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chi_square_cdf_log.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_CHI_SQUARE_CDF_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_CHI_SQUARE_CDF_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/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
26 namespace math {
27
28 template <typename T_y, typename T_dof>
29 typename return_type<T_y, T_dof>::type
30 chi_square_cdf_log(const T_y& y, const T_dof& nu) {
31 static const char* function("stan::math::chi_square_cdf_log");
32 typedef typename stan::partials_return_type<T_y, T_dof>::type
33 T_partials_return;
34
35 using stan::math::check_positive_finite;
36 using stan::math::check_nonnegative;
37 using stan::math::check_not_nan;
38 using stan::math::check_consistent_sizes;
39 using stan::math::value_of;
40
41 T_partials_return cdf_log(0.0);
42
43 // Size checks
44 if (!(stan::length(y) && stan::length(nu)))
45 return cdf_log;
46
47 check_not_nan(function, "Random variable", y);
48 check_nonnegative(function, "Random variable", y);
49 check_positive_finite(function, "Degrees of freedom parameter", nu);
50 check_consistent_sizes(function,
51 "Random variable", y,
52 "Degrees of freedom parameter", nu);
53
54 // Wrap arguments in vectors
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(stan::math::negative_infinity());
67 }
68
69 // Compute cdf_log and its gradients
70 using stan::math::gamma_p;
71 using stan::math::digamma;
72 using boost::math::tgamma;
73 using std::exp;
74 using std::pow;
75 using std::log;
76 using std::exp;
77
78 // Cache a few expensive function calls if nu is a parameter
79 VectorBuilder<!is_constant_struct<T_dof>::value,
80 T_partials_return, T_dof> gamma_vec(stan::length(nu));
81 VectorBuilder<!is_constant_struct<T_dof>::value,
82 T_partials_return, T_dof> digamma_vec(stan::length(nu));
83
84 if (!is_constant_struct<T_dof>::value) {
85 for (size_t i = 0; i < stan::length(nu); i++) {
86 const T_partials_return alpha_dbl = value_of(nu_vec[i]) * 0.5;
87 gamma_vec[i] = tgamma(alpha_dbl);
88 digamma_vec[i] = digamma(alpha_dbl);
89 }
90 }
91
92 // Compute vectorized cdf_log and gradient
93 for (size_t n = 0; n < N; n++) {
94 // Explicit results for extreme values
95 // The gradients are technically ill-defined, but treated as zero
96 if (value_of(y_vec[n]) == std::numeric_limits<double>::infinity())
97 return operands_and_partials.value(0.0);
98
99 // Pull out values
100 const T_partials_return y_dbl = value_of(y_vec[n]);
101 const T_partials_return alpha_dbl = value_of(nu_vec[n]) * 0.5;
102 const T_partials_return beta_dbl = 0.5;
103
104 // Compute
105 const T_partials_return Pn = gamma_p(alpha_dbl, beta_dbl * y_dbl);
106
107 cdf_log += log(Pn);
108
109 if (!is_constant_struct<T_y>::value)
110 operands_and_partials.d_x1[n] += beta_dbl * exp(-beta_dbl * y_dbl)
111 * pow(beta_dbl * y_dbl, alpha_dbl-1) / tgamma(alpha_dbl) / Pn;
112 if (!is_constant_struct<T_dof>::value)
113 operands_and_partials.d_x2[n]
114 -= 0.5 * stan::math::grad_reg_inc_gamma(alpha_dbl, beta_dbl
115 * y_dbl, gamma_vec[n],
116 digamma_vec[n]) / Pn;
117 }
118
119 return operands_and_partials.value(cdf_log);
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:40
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:63
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:15
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:68
stan::length
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
is_constant_struct.hpp
stan::math::grad_reg_inc_gamma
T grad_reg_inc_gamma(T a, T z, T g, T dig, T precision=1e-6)
Definition: grad_reg_inc_gamma.hpp:16
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:38
stan::math::chi_square_cdf_log
return_type< T_y, T_dof >::type chi_square_cdf_log(const T_y &y, const T_dof &nu)
Definition: chi_square_cdf_log.hpp:30
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:15
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::pow
fvar< T > pow(const fvar< T > &x1, const fvar< T > &x2)
Definition: pow.hpp:18
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:66
value_of.hpp
stan::math::tgamma
fvar< T > tgamma(const fvar< T > &x)
Definition: tgamma.hpp:15
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:39
stan::math::negative_infinity
double negative_infinity()
Return negative infinity.
Definition: constants.hpp:132
stan::math::digamma
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:16

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