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beta_cdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_BETA_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_BETA_CDF_HPP
3
4 #include <boost/math/special_functions/gamma.hpp>
5 #include <boost/random/gamma_distribution.hpp>
6 #include <boost/random/variate_generator.hpp>
7 #include <stan/math/prim/scal/meta/OperandsAndPartials.hpp>
8 #include <stan/math/prim/scal/err/check_consistent_sizes.hpp>
9 #include <stan/math/prim/scal/err/check_less_or_equal.hpp>
10 #include <stan/math/prim/scal/err/check_nonnegative.hpp>
11 #include <stan/math/prim/scal/err/check_not_nan.hpp>
12 #include <stan/math/prim/scal/err/check_positive_finite.hpp>
13 #include <stan/math/prim/scal/fun/log1m.hpp>
14 #include <stan/math/prim/scal/fun/multiply_log.hpp>
15 #include <stan/math/prim/scal/fun/value_of.hpp>
16 #include <stan/math/prim/scal/fun/digamma.hpp>
17 #include <stan/math/prim/scal/fun/lgamma.hpp>
18 #include <stan/math/prim/scal/fun/lbeta.hpp>
19 #include <stan/math/prim/scal/meta/VectorBuilder.hpp>
20 #include <stan/math/prim/scal/fun/constants.hpp>
21 #include <stan/math/prim/scal/meta/include_summand.hpp>
22 #include <stan/math/prim/scal/meta/partials_return_type.hpp>
23 #include <stan/math/prim/scal/meta/contains_nonconstant_struct.hpp>
24 #include <stan/math/prim/scal/fun/grad_reg_inc_beta.hpp>
25 #include <stan/math/prim/scal/fun/inc_beta.hpp>
26 #include <cmath>
27
28 namespace stan {
29
30 namespace math {
31
44 template <typename T_y, typename T_scale_succ, typename T_scale_fail>
45 typename return_type<T_y, T_scale_succ, T_scale_fail>::type
46 beta_cdf(const T_y& y, const T_scale_succ& alpha,
47 const T_scale_fail& beta) {
48 typedef typename stan::partials_return_type<T_y, T_scale_succ,
49 T_scale_fail>::type
50 T_partials_return;
51
52
53 // Size checks
54 if ( !( stan::length(y) && stan::length(alpha)
55 && stan::length(beta) ) )
56 return 1.0;
57
58 // Error checks
59 static const char* function("stan::math::beta_cdf");
60
61 using stan::math::check_positive_finite;
62 using stan::math::check_not_nan;
63 using boost::math::tools::promote_args;
64 using stan::math::check_consistent_sizes;
65 using stan::math::value_of;
66 using stan::math::check_nonnegative;
67 using stan::math::check_less_or_equal;
68
69 T_partials_return P(1.0);
70
71 check_positive_finite(function, "First shape parameter", alpha);
72 check_positive_finite(function, "Second shape parameter", beta);
73 check_not_nan(function, "Random variable", y);
74 check_consistent_sizes(function,
75 "Random variable", y,
76 "First shape parameter", alpha,
77 "Second shape parameter", beta);
78 check_nonnegative(function, "Random variable", y);
79 check_less_or_equal(function, "Random variable", y, 1);
80
81 // Wrap arguments in vectors
82 VectorView<const T_y> y_vec(y);
83 VectorView<const T_scale_succ> alpha_vec(alpha);
84 VectorView<const T_scale_fail> beta_vec(beta);
85 size_t N = max_size(y, alpha, beta);
86
87 OperandsAndPartials<T_y, T_scale_succ, T_scale_fail>
88 operands_and_partials(y, alpha, beta);
89
90 // Explicit return for extreme values
91 // The gradients are technically ill-defined, but treated as zero
92 for (size_t i = 0; i < stan::length(y); i++) {
93 if (value_of(y_vec[i]) <= 0)
94 return operands_and_partials.to_var(0.0, y, alpha, beta);
95 }
96
97 // Compute CDF and its gradients
98 using stan::math::inc_beta;
99 using stan::math::digamma;
100 using stan::math::lbeta;
101 using std::pow;
102 using std::exp;
103 using std::exp;
104
105 // Cache a few expensive function calls if alpha or beta is a parameter
106 VectorBuilder<contains_nonconstant_struct<T_scale_succ,
107 T_scale_fail>::value,
108 T_partials_return, T_scale_succ, T_scale_fail>
109 digamma_alpha_vec(max_size(alpha, beta));
110
111 VectorBuilder<contains_nonconstant_struct<T_scale_succ,
112 T_scale_fail>::value,
113 T_partials_return, T_scale_succ, T_scale_fail>
114 digamma_beta_vec(max_size(alpha, beta));
115
116 VectorBuilder<contains_nonconstant_struct<T_scale_succ,
117 T_scale_fail>::value,
118 T_partials_return, T_scale_succ, T_scale_fail>
119 digamma_sum_vec(max_size(alpha, beta));
120
121 if (contains_nonconstant_struct<T_scale_succ, T_scale_fail>::value) {
122 for (size_t i = 0; i < N; i++) {
123 const T_partials_return alpha_dbl = value_of(alpha_vec[i]);
124 const T_partials_return beta_dbl = value_of(beta_vec[i]);
125
126 digamma_alpha_vec[i] = digamma(alpha_dbl);
127 digamma_beta_vec[i] = digamma(beta_dbl);
128 digamma_sum_vec[i] = digamma(alpha_dbl + beta_dbl);
129 }
130 }
131
132 // Compute vectorized CDF and gradient
133 for (size_t n = 0; n < N; n++) {
134 // Explicit results for extreme values
135 // The gradients are technically ill-defined, but treated as zero
136 if (value_of(y_vec[n]) >= 1.0) continue;
137
138 // Pull out values
139 const T_partials_return y_dbl = value_of(y_vec[n]);
140 const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
141 const T_partials_return beta_dbl = value_of(beta_vec[n]);
142 const T_partials_return betafunc_dbl = exp(lbeta(alpha_dbl, beta_dbl));
143
144 // Compute
145 const T_partials_return Pn = inc_beta(alpha_dbl, beta_dbl, y_dbl);
146
147 P *= Pn;
148
149 if (!is_constant_struct<T_y>::value)
150 operands_and_partials.d_x1[n] += pow(1-y_dbl, beta_dbl-1)
151 * pow(y_dbl, alpha_dbl-1) / betafunc_dbl / Pn;
152
153 T_partials_return g1 = 0;
154 T_partials_return g2 = 0;
155
156 if (contains_nonconstant_struct<T_scale_succ, T_scale_fail>::value) {
157 stan::math::grad_reg_inc_beta(g1, g2, alpha_dbl, beta_dbl, y_dbl,
158 digamma_alpha_vec[n],
159 digamma_beta_vec[n], digamma_sum_vec[n],
160 betafunc_dbl);
161 }
162
163 if (!is_constant_struct<T_scale_succ>::value)
164 operands_and_partials.d_x2[n] += g1 / Pn;
165 if (!is_constant_struct<T_scale_fail>::value)
166 operands_and_partials.d_x3[n] += g2 / Pn;
167 }
168
169 if (!is_constant_struct<T_y>::value) {
170 for (size_t n = 0; n < stan::length(y); ++n)
171 operands_and_partials.d_x1[n] *= P;
172 }
173 if (!is_constant_struct<T_scale_succ>::value) {
174 for (size_t n = 0; n < stan::length(alpha); ++n)
175 operands_and_partials.d_x2[n] *= P;
176 }
177 if (!is_constant_struct<T_scale_fail>::value) {
178 for (size_t n = 0; n < stan::length(beta); ++n)
179 operands_and_partials.d_x3[n] *= P;
180 }
181
182 return operands_and_partials.to_var(P, y, alpha, beta);
183 }
184
185 }
186 }
187 #endif
check_not_nan.hpp
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:63
check_positive_finite.hpp
stan::math::value_of
T value_of(const fvar< T > &v)
Return the value of the specified variable.
Definition: value_of.hpp:16
stan::math::lbeta
fvar< T > lbeta(const fvar< T > &x1, const fvar< T > &x2)
Definition: lbeta.hpp:16
digamma.hpp
contains_nonconstant_struct.hpp
stan::length
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
stan::math::OperandsAndPartials::to_var
T_return_type to_var(T_partials_return logp, const T1 &x1=0, const T2 &x2=0, const T3 &x3=0, const T4 &x4=0, const T5 &x5=0, const T6 &x6=0)
Definition: OperandsAndPartials.hpp:322
include_summand.hpp
multiply_log.hpp
stan::math::OperandsAndPartials::d_x1
VectorView< T_partials_return, is_vector< T1 >::value, is_constant_struct< T1 >::value > d_x1
Definition: OperandsAndPartials.hpp:253
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:16
stan::math::inc_beta
fvar< T > inc_beta(const fvar< T > &a, const fvar< T > &b, const fvar< T > &x)
Definition: inc_beta.hpp:20
stan::partials_return_type
Definition: partials_return_type.hpp:16
check_less_or_equal.hpp
stan::math::exp
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:10
stan::math::OperandsAndPartials::d_x3
VectorView< T_partials_return, is_vector< T3 >::value, is_constant_struct< T3 >::value > d_x3
Definition: OperandsAndPartials.hpp:259
stan::math::beta_cdf
return_type< T_y, T_scale_succ, T_scale_fail >::type beta_cdf(const T_y &y, const T_scale_succ &alpha, const T_scale_fail &beta)
Calculates the beta cumulative distribution function for the given variate and scale variables...
Definition: beta_cdf.hpp:46
stan::math::OperandsAndPartials
A variable implementation that stores operands and derivatives with respect to the variable...
Definition: OperandsAndPartials.hpp:238
OperandsAndPartials.hpp
stan::max_size
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
VectorBuilder.hpp
log1m.hpp
partials_return_type.hpp
stan::math::check_less_or_equal
bool check_less_or_equal(const char *function, const char *name, const T_y &y, const T_high &high)
Return true if y is less or equal to high.
Definition: check_less_or_equal.hpp:81
stan::contains_nonconstant_struct
Definition: contains_nonconstant_struct.hpp:14
grad_reg_inc_beta.hpp
stan::VectorBuilder
Definition: VectorBuilder.hpp:61
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
lbeta.hpp
stan::math::OperandsAndPartials::d_x2
VectorView< T_partials_return, is_vector< T2 >::value, is_constant_struct< T2 >::value > d_x2
Definition: OperandsAndPartials.hpp:256
inc_beta.hpp
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::VectorView
VectorView is a template metaprogram that takes its argument and allows it to be used like a vector...
Definition: VectorView.hpp:41
stan::math::grad_reg_inc_beta
void grad_reg_inc_beta(T &g1, T &g2, T a, T b, T z, T digammaA, T digammaB, T digammaSum, T betaAB)
Definition: grad_reg_inc_beta.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::digamma
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:16

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