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beta_cdf_log.hpp
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#ifndef STAN_MATH_PRIM_SCAL_PROB_BETA_CDF_LOG_HPP
#define STAN_MATH_PRIM_SCAL_PROB_BETA_CDF_LOG_HPP
#include <boost/math/special_functions/gamma.hpp>
#include <boost/random/gamma_distribution.hpp>
#include <boost/random/variate_generator.hpp>
#include <stan/math/prim/scal/meta/OperandsAndPartials.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/lgamma.hpp>
#include <stan/math/prim/scal/fun/lbeta.hpp>
#include <stan/math/prim/scal/meta/contains_nonconstant_struct.hpp>
#include <stan/math/prim/scal/fun/constants.hpp>
#include <stan/math/prim/scal/meta/include_summand.hpp>
#include <stan/math/prim/scal/meta/VectorBuilder.hpp>
#include <stan/math/prim/scal/fun/grad_reg_inc_beta.hpp>
#include <stan/math/prim/scal/fun/inc_beta.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_log(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;
// Size checks
if ( !( stan::length(y) && stan::length(alpha)
&& stan::length(beta) ) )
return 0.0;
// Error checks
static const char* function("stan::math::beta_cdf");
using stan::math::check_positive_finite;
using stan::math::check_not_nan;
using stan::math::check_nonnegative;
using stan::math::check_less_or_equal;
using boost::math::tools::promote_args;
using stan::math::check_consistent_sizes;
using stan::math::value_of;
T_partials_return cdf_log(0.0);
check_positive_finite(function, "First shape parameter", alpha);
check_positive_finite(function, "Second shape parameter", beta);
check_not_nan(function, "Random variable", y);
check_nonnegative(function, "Random variable", y);
check_less_or_equal(function, "Random variable", y, 1);
check_consistent_sizes(function,
"Random variable", y,
"First shape parameter", alpha,
"Second shape parameter", beta);
// Wrap arguments in vectors
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);
// Compute CDF and its gradients
using stan::math::inc_beta;
using stan::math::digamma;
using stan::math::lbeta;
using std::pow;
using std::exp;
using std::log;
using std::exp;
// Cache a few expensive function calls if alpha or beta is a parameter
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 i = 0; i < N; i++) {
const T_partials_return alpha_dbl = value_of(alpha_vec[i]);
const T_partials_return beta_dbl = value_of(beta_vec[i]);
digamma_alpha_vec[i] = digamma(alpha_dbl);
digamma_beta_vec[i] = digamma(beta_dbl);
digamma_sum_vec[i] = digamma(alpha_dbl + beta_dbl);
}
}
// Compute vectorized CDFLog and gradient
for (size_t n = 0; n < N; n++) {
// Pull out values
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 betafunc_dbl = exp(lbeta(alpha_dbl, beta_dbl));
// Compute
const T_partials_return Pn = inc_beta(alpha_dbl, beta_dbl, y_dbl);
cdf_log += log(Pn);
if (!is_constant_struct<T_y>::value)
operands_and_partials.d_x1[n] += pow(1-y_dbl, beta_dbl-1)
* pow(y_dbl, alpha_dbl-1) / betafunc_dbl / Pn;
T_partials_return g1 = 0;
T_partials_return g2 = 0;
if (contains_nonconstant_struct<T_scale_succ, T_scale_fail>::value) {
stan::math::grad_reg_inc_beta(g1, g2, alpha_dbl, beta_dbl, y_dbl,
digamma_alpha_vec[n],
digamma_beta_vec[n], digamma_sum_vec[n],
betafunc_dbl);
}
if (!is_constant_struct<T_scale_succ>::value)
operands_and_partials.d_x2[n] += g1 / Pn;
if (!is_constant_struct<T_scale_fail>::value)
operands_and_partials.d_x3[n] += g2 / Pn;
}
return operands_and_partials.to_var(cdf_log, y, alpha, beta);
}
}
}
#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
stan::math::log
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:15
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::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
stan::math::beta_cdf_log
return_type< T_y, T_scale_succ, T_scale_fail >::type beta_cdf_log(const T_y &y, const T_scale_succ &alpha, const T_scale_fail &beta)
Definition: beta_cdf_log.hpp:33
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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