Stan Math Library  2.15.0
reverse mode automatic differentiation
gumbel_cdf.hpp
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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 
40  template <typename T_y, typename T_loc, typename T_scale>
42  gumbel_cdf(const T_y& y, const T_loc& mu, const T_scale& beta) {
43  static const char* function("gumbel_cdf");
45  T_partials_return;
46 
47  using std::exp;
48 
49  T_partials_return cdf(1.0);
50  if (!(stan::length(y)
51  && stan::length(mu)
52  && stan::length(beta)))
53  return cdf;
54 
55  check_not_nan(function, "Random variable", y);
56  check_finite(function, "Location parameter", mu);
57  check_not_nan(function, "Scale parameter", beta);
58  check_positive(function, "Scale parameter", beta);
59  check_consistent_sizes(function,
60  "Random variable", y,
61  "Location parameter", mu,
62  "Scale parameter", beta);
63 
65  operands_and_partials(y, mu, beta);
66 
69  scalar_seq_view<const T_scale> beta_vec(beta);
70  size_t N = max_size(y, mu, beta);
71 
72  for (size_t n = 0; n < N; n++) {
73  const T_partials_return y_dbl = value_of(y_vec[n]);
74  const T_partials_return mu_dbl = value_of(mu_vec[n]);
75  const T_partials_return beta_dbl = value_of(beta_vec[n]);
76  const T_partials_return scaled_diff = (y_dbl - mu_dbl) / beta_dbl;
77  const T_partials_return rep_deriv = exp(-scaled_diff
78  - exp(-scaled_diff))
79  / beta_dbl;
80  const T_partials_return cdf_ = exp(-exp(-scaled_diff));
81  cdf *= cdf_;
82 
84  operands_and_partials.d_x1[n] += rep_deriv / cdf_;
86  operands_and_partials.d_x2[n] -= rep_deriv / cdf_;
88  operands_and_partials.d_x3[n] -= rep_deriv * scaled_diff / cdf_;
89  }
90 
92  for (size_t n = 0; n < stan::length(y); ++n)
93  operands_and_partials.d_x1[n] *= cdf;
94  }
96  for (size_t n = 0; n < stan::length(mu); ++n)
97  operands_and_partials.d_x2[n] *= cdf;
98  }
100  for (size_t n = 0; n < stan::length(beta); ++n)
101  operands_and_partials.d_x3[n] *= cdf;
102  }
103  return operands_and_partials.value(cdf);
104  }
105 
106  }
107 }
108 #endif
109 
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.
scalar_seq_view provides a uniform sequence-like wrapper around either a scalar or a sequence of scal...
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)
Returns the Gumbel distribution cumulative distribution for the given location and scale...
Definition: gumbel_cdf.hpp:42
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.
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

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