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chi_square_cdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_CHI_SQUARE_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_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/multiply_log.hpp>
13 #include <stan/math/prim/scal/fun/value_of.hpp>
14 #include <stan/math/prim/scal/fun/gamma_p.hpp>
15 #include <stan/math/prim/scal/fun/digamma.hpp>
16 #include <stan/math/prim/scal/meta/VectorBuilder.hpp>
17 #include <stan/math/prim/scal/fun/grad_reg_inc_gamma.hpp>
18 #include <stan/math/prim/scal/meta/include_summand.hpp>
19 #include <boost/random/chi_squared_distribution.hpp>
20 #include <boost/random/variate_generator.hpp>
21 #include <cmath>
22 #include <limits>
23
24 namespace stan {
25 namespace math {
26
36 template <typename T_y, typename T_dof>
37 typename return_type<T_y, T_dof>::type
38 chi_square_cdf(const T_y& y, const T_dof& nu) {
39 static const char* function("chi_square_cdf");
40 typedef typename stan::partials_return_type<T_y, T_dof>::type
41 T_partials_return;
42
43 T_partials_return cdf(1.0);
44
45 if (!(stan::length(y) && stan::length(nu)))
46 return cdf;
47
48 check_not_nan(function, "Random variable", y);
49 check_nonnegative(function, "Random variable", y);
50 check_positive_finite(function, "Degrees of freedom parameter", nu);
51 check_consistent_sizes(function,
52 "Random variable", y,
53 "Degrees of freedom parameter", nu);
54
55 VectorView<const T_y> y_vec(y);
56 VectorView<const T_dof> nu_vec(nu);
57 size_t N = max_size(y, nu);
58
59 OperandsAndPartials<T_y, T_dof>
60 operands_and_partials(y, nu);
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]) == 0)
66 return operands_and_partials.value(0.0);
67 }
68
69 using boost::math::tgamma;
70 using std::exp;
71 using std::pow;
72 using std::exp;
73
74 VectorBuilder<!is_constant_struct<T_dof>::value,
75 T_partials_return, T_dof> gamma_vec(stan::length(nu));
76 VectorBuilder<!is_constant_struct<T_dof>::value,
77 T_partials_return, T_dof> digamma_vec(stan::length(nu));
78
79 if (!is_constant_struct<T_dof>::value) {
80 for (size_t i = 0; i < stan::length(nu); i++) {
81 const T_partials_return alpha_dbl = value_of(nu_vec[i]) * 0.5;
82 gamma_vec[i] = tgamma(alpha_dbl);
83 digamma_vec[i] = digamma(alpha_dbl);
84 }
85 }
86
87 for (size_t n = 0; n < N; n++) {
88 // Explicit results for extreme values
89 // The gradients are technically ill-defined, but treated as zero
90 if (value_of(y_vec[n]) == std::numeric_limits<double>::infinity())
91 continue;
92
93 const T_partials_return y_dbl = value_of(y_vec[n]);
94 const T_partials_return alpha_dbl = value_of(nu_vec[n]) * 0.5;
95 const T_partials_return beta_dbl = 0.5;
96
97 const T_partials_return Pn = gamma_p(alpha_dbl, beta_dbl * y_dbl);
98
99 cdf *= Pn;
100
101 if (!is_constant_struct<T_y>::value)
102 operands_and_partials.d_x1[n] += beta_dbl * exp(-beta_dbl * y_dbl)
103 * pow(beta_dbl * y_dbl, alpha_dbl-1) / tgamma(alpha_dbl) / Pn;
104 if (!is_constant_struct<T_dof>::value)
105 operands_and_partials.d_x2[n]
106 -= 0.5 * grad_reg_inc_gamma(alpha_dbl, beta_dbl
107 * y_dbl, gamma_vec[n],
108 digamma_vec[n]) / Pn;
109 }
110
111 if (!is_constant_struct<T_y>::value) {
112 for (size_t n = 0; n < stan::length(y); ++n)
113 operands_and_partials.d_x1[n] *= cdf;
114 }
115 if (!is_constant_struct<T_dof>::value) {
116 for (size_t n = 0; n < stan::length(nu); ++n)
117 operands_and_partials.d_x2[n] *= cdf;
118 }
119 return operands_and_partials.value(cdf);
120 }
121
122 }
123 }
124 #endif
check_not_nan.hpp
stan::math::OperandsAndPartials::d_x2
VectorView< T_return_type, false, true > d_x2
Definition: OperandsAndPartials.hpp:39
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
stan::length
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
is_constant_struct.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
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
stan::math::gamma_p
fvar< T > gamma_p(const fvar< T > &x1, const fvar< T > &x2)
Definition: gamma_p.hpp:14
gamma_p.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::chi_square_cdf
return_type< T_y, T_dof >::type chi_square_cdf(const T_y &y, const T_dof &nu)
Calculates the chi square cumulative distribution function for the given variate and degrees of freed...
Definition: chi_square_cdf.hpp:38
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
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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