Stan Math Library  2.15.0
reverse mode automatic differentiation
beta_lccdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_BETA_LCCDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_BETA_LCCDF_HPP
3 
25 #include <boost/math/special_functions/gamma.hpp>
26 #include <boost/random/gamma_distribution.hpp>
27 #include <boost/random/variate_generator.hpp>
28 #include <cmath>
29 
30 namespace stan {
31  namespace math {
32 
49  template <typename T_y, typename T_scale_succ, typename T_scale_fail>
51  beta_lccdf(const T_y& y, const T_scale_succ& alpha,
52  const T_scale_fail& beta) {
53  typedef typename stan::partials_return_type<T_y, T_scale_succ,
54  T_scale_fail>::type
55  T_partials_return;
56 
57  if ( !( stan::length(y) && stan::length(alpha)
58  && stan::length(beta) ) )
59  return 0.0;
60 
61  static const char* function("beta_lccdf");
62 
63  using boost::math::tools::promote_args;
64 
65  T_partials_return ccdf_log(0.0);
66 
67  check_positive_finite(function, "First shape parameter", alpha);
68  check_positive_finite(function, "Second shape parameter", beta);
69  check_not_nan(function, "Random variable", y);
70  check_nonnegative(function, "Random variable", y);
71  check_less_or_equal(function, "Random variable", y, 1);
72  check_consistent_sizes(function,
73  "Random variable", y,
74  "First shape parameter", alpha,
75  "Second shape parameter", beta);
76 
78  scalar_seq_view<const T_scale_succ> alpha_vec(alpha);
80  size_t N = max_size(y, alpha, beta);
81 
83  operands_and_partials(y, alpha, beta);
84 
85  using std::pow;
86  using std::exp;
87  using std::log;
88  using std::exp;
89 
91  T_scale_fail>::value,
92  T_partials_return, T_scale_succ, T_scale_fail>
93  digamma_alpha_vec(max_size(alpha, beta));
95  T_scale_fail>::value,
96  T_partials_return, T_scale_succ, T_scale_fail>
97  digamma_beta_vec(max_size(alpha, beta));
99  T_scale_fail>::value,
100  T_partials_return, T_scale_succ, T_scale_fail>
101  digamma_sum_vec(max_size(alpha, beta));
102 
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]);
107 
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);
111  }
112  }
113 
114  for (size_t n = 0; n < N; n++) {
115  const T_partials_return y_dbl = value_of(y_vec[n]);
116  const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
117  const T_partials_return beta_dbl = value_of(beta_vec[n]);
118  const T_partials_return betafunc_dbl = exp(lbeta(alpha_dbl, beta_dbl));
119 
120  const T_partials_return Pn = 1.0 - inc_beta(alpha_dbl, beta_dbl, y_dbl);
121 
122  ccdf_log += log(Pn);
123 
125  operands_and_partials.d_x1[n] -= pow(1-y_dbl, beta_dbl-1)
126  * pow(y_dbl, alpha_dbl-1) / betafunc_dbl / Pn;
127 
128  T_partials_return g1 = 0;
129  T_partials_return g2 = 0;
130 
132  grad_reg_inc_beta(g1, g2, alpha_dbl, beta_dbl, y_dbl,
133  digamma_alpha_vec[n],
134  digamma_beta_vec[n],
135  digamma_sum_vec[n],
136  betafunc_dbl);
137  }
139  operands_and_partials.d_x2[n] -= g1 / Pn;
141  operands_and_partials.d_x3[n] -= g2 / Pn;
142  }
143  return operands_and_partials.value(ccdf_log);
144  }
145 
146  }
147 }
148 #endif
VectorView< T_return_type, false, true > d_x2
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.
T value_of(const fvar< T > &v)
Return the value of the specified variable.
Definition: value_of.hpp:16
fvar< T > lbeta(const fvar< T > &x1, const fvar< T > &x2)
Definition: lbeta.hpp:15
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:14
T_return_type value(double value)
Returns a T_return_type with the value specified with the partial derivatves.
scalar_seq_view provides a uniform sequence-like wrapper around either a scalar or a sequence of scal...
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
void check_nonnegative(const char *function, const char *name, const T_y &y)
Check if y is non-negative.
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
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)
Definition: inc_beta.hpp:19
void check_positive_finite(const char *function, const char *name, const T_y &y)
Check if y is positive and finite.
void grad_reg_inc_beta(T &g1, T &g2, const T &a, const T &b, const T &z, const T &digammaA, const T &digammaB, const T &digammaSum, const T &betaAB)
Computes the gradients of the regularized incomplete beta function.
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:10
void check_not_nan(const char *function, const char *name, const T_y &y)
Check if y is not NaN.
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)
Definition: max_size.hpp:9
VectorBuilder allocates type T1 values to be used as intermediate values.
fvar< T > pow(const fvar< T > &x1, const fvar< T > &x2)
Definition: pow.hpp:17
return_type< T_y, T_scale_succ, T_scale_fail >::type beta_lccdf(const T_y &y, const T_scale_succ &alpha, const T_scale_fail &beta)
Returns the beta log complementary cumulative distribution function for the given probability...
Definition: beta_lccdf.hpp:51
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.
VectorView< T_return_type, false, true > d_x1
fvar< T > digamma(const fvar< T > &x)
Return the derivative of the log gamma function at the specified argument.
Definition: digamma.hpp:22

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