Stan Math Library  2.11.0
reverse mode automatic differentiation
beta_cdf.hpp
Go to the documentation of this file.
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 
33  namespace math {
34 
47  template <typename T_y, typename T_scale_succ, typename T_scale_fail>
48  typename return_type<T_y, T_scale_succ, T_scale_fail>::type
49  beta_cdf(const T_y& y, const T_scale_succ& alpha,
50  const T_scale_fail& beta) {
51  typedef typename stan::partials_return_type<T_y, T_scale_succ,
52  T_scale_fail>::type
53  T_partials_return;
54 
55  // Size checks
56  if (!(stan::length(y) && stan::length(alpha)
57  && stan::length(beta)))
58  return 1.0;
59 
60  // Error checks
61  static const char* function("stan::math::beta_cdf");
62  using boost::math::tools::promote_args;
63 
64  T_partials_return P(1.0);
65 
66  check_positive_finite(function, "First shape parameter", alpha);
67  check_positive_finite(function, "Second shape parameter", beta);
68  check_not_nan(function, "Random variable", y);
69  check_consistent_sizes(function,
70  "Random variable", y,
71  "First shape parameter", alpha,
72  "Second shape parameter", beta);
73  check_nonnegative(function, "Random variable", y);
74  check_less_or_equal(function, "Random variable", y, 1);
75 
76  // Wrap arguments in vectors
77  VectorView<const T_y> y_vec(y);
78  VectorView<const T_scale_succ> alpha_vec(alpha);
79  VectorView<const T_scale_fail> beta_vec(beta);
80  size_t N = max_size(y, alpha, beta);
81 
83  operands_and_partials(y, alpha, beta);
84 
85  // Explicit return for extreme values
86  // The gradients are technically ill-defined, but treated as zero
87  for (size_t i = 0; i < stan::length(y); i++) {
88  if (value_of(y_vec[i]) <= 0)
89  return operands_and_partials.value(0.0);
90  }
91 
92  // Compute CDF and its gradients
93 
94  // Cache a few expensive function calls if alpha or beta is a parameter
96  T_scale_fail>::value,
97  T_partials_return, T_scale_succ, T_scale_fail>
98  digamma_alpha_vec(max_size(alpha, beta));
99 
101  T_scale_fail>::value,
102  T_partials_return, T_scale_succ, T_scale_fail>
103  digamma_beta_vec(max_size(alpha, beta));
104 
106  T_scale_fail>::value,
107  T_partials_return, T_scale_succ, T_scale_fail>
108  digamma_sum_vec(max_size(alpha, beta));
109 
111  for (size_t n = 0; n < N; n++) {
112  const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
113  const T_partials_return beta_dbl = value_of(beta_vec[n]);
114 
115  digamma_alpha_vec[n] = digamma(alpha_dbl);
116  digamma_beta_vec[n] = digamma(beta_dbl);
117  digamma_sum_vec[n] = digamma(alpha_dbl + beta_dbl);
118  }
119  }
120 
121  // Compute vectorized CDF and gradient
122  for (size_t n = 0; n < N; n++) {
123  // Explicit results for extreme values
124  // The gradients are technically ill-defined, but treated as zero
125  if (value_of(y_vec[n]) >= 1.0) continue;
126 
127  // Pull out values
128  const T_partials_return y_dbl = value_of(y_vec[n]);
129  const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
130  const T_partials_return beta_dbl = value_of(beta_vec[n]);
131 
132  // Compute
133  const T_partials_return Pn = inc_beta(alpha_dbl, beta_dbl, y_dbl);
134 
135  P *= Pn;
136 
138  operands_and_partials.d_x1[n]
139  += inc_beta_ddz(alpha_dbl, beta_dbl, y_dbl) / Pn;
140 
142  operands_and_partials.d_x2[n]
143  += inc_beta_dda(alpha_dbl, beta_dbl, y_dbl,
144  digamma_alpha_vec[n], digamma_sum_vec[n]) / Pn;
146  operands_and_partials.d_x3[n]
147  += inc_beta_ddb(alpha_dbl, beta_dbl, y_dbl,
148  digamma_beta_vec[n], digamma_sum_vec[n]) / Pn;
149  }
150 
152  for (size_t n = 0; n < stan::length(y); ++n)
153  operands_and_partials.d_x1[n] *= P;
154  }
156  for (size_t n = 0; n < stan::length(alpha); ++n)
157  operands_and_partials.d_x2[n] *= P;
158  }
160  for (size_t n = 0; n < stan::length(beta); ++n)
161  operands_and_partials.d_x3[n] *= P;
162  }
163 
164  return operands_and_partials.value(P);
165  }
166 
167  }
168 }
169 #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
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.
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
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:49
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.
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
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.