1 #ifndef STAN_MATH_PRIM_SCAL_PROB_STUDENT_T_CDF_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_STUDENT_T_CDF_LOG_HPP
4 #include <boost/random/student_t_distribution.hpp>
5 #include <boost/random/variate_generator.hpp>
29 template <
typename T_y,
typename T_dof,
typename T_loc,
typename T_scale>
30 typename return_type<T_y, T_dof, T_loc, T_scale>::type
32 const T_scale& sigma) {
42 static const char*
function(
"stan::math::student_t_cdf_log");
51 T_partials_return P(0.0);
63 size_t N =
max_size(y, nu, mu, sigma);
66 operands_and_partials(y, nu, mu, sigma);
71 if (
value_of(y_vec[i]) == -std::numeric_limits<double>::infinity())
84 T_partials_return digammaHalf = 0;
87 T_partials_return, T_dof>
88 digamma_vec(stan::length(nu));
90 T_partials_return, T_dof>
91 digammaNu_vec(stan::length(nu));
93 T_partials_return, T_dof>
94 digammaNuPlusHalf_vec(stan::length(nu));
100 const T_partials_return nu_dbl =
value_of(nu_vec[i]);
102 digammaNu_vec[i] =
digamma(0.5 * nu_dbl);
103 digammaNuPlusHalf_vec[i] =
digamma(0.5 + 0.5 * nu_dbl);
108 for (
size_t n = 0; n < N; n++) {
111 if (
value_of(y_vec[n]) == std::numeric_limits<double>::infinity()) {
115 const T_partials_return sigma_inv = 1.0 /
value_of(sigma_vec[n]);
118 const T_partials_return nu_dbl =
value_of(nu_vec[n]);
119 const T_partials_return q = nu_dbl / (t * t);
120 const T_partials_return r = 1.0 / (1.0 + q);
121 const T_partials_return J = 2 * r * r * q / t;
122 const T_partials_return betaNuHalf =
exp(
lbeta(0.5, 0.5 * nu_dbl));
123 T_partials_return zJacobian = t > 0 ? - 0.5 : 0.5;
127 =
inc_beta(0.5 * nu_dbl, (T_partials_return)0.5, 1.0 - r);
128 const T_partials_return Pn = t > 0 ? 1.0 - 0.5 * z : 0.5 * z;
129 const T_partials_return d_ibeta =
pow(r, -0.5)
130 *
pow(1.0 - r, 0.5*nu_dbl - 1) / betaNuHalf;
135 operands_and_partials.
d_x1[n]
136 += - zJacobian * d_ibeta * J * sigma_inv / Pn;
139 T_partials_return g1 = 0;
140 T_partials_return g2 = 0;
143 (T_partials_return)0.5, 1.0 - r,
144 digammaNu_vec[n], digammaHalf,
145 digammaNuPlusHalf_vec[n],
148 operands_and_partials.
d_x2[n]
149 += zJacobian * (d_ibeta * (r / t) * (r / t) + 0.5 * g1) / Pn;
153 operands_and_partials.
d_x3[n]
154 += zJacobian * d_ibeta * J * sigma_inv / Pn;
156 operands_and_partials.
d_x4[n]
157 += zJacobian * d_ibeta * J * sigma_inv * t / Pn;
160 T_partials_return z = 1.0 -
inc_beta((T_partials_return)0.5,
164 const T_partials_return Pn = t > 0 ? 1.0 - 0.5 * z : 0.5 * z;
166 T_partials_return d_ibeta =
pow(1.0-r, 0.5*nu_dbl-1) *
pow(r, -0.5)
172 operands_and_partials.
d_x1[n]
173 += zJacobian * d_ibeta * J * sigma_inv / Pn;
176 T_partials_return g1 = 0;
177 T_partials_return g2 = 0;
181 digammaHalf, digammaNu_vec[n],
182 digammaNuPlusHalf_vec[n],
185 operands_and_partials.
d_x2[n]
186 += zJacobian * (- d_ibeta * (r / t) * (r / t) + 0.5 * g2) / Pn;
190 operands_and_partials.
d_x3[n]
191 += - zJacobian * d_ibeta * J * sigma_inv / Pn;
193 operands_and_partials.
d_x4[n]
194 += - zJacobian * d_ibeta * J * sigma_inv * t / Pn;
198 return operands_and_partials.
to_var(P, y, nu, mu, sigma);
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 > lbeta(const fvar< T > &x1, const fvar< T > &x2)
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)
return_type< T_y, T_dof, T_loc, T_scale >::type student_t_cdf_log(const T_y &y, const T_dof &nu, const T_loc &mu, const T_scale &sigma)
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 > inc_beta(const fvar< T > &a, const fvar< T > &b, const fvar< T > &x)
fvar< T > exp(const fvar< T > &x)
VectorView< T_partials_return, is_vector< T3 >::value, is_constant_struct< T3 >::value > d_x3
VectorView< T_partials_return, is_vector< T4 >::value, is_constant_struct< T4 >::value > d_x4
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_finite(const char *function, const char *name, const T_y &y)
Return true if y is finite.
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)
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
void grad_reg_inc_beta(T &g1, T &g2, T a, T b, T z, T digammaA, T digammaB, T digammaSum, T betaAB)
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)