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reverse mode automatic differentiation
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beta_cdf_log.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_BETA_CDF_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_BETA_CDF_LOG_HPP
3 
4 #include <boost/math/special_functions/gamma.hpp>
5 #include <boost/random/gamma_distribution.hpp>
6 #include <boost/random/variate_generator.hpp>
25 #include <cmath>
26 
27 namespace stan {
28 
29  namespace math {
30 
31  template <typename T_y, typename T_scale_succ, typename T_scale_fail>
32  typename return_type<T_y, T_scale_succ, T_scale_fail>::type
33  beta_cdf_log(const T_y& y, const T_scale_succ& alpha,
34  const T_scale_fail& beta) {
35  typedef typename stan::partials_return_type<T_y, T_scale_succ,
36  T_scale_fail>::type
37  T_partials_return;
38 
39  // Size checks
40  if ( !( stan::length(y) && stan::length(alpha)
41  && stan::length(beta) ) )
42  return 0.0;
43 
44  // Error checks
45  static const char* function("stan::math::beta_cdf");
46 
51  using boost::math::tools::promote_args;
54 
55  T_partials_return cdf_log(0.0);
56 
57  check_positive_finite(function, "First shape parameter", alpha);
58  check_positive_finite(function, "Second shape parameter", beta);
59  check_not_nan(function, "Random variable", y);
60  check_nonnegative(function, "Random variable", y);
61  check_less_or_equal(function, "Random variable", y, 1);
62  check_consistent_sizes(function,
63  "Random variable", y,
64  "First shape parameter", alpha,
65  "Second shape parameter", beta);
66 
67  // Wrap arguments in vectors
68  VectorView<const T_y> y_vec(y);
69  VectorView<const T_scale_succ> alpha_vec(alpha);
70  VectorView<const T_scale_fail> beta_vec(beta);
71  size_t N = max_size(y, alpha, beta);
72 
74  operands_and_partials(y, alpha, beta);
75 
76  // Compute CDF and its gradients
78  using stan::math::digamma;
79  using stan::math::lbeta;
80  using std::pow;
81  using std::exp;
82  using std::log;
83  using std::exp;
84 
85  // Cache a few expensive function calls if alpha or beta is a parameter
87  T_scale_fail>::value,
88  T_partials_return, T_scale_succ, T_scale_fail>
89  digamma_alpha_vec(max_size(alpha, beta));
90 
92  T_scale_fail>::value,
93  T_partials_return, T_scale_succ, T_scale_fail>
94  digamma_beta_vec(max_size(alpha, beta));
95 
97  T_scale_fail>::value,
98  T_partials_return, T_scale_succ, T_scale_fail>
99  digamma_sum_vec(max_size(alpha, beta));
100 
102  for (size_t i = 0; i < N; i++) {
103  const T_partials_return alpha_dbl = value_of(alpha_vec[i]);
104  const T_partials_return beta_dbl = value_of(beta_vec[i]);
105 
106  digamma_alpha_vec[i] = digamma(alpha_dbl);
107  digamma_beta_vec[i] = digamma(beta_dbl);
108  digamma_sum_vec[i] = digamma(alpha_dbl + beta_dbl);
109  }
110  }
111 
112  // Compute vectorized CDFLog and gradient
113  for (size_t n = 0; n < N; n++) {
114  // Pull out values
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  // Compute
120  const T_partials_return Pn = inc_beta(alpha_dbl, beta_dbl, y_dbl);
121 
122  cdf_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  stan::math::grad_reg_inc_beta(g1, g2, alpha_dbl, beta_dbl, y_dbl,
133  digamma_alpha_vec[n],
134  digamma_beta_vec[n], digamma_sum_vec[n],
135  betafunc_dbl);
136  }
138  operands_and_partials.d_x2[n] += g1 / Pn;
140  operands_and_partials.d_x3[n] += g2 / Pn;
141  }
142 
143  return operands_and_partials.to_var(cdf_log, y, alpha, beta);
144  }
145 
146  }
147 }
148 #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
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:15
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
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
return_type< T_y, T_scale_succ, T_scale_fail >::type beta_cdf_log(const T_y &y, const T_scale_succ &alpha, const T_scale_fail &beta)
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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