1 #ifndef STAN_MATH_PRIM_PROB_STUDENT_T_LCCDF_HPP
2 #define STAN_MATH_PRIM_PROB_STUDENT_T_LCCDF_HPP
3
4 #include <stan/math/prim/meta.hpp>
5 #include <stan/math/prim/err.hpp>
6 #include <stan/math/prim/fun/beta.hpp>
7 #include <stan/math/prim/fun/constants.hpp>
8 #include <stan/math/prim/fun/digamma.hpp>
9 #include <stan/math/prim/fun/grad_reg_inc_beta.hpp>
10 #include <stan/math/prim/fun/inc_beta.hpp>
11 #include <stan/math/prim/fun/log.hpp>
12 #include <stan/math/prim/fun/max_size.hpp>
13 #include <stan/math/prim/fun/scalar_seq_view.hpp>
14 #include <stan/math/prim/fun/size.hpp>
15 #include <stan/math/prim/fun/size_zero.hpp>
16 #include <stan/math/prim/fun/value_of.hpp>
17 #include <stan/math/prim/functor/operands_and_partials.hpp>
18 #include <cmath>
19
20 namespace stan {
21 namespace math {
22
23 template <typename T_y, typename T_dof, typename T_loc, typename T_scale>
student_t_lccdf(const T_y & y,const T_dof & nu,const T_loc & mu,const T_scale & sigma)24 return_type_t<T_y, T_dof, T_loc, T_scale> student_t_lccdf(
25 const T_y& y, const T_dof& nu, const T_loc& mu, const T_scale& sigma) {
26 using T_partials_return = partials_return_t<T_y, T_dof, T_loc, T_scale>;
27 using T_y_ref = ref_type_t<T_y>;
28 using T_nu_ref = ref_type_t<T_dof>;
29 using T_mu_ref = ref_type_t<T_loc>;
30 using T_sigma_ref = ref_type_t<T_scale>;
31 using std::exp;
32 using std::log;
33 using std::pow;
34 static const char* function = "student_t_lccdf";
35 T_y_ref y_ref = y;
36 T_nu_ref nu_ref = nu;
37 T_mu_ref mu_ref = mu;
38 T_sigma_ref sigma_ref = sigma;
39 check_not_nan(function, "Random variable", y_ref);
40 check_positive_finite(function, "Degrees of freedom parameter", nu_ref);
41 check_finite(function, "Location parameter", mu_ref);
42 check_positive_finite(function, "Scale parameter", sigma_ref);
43
44 if (size_zero(y, nu, mu, sigma)) {
45 return 0;
46 }
47
48 T_partials_return P(0.0);
49 operands_and_partials<T_y_ref, T_nu_ref, T_mu_ref, T_sigma_ref> ops_partials(
50 y_ref, nu_ref, mu_ref, sigma_ref);
51 scalar_seq_view<T_y_ref> y_vec(y_ref);
52 scalar_seq_view<T_nu_ref> nu_vec(nu_ref);
53 scalar_seq_view<T_mu_ref> mu_vec(mu_ref);
54 scalar_seq_view<T_sigma_ref> sigma_vec(sigma_ref);
55 size_t N = max_size(y, nu, mu, sigma);
56
57 // Explicit return for extreme values
58 // The gradients are technically ill-defined, but treated as zero
59 for (size_t i = 0; i < stan::math::size(y); i++) {
60 if (y_vec.val(i) == NEGATIVE_INFTY) {
61 return ops_partials.build(0.0);
62 }
63 }
64
65 T_partials_return digammaHalf = 0;
66
67 VectorBuilder<!is_constant_all<T_dof>::value, T_partials_return, T_dof>
68 digamma_vec(size(nu));
69 VectorBuilder<!is_constant_all<T_dof>::value, T_partials_return, T_dof>
70 digammaNu_vec(size(nu));
71 VectorBuilder<!is_constant_all<T_dof>::value, T_partials_return, T_dof>
72 digammaNuPlusHalf_vec(size(nu));
73
74 if (!is_constant_all<T_dof>::value) {
75 digammaHalf = digamma(0.5);
76
77 for (size_t i = 0; i < stan::math::size(nu); i++) {
78 const T_partials_return nu_dbl = nu_vec.val(i);
79
80 digammaNu_vec[i] = digamma(0.5 * nu_dbl);
81 digammaNuPlusHalf_vec[i] = digamma(0.5 + 0.5 * nu_dbl);
82 }
83 }
84
85 for (size_t n = 0; n < N; n++) {
86 // Explicit results for extreme values
87 // The gradients are technically ill-defined, but treated as zero
88 if (y_vec.val(n) == INFTY) {
89 return ops_partials.build(negative_infinity());
90 }
91
92 const T_partials_return sigma_inv = 1.0 / sigma_vec.val(n);
93 const T_partials_return t = (y_vec.val(n) - mu_vec.val(n)) * sigma_inv;
94 const T_partials_return nu_dbl = nu_vec.val(n);
95 const T_partials_return q = nu_dbl / (t * t);
96 const T_partials_return r = 1.0 / (1.0 + q);
97 const T_partials_return J = 2 * r * r * q / t;
98 const T_partials_return betaNuHalf = beta(0.5, 0.5 * nu_dbl);
99 T_partials_return zJacobian = t > 0 ? -0.5 : 0.5;
100
101 if (q < 2) {
102 T_partials_return z
103 = inc_beta(0.5 * nu_dbl, (T_partials_return)0.5, 1.0 - r);
104 const T_partials_return Pn = t > 0 ? 0.5 * z : 1.0 - 0.5 * z;
105 const T_partials_return d_ibeta
106 = pow(r, -0.5) * pow(1.0 - r, 0.5 * nu_dbl - 1) / betaNuHalf;
107
108 P += log(Pn);
109
110 if (!is_constant_all<T_y>::value) {
111 ops_partials.edge1_.partials_[n]
112 += zJacobian * d_ibeta * J * sigma_inv / Pn;
113 }
114
115 if (!is_constant_all<T_dof>::value) {
116 T_partials_return g1 = 0;
117 T_partials_return g2 = 0;
118
119 grad_reg_inc_beta(g1, g2, 0.5 * nu_dbl, (T_partials_return)0.5, 1.0 - r,
120 digammaNu_vec[n], digammaHalf,
121 digammaNuPlusHalf_vec[n], betaNuHalf);
122
123 ops_partials.edge2_.partials_[n]
124 -= zJacobian * (d_ibeta * (r / t) * (r / t) + 0.5 * g1) / Pn;
125 }
126
127 if (!is_constant_all<T_loc>::value) {
128 ops_partials.edge3_.partials_[n]
129 -= zJacobian * d_ibeta * J * sigma_inv / Pn;
130 }
131 if (!is_constant_all<T_scale>::value) {
132 ops_partials.edge4_.partials_[n]
133 -= zJacobian * d_ibeta * J * sigma_inv * t / Pn;
134 }
135
136 } else {
137 T_partials_return z
138 = 1.0 - inc_beta((T_partials_return)0.5, 0.5 * nu_dbl, r);
139 zJacobian *= -1;
140
141 const T_partials_return Pn = t > 0 ? 0.5 * z : 1.0 - 0.5 * z;
142
143 T_partials_return d_ibeta
144 = pow(1.0 - r, 0.5 * nu_dbl - 1) * pow(r, -0.5) / betaNuHalf;
145
146 P += log(Pn);
147
148 if (!is_constant_all<T_y>::value) {
149 ops_partials.edge1_.partials_[n]
150 -= zJacobian * d_ibeta * J * sigma_inv / Pn;
151 }
152
153 if (!is_constant_all<T_dof>::value) {
154 T_partials_return g1 = 0;
155 T_partials_return g2 = 0;
156
157 grad_reg_inc_beta(g1, g2, (T_partials_return)0.5, 0.5 * nu_dbl, r,
158 digammaHalf, digammaNu_vec[n],
159 digammaNuPlusHalf_vec[n], betaNuHalf);
160
161 ops_partials.edge2_.partials_[n]
162 -= zJacobian * (-d_ibeta * (r / t) * (r / t) + 0.5 * g2) / Pn;
163 }
164
165 if (!is_constant_all<T_loc>::value) {
166 ops_partials.edge3_.partials_[n]
167 += zJacobian * d_ibeta * J * sigma_inv / Pn;
168 }
169 if (!is_constant_all<T_scale>::value) {
170 ops_partials.edge4_.partials_[n]
171 += zJacobian * d_ibeta * J * sigma_inv * t / Pn;
172 }
173 }
174 }
175 return ops_partials.build(P);
176 }
177
178 } // namespace math
179 } // namespace stan
180 #endif
181