Stan Math Library  2.14.0
reverse mode automatic differentiation
gumbel_cdf.hpp
Go to the documentation of this file.
1 #ifndef STAN_MATH_PRIM_SCAL_PROB_GUMBEL_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_GUMBEL_CDF_HPP
3 
4 #include <boost/random/uniform_01.hpp>
5 #include <boost/random/variate_generator.hpp>
20 #include <cmath>
21 
22 namespace stan {
23  namespace math {
24 
25  template <typename T_y, typename T_loc, typename T_scale>
27  gumbel_cdf(const T_y& y, const T_loc& mu, const T_scale& beta) {
28  static const char* function("gumbel_cdf");
30  T_partials_return;
31 
32  using std::exp;
33 
34  T_partials_return cdf(1.0);
35  if (!(stan::length(y)
36  && stan::length(mu)
37  && stan::length(beta)))
38  return cdf;
39 
40  check_not_nan(function, "Random variable", y);
41  check_finite(function, "Location parameter", mu);
42  check_not_nan(function, "Scale parameter", beta);
43  check_positive(function, "Scale parameter", beta);
44  check_consistent_sizes(function,
45  "Random variable", y,
46  "Location parameter", mu,
47  "Scale parameter", beta);
48 
50  operands_and_partials(y, mu, beta);
51 
52  VectorView<const T_y> y_vec(y);
53  VectorView<const T_loc> mu_vec(mu);
54  VectorView<const T_scale> beta_vec(beta);
55  size_t N = max_size(y, mu, beta);
56 
57  for (size_t n = 0; n < N; n++) {
58  const T_partials_return y_dbl = value_of(y_vec[n]);
59  const T_partials_return mu_dbl = value_of(mu_vec[n]);
60  const T_partials_return beta_dbl = value_of(beta_vec[n]);
61  const T_partials_return scaled_diff = (y_dbl - mu_dbl) / beta_dbl;
62  const T_partials_return rep_deriv = exp(-scaled_diff
63  - exp(-scaled_diff))
64  / beta_dbl;
65  const T_partials_return cdf_ = exp(-exp(-scaled_diff));
66  cdf *= cdf_;
67 
69  operands_and_partials.d_x1[n] += rep_deriv / cdf_;
71  operands_and_partials.d_x2[n] -= rep_deriv / cdf_;
73  operands_and_partials.d_x3[n] -= rep_deriv * scaled_diff / cdf_;
74  }
75 
77  for (size_t n = 0; n < stan::length(y); ++n)
78  operands_and_partials.d_x1[n] *= cdf;
79  }
81  for (size_t n = 0; n < stan::length(mu); ++n)
82  operands_and_partials.d_x2[n] *= cdf;
83  }
85  for (size_t n = 0; n < stan::length(beta); ++n)
86  operands_and_partials.d_x3[n] *= cdf;
87  }
88  return operands_and_partials.value(cdf);
89  }
90 
91  }
92 }
93 #endif
94 
VectorView< T_return_type, false, true > d_x2
void check_finite(const char *function, const char *name, const T_y &y)
Check if y is finite.
T value_of(const fvar< T > &v)
Return the value of the specified variable.
Definition: value_of.hpp:16
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
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 > exp(const fvar< T > &x)
Definition: exp.hpp:10
void check_not_nan(const char *function, const char *name, const T_y &y)
Check if y is not NaN.
This class builds partial derivatives with respect to a set of operands.
VectorView< T_return_type, false, true > d_x3
return_type< T_y, T_loc, T_scale >::type gumbel_cdf(const T_y &y, const T_loc &mu, const T_scale &beta)
Definition: gumbel_cdf.hpp:27
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
void check_positive(const char *function, const char *name, const T_y &y)
Check if y is positive.
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.
boost::math::tools::promote_args< typename partials_type< typename scalar_type< T1 >::type >::type, typename partials_type< typename scalar_type< T2 >::type >::type, typename partials_type< typename scalar_type< T3 >::type >::type, typename partials_type< typename scalar_type< T4 >::type >::type, typename partials_type< typename scalar_type< T5 >::type >::type, typename partials_type< typename scalar_type< T6 >::type >::type >::type type
VectorView< T_return_type, false, true > d_x1

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