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scaled_inv_chi_square_log.hpp
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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
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_nonnegative.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/value_of.hpp>
13 #include <stan/math/prim/scal/fun/gamma_q.hpp>
14 #include <stan/math/prim/scal/fun/digamma.hpp>
15 #include <stan/math/prim/scal/fun/lgamma.hpp>
16 #include <stan/math/prim/scal/fun/square.hpp>
17 #include <stan/math/prim/scal/meta/VectorView.hpp>
18 #include <stan/math/prim/scal/meta/VectorBuilder.hpp>
19 #include <stan/math/prim/scal/meta/length.hpp>
20 #include <stan/math/prim/scal/meta/include_summand.hpp>
21 #include <stan/math/prim/scal/fun/grad_reg_inc_gamma.hpp>
22 #include <boost/random/chi_squared_distribution.hpp>
23 #include <boost/random/variate_generator.hpp>
24 #include <cmath>
25
26 namespace stan {
27 namespace math {
28
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
51 scaled_inv_chi_square_log(const T_y& y, const T_dof& nu, const T_scale& s) {
52 static const char* function("scaled_inv_chi_square_log");
53 typedef typename stan::partials_return_type<T_y, T_dof, T_scale>::type
54 T_partials_return;
55
56 if (!(stan::length(y)
57 && stan::length(nu)
58 && stan::length(s)))
59 return 0.0;
60
61 T_partials_return logp(0.0);
62 check_not_nan(function, "Random variable", y);
63 check_positive_finite(function, "Degrees of freedom parameter", nu);
64 check_positive_finite(function, "Scale parameter", s);
65 check_consistent_sizes(function,
66 "Random variable", y,
67 "Degrees of freedom parameter", nu,
68 "Scale parameter", s);
69
70 if (!include_summand<propto, T_y, T_dof, T_scale>::value)
71 return 0.0;
72
73 VectorView<const T_y> y_vec(y);
74 VectorView<const T_dof> nu_vec(nu);
75 VectorView<const T_scale> s_vec(s);
76 size_t N = max_size(y, nu, s);
77
78 for (size_t n = 0; n < N; n++) {
79 if (value_of(y_vec[n]) <= 0)
80 return LOG_ZERO;
81 }
82
83 using std::log;
84
85 VectorBuilder<include_summand<propto, T_dof, T_y, T_scale>::value,
86 T_partials_return, T_dof> half_nu(length(nu));
87 for (size_t i = 0; i < length(nu); i++)
88 if (include_summand<propto, T_dof, T_y, T_scale>::value)
89 half_nu[i] = 0.5 * value_of(nu_vec[i]);
90
91 VectorBuilder<include_summand<propto, T_dof, T_y>::value,
92 T_partials_return, T_y> log_y(length(y));
93 for (size_t i = 0; i < length(y); i++)
94 if (include_summand<propto, T_dof, T_y>::value)
95 log_y[i] = log(value_of(y_vec[i]));
96
97 VectorBuilder<include_summand<propto, T_dof, T_y, T_scale>::value,
98 T_partials_return, T_y> inv_y(length(y));
99 for (size_t i = 0; i < length(y); i++)
100 if (include_summand<propto, T_dof, T_y, T_scale>::value)
101 inv_y[i] = 1.0 / value_of(y_vec[i]);
102
103 VectorBuilder<include_summand<propto, T_dof, T_scale>::value,
104 T_partials_return, T_scale> log_s(length(s));
105 for (size_t i = 0; i < length(s); i++)
106 if (include_summand<propto, T_dof, T_scale>::value)
107 log_s[i] = log(value_of(s_vec[i]));
108
109 VectorBuilder<include_summand<propto, T_dof>::value,
110 T_partials_return, T_dof> log_half_nu(length(nu));
111 VectorBuilder<include_summand<propto, T_dof>::value,
112 T_partials_return, T_dof> lgamma_half_nu(length(nu));
113 VectorBuilder<!is_constant_struct<T_dof>::value,
114 T_partials_return, T_dof>
115 digamma_half_nu_over_two(length(nu));
116 for (size_t i = 0; i < length(nu); i++) {
117 if (include_summand<propto, T_dof>::value)
118 lgamma_half_nu[i] = lgamma(half_nu[i]);
119 if (include_summand<propto, T_dof>::value)
120 log_half_nu[i] = log(half_nu[i]);
121 if (!is_constant_struct<T_dof>::value)
122 digamma_half_nu_over_two[i] = digamma(half_nu[i]) * 0.5;
123 }
124
125 OperandsAndPartials<T_y, T_dof, T_scale>
126 operands_and_partials(y, nu, s);
127 for (size_t n = 0; n < N; n++) {
128 const T_partials_return s_dbl = value_of(s_vec[n]);
129 const T_partials_return nu_dbl = value_of(nu_vec[n]);
130 if (include_summand<propto, T_dof>::value)
131 logp += half_nu[n] * log_half_nu[n] - lgamma_half_nu[n];
132 if (include_summand<propto, T_dof, T_scale>::value)
133 logp += nu_dbl * log_s[n];
134 if (include_summand<propto, T_dof, T_y>::value)
135 logp -= (half_nu[n]+1.0) * log_y[n];
136 if (include_summand<propto, T_dof, T_y, T_scale>::value)
137 logp -= half_nu[n] * s_dbl*s_dbl * inv_y[n];
138
139 if (!is_constant_struct<T_y>::value) {
140 operands_and_partials.d_x1[n]
141 += -(half_nu[n] + 1.0) * inv_y[n]
142 + half_nu[n] * s_dbl*s_dbl * inv_y[n]*inv_y[n];
143 }
144 if (!is_constant_struct<T_dof>::value) {
145 operands_and_partials.d_x2[n]
146 += 0.5 * log_half_nu[n] + 0.5
147 - digamma_half_nu_over_two[n]
148 + log_s[n]
149 - 0.5 * log_y[n]
150 - 0.5* s_dbl*s_dbl * inv_y[n];
151 }
152 if (!is_constant_struct<T_scale>::value) {
153 operands_and_partials.d_x3[n]
154 += nu_dbl / s_dbl - nu_dbl * inv_y[n] * s_dbl;
155 }
156 }
157 return operands_and_partials.value(logp);
158 }
159
160 template <typename T_y, typename T_dof, typename T_scale>
161 inline
162 typename return_type<T_y, T_dof, T_scale>::type
163 scaled_inv_chi_square_log(const T_y& y, const T_dof& nu, const T_scale& s) {
164 return scaled_inv_chi_square_log<false>(y, nu, s);
165 }
166
167 }
168 }
169 #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::lgamma
fvar< T > lgamma(const fvar< T > &x)
Definition: lgamma.hpp:14
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
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
stan::math::scaled_inv_chi_square_log
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...
Definition: scaled_inv_chi_square_log.hpp:51
is_constant_struct.hpp
stan::math::LOG_ZERO
const double LOG_ZERO
Definition: constants.hpp:172
stan::math::include_summand
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) prob...
Definition: include_summand.hpp:35
gamma_q.hpp
stan::return_type::type
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
Definition: return_type.hpp:27
include_summand.hpp
check_nonnegative.hpp
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::OperandsAndPartials
This class builds partial derivatives with respect to a set of operands.
Definition: OperandsAndPartials.hpp:37
VectorView.hpp
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_gamma.hpp
stan::VectorBuilder
VectorBuilder allocates type T1 values to be used as intermediate values.
Definition: VectorBuilder.hpp:28
constants.hpp
stan::math::check_consistent_sizes
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.
Definition: check_consistent_sizes.hpp:31
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
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::digamma
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:15

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