1 #ifndef STAN_MATH_PRIM_SCAL_PROB_INV_GAMMA_LCCDF_HPP 2 #define STAN_MATH_PRIM_SCAL_PROB_INV_GAMMA_LCCDF_HPP 22 template <
typename T_y,
typename T_shape,
typename T_scale>
24 const T_y& y,
const T_shape& alpha,
const T_scale&
beta) {
31 static const char*
function =
"inv_gamma_lccdf";
33 T_partials_return P(0.0);
40 alpha,
"Scale Parameter", beta);
53 return ops_partials.
build(0.0);
61 gamma_vec(stan::length(alpha));
63 digamma_vec(stan::length(alpha));
67 const T_partials_return alpha_dbl =
value_of(alpha_vec[i]);
68 gamma_vec[i] =
tgamma(alpha_dbl);
69 digamma_vec[i] =
digamma(alpha_dbl);
73 for (
size_t n = 0; n < N; n++) {
76 if (
value_of(y_vec[n]) == std::numeric_limits<double>::infinity())
79 const T_partials_return y_dbl =
value_of(y_vec[n]);
80 const T_partials_return y_inv_dbl = 1.0 / y_dbl;
81 const T_partials_return alpha_dbl =
value_of(alpha_vec[n]);
82 const T_partials_return beta_dbl =
value_of(beta_vec[n]);
84 const T_partials_return Pn =
gamma_p(alpha_dbl, beta_dbl * y_inv_dbl);
89 ops_partials.
edge1_.partials_[n]
90 -= beta_dbl * y_inv_dbl * y_inv_dbl *
exp(-beta_dbl * y_inv_dbl)
91 *
pow(beta_dbl * y_inv_dbl, alpha_dbl - 1) /
tgamma(alpha_dbl)
94 ops_partials.
edge2_.partials_[n]
99 ops_partials.
edge3_.partials_[n]
100 += y_inv_dbl *
exp(-beta_dbl * y_inv_dbl)
101 *
pow(beta_dbl * y_inv_dbl, alpha_dbl - 1) /
tgamma(alpha_dbl)
104 return ops_partials.
build(P);
boost::math::tools::promote_args< double, typename partials_type< typename scalar_type< T >::type >::type, typename partials_return_type< T_pack... >::type >::type type
T value_of(const fvar< T > &v)
Return the value of the specified variable.
return_type< T_y, T_shape, T_scale >::type inv_gamma_lccdf(const T_y &y, const T_shape &alpha, const T_scale &beta)
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.
void check_nonnegative(const char *function, const char *name, const T_y &y)
Check if y is non-negative.
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.
return_type< T1, T2 >::type grad_reg_inc_gamma(T1 a, T2 z, T1 g, T1 dig, double precision=1e-6, int max_steps=1e5)
Gradient of the regularized incomplete gamma functions igamma(a, z)
boost::math::tools::promote_args< double, typename scalar_type< T >::type, typename return_type< Types_pack... >::type >::type type
fvar< T > exp(const fvar< T > &x)
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.
fvar< T > gamma_p(const fvar< T > &x1, const fvar< T > &x2)
VectorBuilder allocates type T1 values to be used as intermediate values.
internal::ops_partials_edge< double, Op2 > edge2_
fvar< T > pow(const fvar< T > &x1, const fvar< T > &x2)
fvar< T > tgamma(const fvar< T > &x)
Return the result of applying the gamma function to the specified argument.
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_
double negative_infinity()
Return negative infinity.
fvar< T > digamma(const fvar< T > &x)
Return the derivative of the log gamma function at the specified argument.