parameter", beta);
90 operands_and_partials(y, alpha, beta);
97 return operands_and_partials.
value(0.0);
109 T_partials_return, T_shape>
110 gamma_vec(stan::length(alpha));
112 T_partials_return, T_shape>
113 digamma_vec(stan::length(alpha));
117 const T_partials_return alpha_dbl =
value_of(alpha_vec[i]);
118 gamma_vec[i] =
tgamma(alpha_dbl);
119 digamma_vec[i] =
digamma(alpha_dbl);
124 for (
size_t n = 0; n < N; n++) {
127 if (
value_of(y_vec[n]) == std::numeric_limits<double>::infinity())
131 const T_partials_return y_dbl =
value_of(y_vec[n]);
132 const T_partials_return y_inv_dbl = 1.0 / y_dbl;
133 const T_partials_return alpha_dbl =
value_of(alpha_vec[n]);
134 const T_partials_return beta_dbl =
value_of(beta_vec[n]);
137 const T_partials_return Pn =
gamma_q(alpha_dbl, beta_dbl * y_inv_dbl);
142 operands_and_partials.
d_x1[n] += beta_dbl * y_inv_dbl * y_inv_dbl
143 *
exp(-beta_dbl * y_inv_dbl) *
pow(beta_dbl
144 * y_inv_dbl, alpha_dbl-1)
147 operands_and_partials.
d_x2[n]
149 * y_inv_dbl, gamma_vec[n],
150 digamma_vec[n]) / Pn;
152 operands_and_partials.
d_x3[n] += - y_inv_dbl
153 *
exp(-beta_dbl * y_inv_dbl)
154 *
pow(beta_dbl * y_inv_dbl, alpha_dbl-1)
160 operands_and_partials.
d_x1[n] *= P;
164 operands_and_partials.
d_x2[n] *= P;
168 operands_and_partials.
d_x3[n] *= P;
171 return operands_and_partials.
value(P);
VectorView< T_return_type, false, true > d_x2
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.
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)
T grad_reg_inc_gamma(T a, T z, T g, T dig, T precision=1e-6)
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)
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.
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.
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[].
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.
return_type< T_y, T_shape, T_scale >::type inv_gamma_cdf(const T_y &y, const T_shape &alpha, const T_scale &beta)
The CDF of an inverse gamma density for y with the specified shape and scale parameters.
VectorView< T_return_type, false, true > d_x1
fvar< T > digamma(const fvar< T > &x)