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student_t_ccdf_log.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_STUDENT_T_CCDF_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_STUDENT_T_CCDF_LOG_HPP
3
4 #include <stan/math/prim/scal/meta/is_constant_struct.hpp>
5 #include <stan/math/prim/scal/meta/partials_return_type.hpp>
6 #include <stan/math/prim/scal/meta/OperandsAndPartials.hpp>
7 #include <stan/math/prim/scal/err/check_consistent_sizes.hpp>
8 #include <stan/math/prim/scal/err/check_finite.hpp>
9 #include <stan/math/prim/scal/err/check_not_nan.hpp>
10 #include <stan/math/prim/scal/err/check_positive_finite.hpp>
11 #include <stan/math/prim/scal/fun/constants.hpp>
12 #include <stan/math/prim/scal/fun/square.hpp>
13 #include <stan/math/prim/scal/fun/value_of.hpp>
14 #include <stan/math/prim/scal/fun/lbeta.hpp>
15 #include <stan/math/prim/scal/fun/lgamma.hpp>
16 #include <stan/math/prim/scal/fun/digamma.hpp>
17 #include <stan/math/prim/scal/meta/length.hpp>
18 #include <stan/math/prim/scal/fun/grad_reg_inc_beta.hpp>
19 #include <stan/math/prim/scal/fun/inc_beta.hpp>
20 #include <stan/math/prim/scal/meta/include_summand.hpp>
21 #include <stan/math/prim/scal/meta/VectorBuilder.hpp>
22 #include <boost/random/student_t_distribution.hpp>
23 #include <boost/random/variate_generator.hpp>
24 #include <limits>
25 #include <cmath>
26
27 namespace stan {
28 namespace math {
29
30 template <typename T_y, typename T_dof, typename T_loc, typename T_scale>
31 typename return_type<T_y, T_dof, T_loc, T_scale>::type
32 student_t_ccdf_log(const T_y& y, const T_dof& nu, const T_loc& mu,
33 const T_scale& sigma) {
34 typedef
35 typename stan::partials_return_type<T_y, T_dof, T_loc, T_scale>::type
36 T_partials_return;
37
38 if (!(stan::length(y) && stan::length(nu) && stan::length(mu)
39 && stan::length(sigma)))
40 return 0.0;
41
42 static const char* function("student_t_ccdf_log");
43
44 using std::exp;
45
46 T_partials_return P(0.0);
47
48 check_not_nan(function, "Random variable", y);
49 check_positive_finite(function, "Degrees of freedom parameter", nu);
50 check_finite(function, "Location parameter", mu);
51 check_positive_finite(function, "Scale parameter", sigma);
52
53 VectorView<const T_y> y_vec(y);
54 VectorView<const T_dof> nu_vec(nu);
55 VectorView<const T_loc> mu_vec(mu);
56 VectorView<const T_scale> sigma_vec(sigma);
57 size_t N = max_size(y, nu, mu, sigma);
58
59 OperandsAndPartials<T_y, T_dof, T_loc, T_scale>
60 operands_and_partials(y, nu, mu, sigma);
61
62 // Explicit return for extreme values
63 // The gradients are technically ill-defined, but treated as zero
64 for (size_t i = 0; i < stan::length(y); i++) {
65 if (value_of(y_vec[i]) == -std::numeric_limits<double>::infinity())
66 return operands_and_partials.value(0.0);
67 }
68
69 using std::pow;
70 using std::exp;
71 using std::log;
72
73 T_partials_return digammaHalf = 0;
74
75 VectorBuilder<!is_constant_struct<T_dof>::value,
76 T_partials_return, T_dof>
77 digamma_vec(stan::length(nu));
78 VectorBuilder<!is_constant_struct<T_dof>::value,
79 T_partials_return, T_dof>
80 digammaNu_vec(stan::length(nu));
81 VectorBuilder<!is_constant_struct<T_dof>::value,
82 T_partials_return, T_dof>
83 digammaNuPlusHalf_vec(stan::length(nu));
84
85 if (!is_constant_struct<T_dof>::value) {
86 digammaHalf = digamma(0.5);
87
88 for (size_t i = 0; i < stan::length(nu); i++) {
89 const T_partials_return nu_dbl = value_of(nu_vec[i]);
90
91 digammaNu_vec[i] = digamma(0.5 * nu_dbl);
92 digammaNuPlusHalf_vec[i] = digamma(0.5 + 0.5 * nu_dbl);
93 }
94 }
95
96 for (size_t n = 0; n < N; n++) {
97 // Explicit results for extreme values
98 // The gradients are technically ill-defined, but treated as zero
99 if (value_of(y_vec[n]) == std::numeric_limits<double>::infinity()) {
100 return operands_and_partials.value(negative_infinity());
101 }
102
103 const T_partials_return sigma_inv = 1.0 / value_of(sigma_vec[n]);
104 const T_partials_return t = (value_of(y_vec[n]) - value_of(mu_vec[n]))
105 * sigma_inv;
106 const T_partials_return nu_dbl = value_of(nu_vec[n]);
107 const T_partials_return q = nu_dbl / (t * t);
108 const T_partials_return r = 1.0 / (1.0 + q);
109 const T_partials_return J = 2 * r * r * q / t;
110 const T_partials_return betaNuHalf = exp(lbeta(0.5, 0.5 * nu_dbl));
111 T_partials_return zJacobian = t > 0 ? - 0.5 : 0.5;
112
113 if (q < 2) {
114 T_partials_return z = inc_beta(0.5 * nu_dbl, (T_partials_return)0.5,
115 1.0 - r);
116 const T_partials_return Pn = t > 0 ? 0.5 * z : 1.0 - 0.5 * z;
117 const T_partials_return d_ibeta = pow(r, -0.5)
118 * pow(1.0 - r, 0.5*nu_dbl - 1) / betaNuHalf;
119
120 P += log(Pn);
121
122 if (!is_constant_struct<T_y>::value)
123 operands_and_partials.d_x1[n]
124 += zJacobian * d_ibeta * J * sigma_inv / Pn;
125
126 if (!is_constant_struct<T_dof>::value) {
127 T_partials_return g1 = 0;
128 T_partials_return g2 = 0;
129
130 grad_reg_inc_beta(g1, g2, 0.5 * nu_dbl,
131 (T_partials_return)0.5, 1.0 - r,
132 digammaNu_vec[n], digammaHalf,
133 digammaNuPlusHalf_vec[n],
134 betaNuHalf);
135
136 operands_and_partials.d_x2[n]
137 -= zJacobian * (d_ibeta * (r / t) * (r / t) + 0.5 * g1) / Pn;
138 }
139
140 if (!is_constant_struct<T_loc>::value)
141 operands_and_partials.d_x3[n]
142 -= zJacobian * d_ibeta * J * sigma_inv / Pn;
143 if (!is_constant_struct<T_scale>::value)
144 operands_and_partials.d_x4[n]
145 -= zJacobian * d_ibeta * J * sigma_inv * t / Pn;
146
147 } else {
148 T_partials_return z = 1.0 - inc_beta((T_partials_return)0.5,
149 0.5*nu_dbl, r);
150 zJacobian *= -1;
151
152 const T_partials_return Pn = t > 0 ? 0.5 * z : 1.0 - 0.5 * z;
153
154 T_partials_return d_ibeta = pow(1.0-r, 0.5*nu_dbl-1) * pow(r, -0.5)
155 / betaNuHalf;
156
157 P += log(Pn);
158
159 if (!is_constant_struct<T_y>::value)
160 operands_and_partials.d_x1[n]
161 -= zJacobian * d_ibeta * J * sigma_inv / Pn;
162
163 if (!is_constant_struct<T_dof>::value) {
164 T_partials_return g1 = 0;
165 T_partials_return g2 = 0;
166
167 grad_reg_inc_beta(g1, g2, (T_partials_return)0.5,
168 0.5 * nu_dbl, r,
169 digammaHalf, digammaNu_vec[n],
170 digammaNuPlusHalf_vec[n],
171 betaNuHalf);
172
173 operands_and_partials.d_x2[n]
174 -= zJacobian * (- d_ibeta * (r / t) * (r / t) + 0.5 * g2) / Pn;
175 }
176
177 if (!is_constant_struct<T_loc>::value)
178 operands_and_partials.d_x3[n]
179 += zJacobian * d_ibeta * J * sigma_inv / Pn;
180 if (!is_constant_struct<T_scale>::value)
181 operands_and_partials.d_x4[n]
182 += zJacobian * d_ibeta * J * sigma_inv * t / Pn;
183 }
184 }
185 return operands_and_partials.value(P);
186 }
187
188 }
189 }
190 #endif
check_not_nan.hpp
stan::math::OperandsAndPartials::d_x2
VectorView< T_return_type, false, true > d_x2
Definition: OperandsAndPartials.hpp:39
lgamma.hpp
stan::math::check_not_nan
bool check_not_nan(const char *function, const char *name, const T_y &y)
Return true if y is not NaN.
Definition: check_not_nan.hpp:60
check_positive_finite.hpp
stan
Definition: log_sum_exp.hpp:8
stan::math::value_of
T value_of(const fvar< T > &v)
Return the value of the specified variable.
Definition: value_of.hpp:16
stan::math::lbeta
fvar< T > lbeta(const fvar< T > &x1, const fvar< T > &x2)
Definition: lbeta.hpp:15
digamma.hpp
stan::math::log
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:14
stan::math::OperandsAndPartials::value
T_return_type value(double value)
Returns a T_return_type with the value specified with the partial derivatves.
Definition: OperandsAndPartials.hpp:67
square.hpp
stan::length
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
is_constant_struct.hpp
include_summand.hpp
stan::math::student_t_ccdf_log
return_type< T_y, T_dof, T_loc, T_scale >::type student_t_ccdf_log(const T_y &y, const T_dof &nu, const T_loc &mu, const T_scale &sigma)
Definition: student_t_ccdf_log.hpp:32
stan::is_constant_struct
Metaprogram to determine if a type has a base scalar type that can be assigned to type double...
Definition: is_constant_struct.hpp:13
stan::math::inc_beta
fvar< T > inc_beta(const fvar< T > &a, const fvar< T > &b, const fvar< T > &x)
Definition: inc_beta.hpp:19
stan::math::exp
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:10
stan::math::OperandsAndPartials
This class builds partial derivatives with respect to a set of operands.
Definition: OperandsAndPartials.hpp:37
stan::math::OperandsAndPartials::d_x3
VectorView< T_return_type, false, true > d_x3
Definition: OperandsAndPartials.hpp:40
stan::max_size
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
VectorBuilder.hpp
partials_return_type.hpp
OperandsAndPartials.hpp
length.hpp
grad_reg_inc_beta.hpp
stan::math::check_finite
bool check_finite(const char *function, const char *name, const T_y &y)
Return true if y is finite.
Definition: check_finite.hpp:60
stan::VectorBuilder
VectorBuilder allocates type T1 values to be used as intermediate values.
Definition: VectorBuilder.hpp:28
constants.hpp
check_finite.hpp
lbeta.hpp
inc_beta.hpp
stan::math::pow
fvar< T > pow(const fvar< T > &x1, const fvar< T > &x2)
Definition: pow.hpp:17
value_of.hpp
stan::VectorView
VectorView is a template expression that is constructed with a container or scalar, which it then allows to be used as an array using operator[].
Definition: VectorView.hpp:48
stan::partials_return_type::type
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
Definition: partials_return_type.hpp:26
stan::math::grad_reg_inc_beta
void grad_reg_inc_beta(T &g1, T &g2, T a, T b, T z, T digammaA, T digammaB, T digammaSum, T betaAB)
Definition: grad_reg_inc_beta.hpp:14
check_consistent_sizes.hpp
stan::math::check_positive_finite
bool check_positive_finite(const char *function, const char *name, const T_y &y)
Return true if y is positive and finite.
Definition: check_positive_finite.hpp:28
stan::math::OperandsAndPartials::d_x1
VectorView< T_return_type, false, true > d_x1
Definition: OperandsAndPartials.hpp:38
stan::math::negative_infinity
double negative_infinity()
Return negative infinity.
Definition: constants.hpp:130
stan::math::digamma
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:15
stan::math::OperandsAndPartials::d_x4
VectorView< T_return_type, false, true > d_x4
Definition: OperandsAndPartials.hpp:41

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