1 #ifndef STAN_MATH_PRIM_SCAL_PROB_SCALED_INV_CHI_SQUARE_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_SCALED_INV_CHI_SQUARE_LOG_HPP
4 #include <boost/random/chi_squared_distribution.hpp>
5 #include <boost/random/variate_generator.hpp>
48 template <
bool propto,
49 typename T_y,
typename T_dof,
typename T_scale>
50 typename return_type<T_y, T_dof, T_scale>::type
52 static const char*
function(
"stan::math::scaled_inv_chi_square_log");
67 T_partials_return logp(0.0);
73 "Degrees of freedom parameter", nu,
74 "Scale parameter", s);
85 for (
size_t n = 0; n < N; n++) {
96 T_partials_return, T_dof> half_nu(
length(nu));
97 for (
size_t i = 0; i <
length(nu); i++)
99 half_nu[i] = 0.5 *
value_of(nu_vec[i]);
102 T_partials_return, T_y> log_y(
length(y));
103 for (
size_t i = 0; i <
length(y); i++)
108 T_partials_return, T_y> inv_y(
length(y));
109 for (
size_t i = 0; i <
length(y); i++)
111 inv_y[i] = 1.0 /
value_of(y_vec[i]);
114 T_partials_return, T_scale> log_s(
length(s));
115 for (
size_t i = 0; i <
length(s); i++)
120 T_partials_return, T_dof> log_half_nu(
length(nu));
122 T_partials_return, T_dof> lgamma_half_nu(
length(nu));
124 T_partials_return, T_dof>
125 digamma_half_nu_over_two(
length(nu));
126 for (
size_t i = 0; i <
length(nu); i++) {
128 lgamma_half_nu[i] =
lgamma(half_nu[i]);
130 log_half_nu[i] =
log(half_nu[i]);
132 digamma_half_nu_over_two[i] =
digamma(half_nu[i]) * 0.5;
136 operands_and_partials(y, nu, s);
137 for (
size_t n = 0; n < N; n++) {
138 const T_partials_return s_dbl =
value_of(s_vec[n]);
139 const T_partials_return nu_dbl =
value_of(nu_vec[n]);
141 logp += half_nu[n] * log_half_nu[n] - lgamma_half_nu[n];
143 logp += nu_dbl * log_s[n];
145 logp -= (half_nu[n]+1.0) * log_y[n];
147 logp -= half_nu[n] * s_dbl*s_dbl * inv_y[n];
150 operands_and_partials.
d_x1[n]
151 += -(half_nu[n] + 1.0) * inv_y[n]
152 + half_nu[n] * s_dbl*s_dbl * inv_y[n]*inv_y[n];
155 operands_and_partials.
d_x2[n]
156 += 0.5 * log_half_nu[n] + 0.5
157 - digamma_half_nu_over_two[n]
160 - 0.5* s_dbl*s_dbl * inv_y[n];
163 operands_and_partials.
d_x3[n]
164 += nu_dbl / s_dbl - nu_dbl * inv_y[n] * s_dbl;
167 return operands_and_partials.
to_var(logp, y, nu, s);
170 template <
typename T_y,
typename T_dof,
typename T_scale>
174 return scaled_inv_chi_square_log<false>(y, nu, s);
fvar< T > lgamma(const fvar< T > &x)
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)
return_type< T_y, T_dof, T_scale >::type scaled_inv_chi_square_log(const T_y &y, const T_dof &nu, const T_scale &s)
The log of a scaled inverse chi-squared density for y with the specified degrees of freedom parameter...
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)
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) prob...
boost::math::tools::promote_args< typename scalar_type< T1 >::type, typename scalar_type< T2 >::type, typename scalar_type< T3 >::type, typename scalar_type< T4 >::type, typename scalar_type< T5 >::type, typename scalar_type< T6 >::type >::type type
fvar< T > square(const fvar< T > &x)
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...
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)
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
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
bool check_positive_finite(const char *function, const char *name, const T_y &y)
Return true if y is positive and finite.
fvar< T > digamma(const fvar< T > &x)