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scaled_inv_chi_square_cdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_SCALED_INV_CHI_SQUARE_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_SCALED_INV_CHI_SQUARE_CDF_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 <limits>
25 #include <cmath>
26
27 namespace stan {
28 namespace math {
29
43 template <typename T_y, typename T_dof, typename T_scale>
44 typename return_type<T_y, T_dof, T_scale>::type
45 scaled_inv_chi_square_cdf(const T_y& y, const T_dof& nu,
46 const T_scale& s) {
47 typedef typename stan::partials_return_type<T_y, T_dof, T_scale>::type
48 T_partials_return;
49
50 if (!(stan::length(y) && stan::length(nu) && stan::length(s)))
51 return 1.0;
52
53 static const char* function("scaled_inv_chi_square_cdf");
54
55 using std::exp;
56
57 T_partials_return P(1.0);
58
59 check_not_nan(function, "Random variable", y);
60 check_nonnegative(function, "Random variable", y);
61 check_positive_finite(function, "Degrees of freedom parameter", nu);
62 check_positive_finite(function, "Scale parameter", s);
63 check_consistent_sizes(function,
64 "Random variable", y,
65 "Degrees of freedom parameter", nu,
66 "Scale parameter", s);
67
68 VectorView<const T_y> y_vec(y);
69 VectorView<const T_dof> nu_vec(nu);
70 VectorView<const T_scale> s_vec(s);
71 size_t N = max_size(y, nu, s);
72
73 OperandsAndPartials<T_y, T_dof, T_scale>
74 operands_and_partials(y, nu, s);
75
76 // Explicit return for extreme values
77 // The gradients are technically ill-defined, but treated as zero
78 for (size_t i = 0; i < stan::length(y); i++) {
79 if (value_of(y_vec[i]) == 0)
80 return operands_and_partials.value(0.0);
81 }
82
83 using boost::math::tgamma;
84 using std::exp;
85 using std::pow;
86
87 VectorBuilder<!is_constant_struct<T_dof>::value,
88 T_partials_return, T_dof> gamma_vec(stan::length(nu));
89 VectorBuilder<!is_constant_struct<T_dof>::value,
90 T_partials_return, T_dof> digamma_vec(stan::length(nu));
91
92 if (!is_constant_struct<T_dof>::value) {
93 for (size_t i = 0; i < stan::length(nu); i++) {
94 const T_partials_return half_nu_dbl = 0.5 * value_of(nu_vec[i]);
95 gamma_vec[i] = tgamma(half_nu_dbl);
96 digamma_vec[i] = digamma(half_nu_dbl);
97 }
98 }
99
100 for (size_t n = 0; n < N; n++) {
101 // Explicit results for extreme values
102 // The gradients are technically ill-defined, but treated as zero
103 if (value_of(y_vec[n]) == std::numeric_limits<double>::infinity()) {
104 continue;
105 }
106
107 const T_partials_return y_dbl = value_of(y_vec[n]);
108 const T_partials_return y_inv_dbl = 1.0 / y_dbl;
109 const T_partials_return half_nu_dbl = 0.5 * value_of(nu_vec[n]);
110 const T_partials_return s_dbl = value_of(s_vec[n]);
111 const T_partials_return half_s2_overx_dbl = 0.5 * s_dbl * s_dbl
112 * y_inv_dbl;
113 const T_partials_return half_nu_s2_overx_dbl
114 = 2.0 * half_nu_dbl * half_s2_overx_dbl;
115
116 const T_partials_return Pn = gamma_q(half_nu_dbl, half_nu_s2_overx_dbl);
117 const T_partials_return gamma_p_deriv = exp(-half_nu_s2_overx_dbl)
118 * pow(half_nu_s2_overx_dbl, half_nu_dbl-1) / tgamma(half_nu_dbl);
119
120 P *= Pn;
121
122 if (!is_constant_struct<T_y>::value)
123 operands_and_partials.d_x1[n] += half_nu_s2_overx_dbl * y_inv_dbl
124 * gamma_p_deriv / Pn;
125
126 if (!is_constant_struct<T_dof>::value)
127 operands_and_partials.d_x2[n]
128 += (0.5 * grad_reg_inc_gamma(half_nu_dbl,
129 half_nu_s2_overx_dbl,
130 gamma_vec[n],
131 digamma_vec[n])
132 - half_s2_overx_dbl * gamma_p_deriv)
133 / Pn;
134
135 if (!is_constant_struct<T_scale>::value)
136 operands_and_partials.d_x3[n]
137 += - 2.0 * half_nu_dbl * s_dbl * y_inv_dbl
138 * gamma_p_deriv / Pn;
139 }
140
141 if (!is_constant_struct<T_y>::value) {
142 for (size_t n = 0; n < stan::length(y); ++n)
143 operands_and_partials.d_x1[n] *= P;
144 }
145 if (!is_constant_struct<T_dof>::value) {
146 for (size_t n = 0; n < stan::length(nu); ++n)
147 operands_and_partials.d_x2[n] *= P;
148 }
149 if (!is_constant_struct<T_scale>::value) {
150 for (size_t n = 0; n < stan::length(s); ++n)
151 operands_and_partials.d_x3[n] *= P;
152 }
153 return operands_and_partials.value(P);
154 }
155
156 }
157 }
158 #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
digamma.hpp
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::math::scaled_inv_chi_square_cdf
return_type< T_y, T_dof, T_scale >::type scaled_inv_chi_square_cdf(const T_y &y, const T_dof &nu, const T_scale &s)
The CDF of a scaled inverse chi-squared density for y with the specified degrees of freedom parameter...
Definition: scaled_inv_chi_square_cdf.hpp:45
stan::length
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
is_constant_struct.hpp
gamma_q.hpp
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::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
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
stan::math::grad_reg_inc_gamma
T grad_reg_inc_gamma(T a, T z, T g, T dig, double precision=1e-6)
Gradient of the regularized incomplete gamma functions igamma(a, z)
Definition: grad_reg_inc_gamma.hpp:40
stan::math::pow
fvar< T > pow(const fvar< T > &x1, const fvar< T > &x2)
Definition: pow.hpp:17
stan::math::check_nonnegative
bool check_nonnegative(const char *function, const char *name, const T_y &y)
Return true if y is non-negative.
Definition: check_nonnegative.hpp:64
value_of.hpp
stan::math::tgamma
fvar< T > tgamma(const fvar< T > &x)
Definition: tgamma.hpp:14
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::gamma_q
fvar< T > gamma_q(const fvar< T > &x1, const fvar< T > &x2)
Definition: gamma_q.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::digamma
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:15

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