| Stan Math Library 2.12.0 reverse mode automatic differentiation

- Main Page
- Modules
- Namespaces
- Classes
- Files

- File List
- File Members

inv_chi_square_cdf_log.hpp
Go to the documentation of this file.
1 #ifndef STAN_MATH_PRIM_SCAL_PROB_INV_CHI_SQUARE_CDF_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_INV_CHI_SQUARE_CDF_LOG_HPP
3
4 #include <stan/math/prim/scal/meta/OperandsAndPartials.hpp>
5 #include <stan/math/prim/scal/err/check_consistent_sizes.hpp>
6 #include <stan/math/prim/scal/err/check_nonnegative.hpp>
7 #include <stan/math/prim/scal/err/check_not_nan.hpp>
8 #include <stan/math/prim/scal/err/check_positive_finite.hpp>
9 #include <stan/math/prim/scal/fun/constants.hpp>
10 #include <stan/math/prim/scal/fun/multiply_log.hpp>
11 #include <stan/math/prim/scal/fun/value_of.hpp>
12 #include <stan/math/prim/scal/fun/gamma_q.hpp>
13 #include <stan/math/prim/scal/fun/digamma.hpp>
14 #include <stan/math/prim/scal/meta/length.hpp>
15 #include <stan/math/prim/scal/meta/is_constant_struct.hpp>
16 #include <stan/math/prim/scal/meta/VectorView.hpp>
17 #include <stan/math/prim/scal/meta/VectorBuilder.hpp>
18 #include <stan/math/prim/scal/meta/partials_return_type.hpp>
19 #include <stan/math/prim/scal/meta/return_type.hpp>
20 #include <stan/math/prim/scal/fun/grad_reg_inc_gamma.hpp>
21 #include <stan/math/prim/scal/meta/include_summand.hpp>
22 #include <boost/random/chi_squared_distribution.hpp>
23 #include <boost/random/variate_generator.hpp>
24 #include <cmath>
25 #include <limits>
26
27 namespace stan {
28 namespace math {
29
30 template <typename T_y, typename T_dof>
31 typename return_type<T_y, T_dof>::type
32 inv_chi_square_cdf_log(const T_y& y, const T_dof& nu) {
33 typedef typename stan::partials_return_type<T_y, T_dof>::type
34 T_partials_return;
35
36 if ( !( stan::length(y) && stan::length(nu) ) ) return 0.0;
37
38 static const char* function("inv_chi_square_cdf_log");
39
40 using boost::math::tools::promote_args;
41 using std::exp;
42
43 T_partials_return P(0.0);
44
45 check_positive_finite(function, "Degrees of freedom parameter", nu);
46 check_not_nan(function, "Random variable", y);
47 check_nonnegative(function, "Random variable", y);
48 check_consistent_sizes(function,
49 "Random variable", y,
50 "Degrees of freedom parameter", nu);
51
52 VectorView<const T_y> y_vec(y);
53 VectorView<const T_dof> nu_vec(nu);
54 size_t N = max_size(y, nu);
55
56 OperandsAndPartials<T_y, T_dof> operands_and_partials(y, nu);
57
58 // Explicit return for extreme values
59 // The gradients are technically ill-defined, but treated as zero
60 for (size_t i = 0; i < stan::length(y); i++)
61 if (value_of(y_vec[i]) == 0)
62 return operands_and_partials.value(negative_infinity());
63
64 using boost::math::tgamma;
65 using std::exp;
66 using std::pow;
67 using std::log;
68
69 VectorBuilder<!is_constant_struct<T_dof>::value,
70 T_partials_return, T_dof> gamma_vec(stan::length(nu));
71 VectorBuilder<!is_constant_struct<T_dof>::value,
72 T_partials_return, T_dof> digamma_vec(stan::length(nu));
73
74 if (!is_constant_struct<T_dof>::value) {
75 for (size_t i = 0; i < stan::length(nu); i++) {
76 const T_partials_return nu_dbl = value_of(nu_vec[i]);
77 gamma_vec[i] = tgamma(0.5 * nu_dbl);
78 digamma_vec[i] = digamma(0.5 * nu_dbl);
79 }
80 }
81
82 for (size_t n = 0; n < N; n++) {
83 // Explicit results for extreme values
84 // The gradients are technically ill-defined, but treated as zero
85 if (value_of(y_vec[n]) == std::numeric_limits<double>::infinity()) {
86 continue;
87 }
88
89 const T_partials_return y_dbl = value_of(y_vec[n]);
90 const T_partials_return y_inv_dbl = 1.0 / y_dbl;
91 const T_partials_return nu_dbl = value_of(nu_vec[n]);
92
93 const T_partials_return Pn = gamma_q(0.5 * nu_dbl, 0.5 * y_inv_dbl);
94
95 P += log(Pn);
96
97 if (!is_constant_struct<T_y>::value)
98 operands_and_partials.d_x1[n] += 0.5 * y_inv_dbl * y_inv_dbl
99 * exp(-0.5*y_inv_dbl) * pow(0.5*y_inv_dbl, 0.5*nu_dbl-1)
100 / tgamma(0.5*nu_dbl) / Pn;
101 if (!is_constant_struct<T_dof>::value)
102 operands_and_partials.d_x2[n]
103 += 0.5 * grad_reg_inc_gamma(0.5 * nu_dbl,
104 0.5 * y_inv_dbl,
105 gamma_vec[n],
106 digamma_vec[n]) / Pn;
107 }
108 return operands_and_partials.value(P);
109 }
110
111 }
112 }
113 #endif
check_not_nan.hpp
stan::math::OperandsAndPartials::d_x2
VectorView< T_return_type, false, true > d_x2
Definition: OperandsAndPartials.hpp:39
stan::math::inv_chi_square_cdf_log
return_type< T_y, T_dof >::type inv_chi_square_cdf_log(const T_y &y, const T_dof &nu)
Definition: inv_chi_square_cdf_log.hpp:32
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
stan::length
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
is_constant_struct.hpp
return_type.hpp
gamma_q.hpp
include_summand.hpp
multiply_log.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::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::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 Home Page ] © 2011–2016, Stan Development Team.