1 #ifndef STAN_MATH_PRIM_SCAL_PROB_BETA_CDF_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_BETA_CDF_LOG_HPP
24 #include <boost/math/special_functions/gamma.hpp>
25 #include <boost/random/gamma_distribution.hpp>
26 #include <boost/random/variate_generator.hpp>
33 template <
typename T_y,
typename T_scale_succ,
typename T_scale_fail>
34 typename return_type<T_y, T_scale_succ, T_scale_fail>::type
36 const T_scale_fail& beta) {
47 static const char*
function(
"stan::math::beta_cdf");
53 using boost::math::tools::promote_args;
57 T_partials_return cdf_log(0.0);
66 "First shape parameter", alpha,
67 "Second shape parameter", beta);
76 operands_and_partials(y, alpha, beta);
90 T_partials_return, T_scale_succ, T_scale_fail>
91 digamma_alpha_vec(
max_size(alpha, beta));
95 T_partials_return, T_scale_succ, T_scale_fail>
96 digamma_beta_vec(
max_size(alpha, beta));
100 T_partials_return, T_scale_succ, T_scale_fail>
101 digamma_sum_vec(
max_size(alpha, beta));
104 for (
size_t i = 0; i < N; i++) {
105 const T_partials_return alpha_dbl =
value_of(alpha_vec[i]);
106 const T_partials_return beta_dbl =
value_of(beta_vec[i]);
108 digamma_alpha_vec[i] =
digamma(alpha_dbl);
109 digamma_beta_vec[i] =
digamma(beta_dbl);
110 digamma_sum_vec[i] =
digamma(alpha_dbl + beta_dbl);
115 for (
size_t n = 0; n < N; n++) {
117 const T_partials_return y_dbl =
value_of(y_vec[n]);
118 const T_partials_return alpha_dbl =
value_of(alpha_vec[n]);
119 const T_partials_return beta_dbl =
value_of(beta_vec[n]);
120 const T_partials_return betafunc_dbl =
exp(
lbeta(alpha_dbl, beta_dbl));
122 const T_partials_return Pn =
inc_beta(alpha_dbl, beta_dbl, y_dbl);
127 operands_and_partials.
d_x1[n] +=
pow(1-y_dbl, beta_dbl-1)
128 *
pow(y_dbl, alpha_dbl-1) / betafunc_dbl / Pn;
130 T_partials_return g1 = 0;
131 T_partials_return g2 = 0;
135 digamma_alpha_vec[n],
136 digamma_beta_vec[n], digamma_sum_vec[n],
140 operands_and_partials.
d_x2[n] += g1 / Pn;
142 operands_and_partials.
d_x3[n] += g2 / Pn;
145 return operands_and_partials.
value(cdf_log);
VectorView< T_return_type, false, true > d_x2
bool check_not_nan(const char *function, const char *name, const T_y &y)
Return true if y is not NaN.
T value_of(const fvar< T > &v)
Return the value of the specified variable.
fvar< T > lbeta(const fvar< T > &x1, const fvar< T > &x2)
fvar< T > log(const fvar< T > &x)
T_return_type value(double value)
Returns a T_return_type with the value specified with the partial derivatves.
size_t length(const std::vector< T > &x)
Metaprogram to determine if a type has a base scalar type that can be assigned to type double...
fvar< T > inc_beta(const fvar< T > &a, const fvar< T > &b, const fvar< T > &x)
fvar< T > exp(const fvar< T > &x)
This class builds partial derivatives with respect to a set of operands.
VectorView< T_return_type, false, true > d_x3
size_t max_size(const T1 &x1, const T2 &x2)
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)
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.
VectorBuilder allocates type T1 values to be used as intermediate values.
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.
fvar< T > pow(const fvar< T > &x1, const fvar< T > &x2)
bool check_nonnegative(const char *function, const char *name, const T_y &y)
Return true if y is non-negative.
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[].
void grad_reg_inc_beta(T &g1, T &g2, T a, T b, T z, T digammaA, T digammaB, T digammaSum, T betaAB)
bool check_positive_finite(const char *function, const char *name, const T_y &y)
Return true if y is positive and finite.
VectorView< T_return_type, false, true > d_x1
fvar< T > digamma(const fvar< T > &x)