Stan Math Library  2.14.0
reverse mode automatic differentiation
beta_cdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_BETA_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_BETA_CDF_HPP
3 
26 #include <boost/math/special_functions/gamma.hpp>
27 #include <boost/random/gamma_distribution.hpp>
28 #include <boost/random/variate_generator.hpp>
29 #include <cmath>
30 
31 namespace stan {
32  namespace math {
33 
46  template <typename T_y, typename T_scale_succ, typename T_scale_fail>
48  beta_cdf(const T_y& y, const T_scale_succ& alpha,
49  const T_scale_fail& beta) {
50  typedef typename stan::partials_return_type<T_y, T_scale_succ,
51  T_scale_fail>::type
52  T_partials_return;
53 
54  if (!(stan::length(y) && stan::length(alpha)
55  && stan::length(beta)))
56  return 1.0;
57 
58  static const char* function("beta_cdf");
59  using boost::math::tools::promote_args;
60 
61  T_partials_return P(1.0);
62 
63  check_positive_finite(function, "First shape parameter", alpha);
64  check_positive_finite(function, "Second shape parameter", beta);
65  check_not_nan(function, "Random variable", y);
66  check_consistent_sizes(function,
67  "Random variable", y,
68  "First shape parameter", alpha,
69  "Second shape parameter", beta);
70  check_nonnegative(function, "Random variable", y);
71  check_less_or_equal(function, "Random variable", y, 1);
72 
73  VectorView<const T_y> y_vec(y);
74  VectorView<const T_scale_succ> alpha_vec(alpha);
75  VectorView<const T_scale_fail> beta_vec(beta);
76  size_t N = max_size(y, alpha, beta);
77 
79  operands_and_partials(y, alpha, beta);
80 
81  // Explicit return for extreme values
82  // The gradients are technically ill-defined, but treated as zero
83  for (size_t i = 0; i < stan::length(y); i++) {
84  if (value_of(y_vec[i]) <= 0)
85  return operands_and_partials.value(0.0);
86  }
87 
89  T_scale_fail>::value,
90  T_partials_return, T_scale_succ, T_scale_fail>
91  digamma_alpha_vec(max_size(alpha, beta));
92 
94  T_scale_fail>::value,
95  T_partials_return, T_scale_succ, T_scale_fail>
96  digamma_beta_vec(max_size(alpha, beta));
97 
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 n = 0; n < N; n++) {
105  const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
106  const T_partials_return beta_dbl = value_of(beta_vec[n]);
107 
108  digamma_alpha_vec[n] = digamma(alpha_dbl);
109  digamma_beta_vec[n] = digamma(beta_dbl);
110  digamma_sum_vec[n] = digamma(alpha_dbl + beta_dbl);
111  }
112  }
113 
114  for (size_t n = 0; n < N; n++) {
115  // Explicit results for extreme values
116  // The gradients are technically ill-defined, but treated as zero
117  if (value_of(y_vec[n]) >= 1.0) continue;
118 
119  const T_partials_return y_dbl = value_of(y_vec[n]);
120  const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
121  const T_partials_return beta_dbl = value_of(beta_vec[n]);
122 
123  const T_partials_return Pn = inc_beta(alpha_dbl, beta_dbl, y_dbl);
124 
125  P *= Pn;
126 
128  operands_and_partials.d_x1[n]
129  += inc_beta_ddz(alpha_dbl, beta_dbl, y_dbl) / Pn;
130 
132  operands_and_partials.d_x2[n]
133  += inc_beta_dda(alpha_dbl, beta_dbl, y_dbl,
134  digamma_alpha_vec[n], digamma_sum_vec[n]) / Pn;
136  operands_and_partials.d_x3[n]
137  += inc_beta_ddb(alpha_dbl, beta_dbl, y_dbl,
138  digamma_beta_vec[n], digamma_sum_vec[n]) / Pn;
139  }
140 
142  for (size_t n = 0; n < stan::length(y); ++n)
143  operands_and_partials.d_x1[n] *= P;
144  }
146  for (size_t n = 0; n < stan::length(alpha); ++n)
147  operands_and_partials.d_x2[n] *= P;
148  }
150  for (size_t n = 0; n < stan::length(beta); ++n)
151  operands_and_partials.d_x3[n] *= P;
152  }
153 
154  return operands_and_partials.value(P);
155  }
156 
157  }
158 }
159 #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
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.
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
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.
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.
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 check_not_nan(const char *function, const char *name, const T_y &y)
Check if y is not NaN.
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
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.
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 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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