Stan Math Library  2.11.0
reverse mode automatic differentiation
beta_ccdf_log.hpp
Go to the documentation of this file.
1 #ifndef STAN_MATH_PRIM_SCAL_PROB_BETA_CCDF_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_BETA_CCDF_LOG_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 
32  namespace math {
33 
34  template <typename T_y, typename T_scale_succ, typename T_scale_fail>
35  typename return_type<T_y, T_scale_succ, T_scale_fail>::type
36  beta_ccdf_log(const T_y& y, const T_scale_succ& alpha,
37  const T_scale_fail& beta) {
38  typedef typename stan::partials_return_type<T_y, T_scale_succ,
39  T_scale_fail>::type
40  T_partials_return;
41 
42  // Size checks
43  if ( !( stan::length(y) && stan::length(alpha)
44  && stan::length(beta) ) )
45  return 0.0;
46 
47  // Error checks
48  static const char* function("stan::math::beta_cdf");
49 
54  using boost::math::tools::promote_args;
57 
58  T_partials_return ccdf_log(0.0);
59 
60  check_positive_finite(function, "First shape parameter", alpha);
61  check_positive_finite(function, "Second shape parameter", beta);
62  check_not_nan(function, "Random variable", y);
63  check_nonnegative(function, "Random variable", y);
64  check_less_or_equal(function, "Random variable", y, 1);
65  check_consistent_sizes(function,
66  "Random variable", y,
67  "First shape parameter", alpha,
68  "Second shape parameter", beta);
69 
70  // Wrap arguments in vectors
71  VectorView<const T_y> y_vec(y);
72  VectorView<const T_scale_succ> alpha_vec(alpha);
73  VectorView<const T_scale_fail> beta_vec(beta);
74  size_t N = max_size(y, alpha, beta);
75 
77  operands_and_partials(y, alpha, beta);
78 
79  // Compute CDF and its gradients
81  using stan::math::digamma;
82  using stan::math::lbeta;
83  using std::pow;
84  using std::exp;
85  using std::log;
86  using std::exp;
87 
88  // Cache a few expensive function calls if alpha or beta is a parameter
90  T_scale_fail>::value,
91  T_partials_return, T_scale_succ, T_scale_fail>
92  digamma_alpha_vec(max_size(alpha, beta));
94  T_scale_fail>::value,
95  T_partials_return, T_scale_succ, T_scale_fail>
96  digamma_beta_vec(max_size(alpha, beta));
98  T_scale_fail>::value,
99  T_partials_return, T_scale_succ, T_scale_fail>
100  digamma_sum_vec(max_size(alpha, beta));
101 
103  for (size_t i = 0; i < N; i++) {
104  const T_partials_return alpha_dbl = value_of(alpha_vec[i]);
105  const T_partials_return beta_dbl = value_of(beta_vec[i]);
106 
107  digamma_alpha_vec[i] = digamma(alpha_dbl);
108  digamma_beta_vec[i] = digamma(beta_dbl);
109  digamma_sum_vec[i] = digamma(alpha_dbl + beta_dbl);
110  }
111  }
112 
113  // Compute vectorized CDFLog and gradient
114  for (size_t n = 0; n < N; n++) {
115  // Pull out values
116  const T_partials_return y_dbl = value_of(y_vec[n]);
117  const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
118  const T_partials_return beta_dbl = value_of(beta_vec[n]);
119  const T_partials_return betafunc_dbl = exp(lbeta(alpha_dbl, beta_dbl));
120 
121  // Compute
122  const T_partials_return Pn = 1.0 - inc_beta(alpha_dbl, beta_dbl, y_dbl);
123 
124  ccdf_log += log(Pn);
125 
127  operands_and_partials.d_x1[n] -= pow(1-y_dbl, beta_dbl-1)
128  * pow(y_dbl, alpha_dbl-1) / betafunc_dbl / Pn;
129 
130  T_partials_return g1 = 0;
131  T_partials_return g2 = 0;
132 
134  stan::math::grad_reg_inc_beta(g1, g2, alpha_dbl, beta_dbl, y_dbl,
135  digamma_alpha_vec[n],
136  digamma_beta_vec[n],
137  digamma_sum_vec[n],
138  betafunc_dbl);
139  }
141  operands_and_partials.d_x2[n] -= g1 / Pn;
143  operands_and_partials.d_x3[n] -= g2 / Pn;
144  }
145 
146  return operands_and_partials.value(ccdf_log);
147  }
148  }
149 }
150 #endif
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.
Definition: value_of.hpp:16
fvar< T > lbeta(const fvar< T > &x1, const fvar< T > &x2)
Definition: lbeta.hpp:16
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:15
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)
Definition: length.hpp:10
return_type< T_y, T_scale_succ, T_scale_fail >::type beta_ccdf_log(const T_y &y, const T_scale_succ &alpha, const T_scale_fail &beta)
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:20
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:10
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
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)
Definition: pow.hpp:18
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[].
Definition: VectorView.hpp:48
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)
Definition: digamma.hpp:16

     [ Stan Home Page ] © 2011–2016, Stan Development Team.