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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 
4 #include <boost/math/special_functions/gamma.hpp>
5 #include <boost/random/gamma_distribution.hpp>
6 #include <boost/random/variate_generator.hpp>
26 #include <cmath>
27 
28 namespace stan {
29 
30  namespace math {
31 
44  template <typename T_y, typename T_scale_succ, typename T_scale_fail>
45  typename return_type<T_y, T_scale_succ, T_scale_fail>::type
46  beta_cdf(const T_y& y, const T_scale_succ& alpha,
47  const T_scale_fail& beta) {
48  typedef typename stan::partials_return_type<T_y, T_scale_succ,
49  T_scale_fail>::type
50  T_partials_return;
51 
52 
53  // Size checks
54  if ( !( stan::length(y) && stan::length(alpha)
55  && stan::length(beta) ) )
56  return 1.0;
57 
58  // Error checks
59  static const char* function("stan::math::beta_cdf");
60 
63  using boost::math::tools::promote_args;
68 
69  T_partials_return P(1.0);
70 
71  check_positive_finite(function, "First shape parameter", alpha);
72  check_positive_finite(function, "Second shape parameter", beta);
73  check_not_nan(function, "Random variable", y);
74  check_consistent_sizes(function,
75  "Random variable", y,
76  "First shape parameter", alpha,
77  "Second shape parameter", beta);
78  check_nonnegative(function, "Random variable", y);
79  check_less_or_equal(function, "Random variable", y, 1);
80 
81  // Wrap arguments in vectors
82  VectorView<const T_y> y_vec(y);
83  VectorView<const T_scale_succ> alpha_vec(alpha);
84  VectorView<const T_scale_fail> beta_vec(beta);
85  size_t N = max_size(y, alpha, beta);
86 
88  operands_and_partials(y, alpha, beta);
89 
90  // Explicit return for extreme values
91  // The gradients are technically ill-defined, but treated as zero
92  for (size_t i = 0; i < stan::length(y); i++) {
93  if (value_of(y_vec[i]) <= 0)
94  return operands_and_partials.to_var(0.0, y, alpha, beta);
95  }
96 
97  // Compute CDF and its gradients
99  using stan::math::digamma;
100  using stan::math::lbeta;
101  using std::pow;
102  using std::exp;
103  using std::exp;
104 
105  // Cache a few expensive function calls if alpha or beta is a parameter
107  T_scale_fail>::value,
108  T_partials_return, T_scale_succ, T_scale_fail>
109  digamma_alpha_vec(max_size(alpha, beta));
110 
112  T_scale_fail>::value,
113  T_partials_return, T_scale_succ, T_scale_fail>
114  digamma_beta_vec(max_size(alpha, beta));
115 
117  T_scale_fail>::value,
118  T_partials_return, T_scale_succ, T_scale_fail>
119  digamma_sum_vec(max_size(alpha, beta));
120 
122  for (size_t i = 0; i < N; i++) {
123  const T_partials_return alpha_dbl = value_of(alpha_vec[i]);
124  const T_partials_return beta_dbl = value_of(beta_vec[i]);
125 
126  digamma_alpha_vec[i] = digamma(alpha_dbl);
127  digamma_beta_vec[i] = digamma(beta_dbl);
128  digamma_sum_vec[i] = digamma(alpha_dbl + beta_dbl);
129  }
130  }
131 
132  // Compute vectorized CDF and gradient
133  for (size_t n = 0; n < N; n++) {
134  // Explicit results for extreme values
135  // The gradients are technically ill-defined, but treated as zero
136  if (value_of(y_vec[n]) >= 1.0) continue;
137 
138  // Pull out values
139  const T_partials_return y_dbl = value_of(y_vec[n]);
140  const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
141  const T_partials_return beta_dbl = value_of(beta_vec[n]);
142  const T_partials_return betafunc_dbl = exp(lbeta(alpha_dbl, beta_dbl));
143 
144  // Compute
145  const T_partials_return Pn = inc_beta(alpha_dbl, beta_dbl, y_dbl);
146 
147  P *= Pn;
148 
150  operands_and_partials.d_x1[n] += pow(1-y_dbl, beta_dbl-1)
151  * pow(y_dbl, alpha_dbl-1) / betafunc_dbl / Pn;
152 
153  T_partials_return g1 = 0;
154  T_partials_return g2 = 0;
155 
157  stan::math::grad_reg_inc_beta(g1, g2, alpha_dbl, beta_dbl, y_dbl,
158  digamma_alpha_vec[n],
159  digamma_beta_vec[n], digamma_sum_vec[n],
160  betafunc_dbl);
161  }
162 
164  operands_and_partials.d_x2[n] += g1 / Pn;
166  operands_and_partials.d_x3[n] += g2 / Pn;
167  }
168 
170  for (size_t n = 0; n < stan::length(y); ++n)
171  operands_and_partials.d_x1[n] *= P;
172  }
174  for (size_t n = 0; n < stan::length(alpha); ++n)
175  operands_and_partials.d_x2[n] *= P;
176  }
178  for (size_t n = 0; n < stan::length(beta); ++n)
179  operands_and_partials.d_x3[n] *= P;
180  }
181 
182  return operands_and_partials.to_var(P, y, alpha, beta);
183  }
184 
185  }
186 }
187 #endif
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
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
T_return_type to_var(T_partials_return logp, const T1 &x1=0, const T2 &x2=0, const T3 &x3=0, const T4 &x4=0, const T5 &x5=0, const T6 &x6=0)
VectorView< T_partials_return, is_vector< T1 >::value, is_constant_struct< T1 >::value > d_x1
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
VectorView< T_partials_return, is_vector< T3 >::value, is_constant_struct< T3 >::value > d_x3
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:46
A variable implementation that stores operands and derivatives with respect to the variable...
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.
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.
VectorView< T_partials_return, is_vector< T2 >::value, is_constant_struct< T2 >::value > d_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 metaprogram that takes its argument and allows it to be used like a vector...
Definition: VectorView.hpp:41
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.
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:16

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