1 #ifndef STAN_MATH_PRIM_SCAL_PROB_SCALED_INV_CHI_SQUARE_CDF_HPP 2 #define STAN_MATH_PRIM_SCAL_PROB_SCALED_INV_CHI_SQUARE_CDF_HPP 34 template <
typename T_y,
typename T_dof,
typename T_scale>
36 const T_y& y,
const T_dof& nu,
const T_scale& s) {
43 static const char*
function =
"scaled_inv_chi_square_cdf";
45 T_partials_return P(1.0);
52 "Degrees of freedom parameter", nu,
"Scale parameter",
66 return ops_partials.
build(0.0);
73 gamma_vec(stan::length(nu));
75 digamma_vec(stan::length(nu));
79 const T_partials_return half_nu_dbl = 0.5 *
value_of(nu_vec[i]);
80 gamma_vec[i] =
tgamma(half_nu_dbl);
81 digamma_vec[i] =
digamma(half_nu_dbl);
85 for (
size_t n = 0; n < N; n++) {
88 if (
value_of(y_vec[n]) == std::numeric_limits<double>::infinity()) {
92 const T_partials_return y_dbl =
value_of(y_vec[n]);
93 const T_partials_return y_inv_dbl = 1.0 / y_dbl;
94 const T_partials_return half_nu_dbl = 0.5 *
value_of(nu_vec[n]);
95 const T_partials_return s_dbl =
value_of(s_vec[n]);
96 const T_partials_return half_s2_overx_dbl = 0.5 * s_dbl * s_dbl * y_inv_dbl;
97 const T_partials_return half_nu_s2_overx_dbl
98 = 2.0 * half_nu_dbl * half_s2_overx_dbl;
100 const T_partials_return Pn =
gamma_q(half_nu_dbl, half_nu_s2_overx_dbl);
101 const T_partials_return gamma_p_deriv
102 =
exp(-half_nu_s2_overx_dbl)
103 *
pow(half_nu_s2_overx_dbl, half_nu_dbl - 1) /
tgamma(half_nu_dbl);
108 ops_partials.
edge1_.partials_[n]
109 += half_nu_s2_overx_dbl * y_inv_dbl * gamma_p_deriv / Pn;
112 ops_partials.
edge2_.partials_[n]
115 gamma_vec[n], digamma_vec[n])
116 - half_s2_overx_dbl * gamma_p_deriv)
120 ops_partials.
edge3_.partials_[n]
121 += -2.0 * half_nu_dbl * s_dbl * y_inv_dbl * gamma_p_deriv / Pn;
126 ops_partials.
edge1_.partials_[n] *= P;
130 ops_partials.
edge2_.partials_[n] *= P;
134 ops_partials.
edge3_.partials_[n] *= P;
136 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.
Extends std::true_type when instantiated with zero or more template parameters, all of which extend t...
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.
return_type< T_y, T_dof, T_scale >::type scaled_inv_chi_square_cdf(const T_y &y, const T_dof &nu, const T_scale &s)
The CDF of a scaled inverse chi-squared density for y with the specified degrees of freedom parameter...
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.
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.
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.
fvar< T > gamma_q(const fvar< T > &x1, const fvar< T > &x2)
internal::ops_partials_edge< double, Op3 > edge3_
internal::ops_partials_edge< double, Op1 > edge1_
fvar< T > digamma(const fvar< T > &x)
Return the derivative of the log gamma function at the specified argument.