beta_cdf.hpp
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#ifndef STAN_MATH_PRIM_SCAL_PROB_BETA_CDF_HPP
#define STAN_MATH_PRIM_SCAL_PROB_BETA_CDF_HPP
#include <stan/math/prim/scal/meta/is_constant_struct.hpp>
#include <stan/math/prim/scal/meta/OperandsAndPartials.hpp>
#include <stan/math/prim/scal/meta/VectorBuilder.hpp>
#include <stan/math/prim/scal/meta/include_summand.hpp>
#include <stan/math/prim/scal/meta/partials_return_type.hpp>
#include <stan/math/prim/scal/meta/contains_nonconstant_struct.hpp>
#include <stan/math/prim/scal/err/check_consistent_sizes.hpp>
#include <stan/math/prim/scal/err/check_less_or_equal.hpp>
#include <stan/math/prim/scal/err/check_nonnegative.hpp>
#include <stan/math/prim/scal/err/check_not_nan.hpp>
#include <stan/math/prim/scal/err/check_positive_finite.hpp>
#include <stan/math/prim/scal/fun/log1m.hpp>
#include <stan/math/prim/scal/fun/multiply_log.hpp>
#include <stan/math/prim/scal/fun/value_of.hpp>
#include <stan/math/prim/scal/fun/digamma.hpp>
#include <stan/math/prim/scal/fun/inc_beta.hpp>
#include <stan/math/prim/scal/fun/inc_beta_dda.hpp>
#include <stan/math/prim/scal/fun/inc_beta_ddb.hpp>
#include <stan/math/prim/scal/fun/inc_beta_ddz.hpp>
#include <stan/math/prim/scal/fun/lgamma.hpp>
#include <stan/math/prim/scal/fun/lbeta.hpp>
#include <stan/math/prim/scal/fun/constants.hpp>
#include <boost/math/special_functions/gamma.hpp>
#include <boost/random/gamma_distribution.hpp>
#include <boost/random/variate_generator.hpp>
#include <cmath>
namespace stan {
namespace math {
template <typename T_y, typename T_scale_succ, typename T_scale_fail>
typename 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) {
typedef typename stan::partials_return_type<T_y, T_scale_succ,
T_scale_fail>::type
T_partials_return;
if (!(stan::length(y) && stan::length(alpha)
&& stan::length(beta)))
return 1.0;
static const char* function("beta_cdf");
using boost::math::tools::promote_args;
T_partials_return P(1.0);
check_positive_finite(function, "First shape parameter", alpha);
check_positive_finite(function, "Second shape parameter", beta);
check_not_nan(function, "Random variable", y);
check_consistent_sizes(function,
"Random variable", y,
"First shape parameter", alpha,
"Second shape parameter", beta);
check_nonnegative(function, "Random variable", y);
check_less_or_equal(function, "Random variable", y, 1);
VectorView<const T_y> y_vec(y);
VectorView<const T_scale_succ> alpha_vec(alpha);
VectorView<const T_scale_fail> beta_vec(beta);
size_t N = max_size(y, alpha, beta);
OperandsAndPartials<T_y, T_scale_succ, T_scale_fail>
operands_and_partials(y, alpha, beta);
// Explicit return for extreme values
// The gradients are technically ill-defined, but treated as zero
for (size_t i = 0; i < stan::length(y); i++) {
if (value_of(y_vec[i]) <= 0)
return operands_and_partials.value(0.0);
}
VectorBuilder<contains_nonconstant_struct<T_scale_succ,
T_scale_fail>::value,
T_partials_return, T_scale_succ, T_scale_fail>
digamma_alpha_vec(max_size(alpha, beta));
VectorBuilder<contains_nonconstant_struct<T_scale_succ,
T_scale_fail>::value,
T_partials_return, T_scale_succ, T_scale_fail>
digamma_beta_vec(max_size(alpha, beta));
VectorBuilder<contains_nonconstant_struct<T_scale_succ,
T_scale_fail>::value,
T_partials_return, T_scale_succ, T_scale_fail>
digamma_sum_vec(max_size(alpha, beta));
if (contains_nonconstant_struct<T_scale_succ, T_scale_fail>::value) {
for (size_t n = 0; n < N; n++) {
const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
const T_partials_return beta_dbl = value_of(beta_vec[n]);
digamma_alpha_vec[n] = digamma(alpha_dbl);
digamma_beta_vec[n] = digamma(beta_dbl);
digamma_sum_vec[n] = digamma(alpha_dbl + beta_dbl);
}
}
for (size_t n = 0; n < N; n++) {
// Explicit results for extreme values
// The gradients are technically ill-defined, but treated as zero
if (value_of(y_vec[n]) >= 1.0) continue;
const T_partials_return y_dbl = value_of(y_vec[n]);
const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
const T_partials_return beta_dbl = value_of(beta_vec[n]);
const T_partials_return Pn = inc_beta(alpha_dbl, beta_dbl, y_dbl);
P *= Pn;
if (!is_constant_struct<T_y>::value)
operands_and_partials.d_x1[n]
+= inc_beta_ddz(alpha_dbl, beta_dbl, y_dbl) / Pn;
if (!is_constant_struct<T_scale_succ>::value)
operands_and_partials.d_x2[n]
+= inc_beta_dda(alpha_dbl, beta_dbl, y_dbl,
digamma_alpha_vec[n], digamma_sum_vec[n]) / Pn;
if (!is_constant_struct<T_scale_fail>::value)
operands_and_partials.d_x3[n]
+= inc_beta_ddb(alpha_dbl, beta_dbl, y_dbl,
digamma_beta_vec[n], digamma_sum_vec[n]) / Pn;
}
if (!is_constant_struct<T_y>::value) {
for (size_t n = 0; n < stan::length(y); ++n)
operands_and_partials.d_x1[n] *= P;
}
if (!is_constant_struct<T_scale_succ>::value) {
for (size_t n = 0; n < stan::length(alpha); ++n)
operands_and_partials.d_x2[n] *= P;
}
if (!is_constant_struct<T_scale_fail>::value) {
for (size_t n = 0; n < stan::length(beta); ++n)
operands_and_partials.d_x3[n] *= P;
}
return operands_and_partials.value(P);
}
}
}
#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_less_or_equal
void check_less_or_equal(const char *function, const char *name, const T_y &y, const T_high &high)
Check if y is less or equal to high.
Definition: check_less_or_equal.hpp:78
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
stan::math::inc_beta_dda
T inc_beta_dda(T a, T b, T z, T digamma_a, T digamma_ab)
Returns the partial derivative of the regularized incomplete beta function, I_{z}(a, b) with respect to a.
Definition: inc_beta_dda.hpp:39
inc_beta_ddz.hpp
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
contains_nonconstant_struct.hpp
stan::length
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
is_constant_struct.hpp
stan::math::inc_beta_ddb
T inc_beta_ddb(T a, T b, T z, T digamma_b, T digamma_ab)
Returns the partial derivative of the regularized incomplete beta function, I_{z}(a, b) with respect to b.
Definition: inc_beta_ddb.hpp:39
stan::math::inc_beta_ddz
T inc_beta_ddz(T a, T b, T z)
Returns the partial derivative of the regularized incomplete beta function, I_{z}(a, b) with respect to z.
Definition: inc_beta_ddz.hpp:27
inc_beta_ddb.hpp
stan::math::check_nonnegative
void check_nonnegative(const char *function, const char *name, const T_y &y)
Check if y is non-negative.
Definition: check_nonnegative.hpp:61
stan::return_type::type
boost::math::tools::promote_args< typename scalar_type< T1 >::type, typename scalar_type< T2 >::type, typename scalar_type< T3 >::type, typename scalar_type< T4 >::type, typename scalar_type< T5 >::type, typename scalar_type< T6 >::type >::type type
Definition: return_type.hpp:27
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::inc_beta
fvar< T > inc_beta(const fvar< T > &a, const fvar< T > &b, const fvar< T > &x)
Definition: inc_beta.hpp:19
stan::math::check_positive_finite
void check_positive_finite(const char *function, const char *name, const T_y &y)
Check if y is positive and finite.
Definition: check_positive_finite.hpp:26
stan::partials_return_type
Definition: partials_return_type.hpp:16
check_less_or_equal.hpp
stan::math::check_not_nan
void check_not_nan(const char *function, const char *name, const T_y &y)
Check if y is not NaN.
Definition: check_not_nan.hpp:57
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:48
stan::math::OperandsAndPartials
This class builds partial derivatives with respect to a set of operands.
Definition: OperandsAndPartials.hpp:37
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
log1m.hpp
partials_return_type.hpp
OperandsAndPartials.hpp
stan::contains_nonconstant_struct
Definition: contains_nonconstant_struct.hpp:14
stan::VectorBuilder
VectorBuilder allocates type T1 values to be used as intermediate values.
Definition: VectorBuilder.hpp:28
constants.hpp
lbeta.hpp
inc_beta.hpp
value_of.hpp
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::math::check_consistent_sizes
void check_consistent_sizes(const char *function, const char *name1, const T1 &x1, const char *name2, const T2 &x2)
Check if the dimension of x1 is consistent with x2.
Definition: check_consistent_sizes.hpp:30
check_consistent_sizes.hpp
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)
Return the derivative of the log gamma function at the specified argument.
Definition: digamma.hpp:22
inc_beta_dda.hpp

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