Stan Math Library  2.20.0
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 
11 #include <cmath>
12 
13 namespace stan {
14 namespace math {
15 
31 template <typename T_y, typename T_loc, typename T_scale>
33  const T_y& y, const T_loc& mu, const T_scale& beta) {
34  static const char* function = "gumbel_cdf";
36  T_partials_return;
37 
38  using std::exp;
39 
40  T_partials_return cdf(1.0);
41  if (size_zero(y, mu, beta))
42  return cdf;
43 
44  check_not_nan(function, "Random variable", y);
45  check_finite(function, "Location parameter", mu);
46  check_not_nan(function, "Scale parameter", beta);
47  check_positive(function, "Scale parameter", beta);
48  check_consistent_sizes(function, "Random variable", y, "Location parameter",
49  mu, "Scale parameter", beta);
50 
51  operands_and_partials<T_y, T_loc, T_scale> ops_partials(y, mu, beta);
52 
53  scalar_seq_view<T_y> y_vec(y);
54  scalar_seq_view<T_loc> mu_vec(mu);
55  scalar_seq_view<T_scale> beta_vec(beta);
56  size_t N = max_size(y, mu, beta);
57 
58  for (size_t n = 0; n < N; n++) {
59  const T_partials_return y_dbl = value_of(y_vec[n]);
60  const T_partials_return mu_dbl = value_of(mu_vec[n]);
61  const T_partials_return beta_dbl = value_of(beta_vec[n]);
62  const T_partials_return scaled_diff = (y_dbl - mu_dbl) / beta_dbl;
63  const T_partials_return rep_deriv
64  = exp(-scaled_diff - exp(-scaled_diff)) / beta_dbl;
65  const T_partials_return cdf_ = exp(-exp(-scaled_diff));
66  cdf *= cdf_;
67 
69  ops_partials.edge1_.partials_[n] += rep_deriv / cdf_;
71  ops_partials.edge2_.partials_[n] -= rep_deriv / cdf_;
73  ops_partials.edge3_.partials_[n] -= rep_deriv * scaled_diff / cdf_;
74  }
75 
77  for (size_t n = 0; n < stan::length(y); ++n)
78  ops_partials.edge1_.partials_[n] *= cdf;
79  }
81  for (size_t n = 0; n < stan::length(mu); ++n)
82  ops_partials.edge2_.partials_[n] *= cdf;
83  }
85  for (size_t n = 0; n < stan::length(beta); ++n)
86  ops_partials.edge3_.partials_[n] *= cdf;
87  }
88  return ops_partials.build(cdf);
89 }
90 
91 } // namespace math
92 } // namespace stan
93 #endif
void check_finite(const char *function, const char *name, const T_y &y)
Check if y is finite.
boost::math::tools::promote_args< double, typename partials_type< typename scalar_type< T >::type >::type, typename partials_return_type< T_pack... >::type >::type type
T value_of(const fvar< T > &v)
Return the value of the specified variable.
Definition: value_of.hpp:17
Extends std::true_type when instantiated with zero or more template parameters, all of which extend t...
Definition: conjunction.hpp:14
scalar_seq_view provides a uniform sequence-like wrapper around either a scalar or a sequence of scal...
This template builds partial derivatives with respect to a set of operands.
size_t length(const std::vector< T > &x)
Returns the length of the provided std::vector.
Definition: length.hpp:16
bool size_zero(T &x)
Returns 1 if input is of length 0, returns 0 otherwise.
Definition: size_zero.hpp:18
fvar< T > beta(const fvar< T > &x1, const fvar< T > &x2)
Return fvar with the beta function applied to the specified arguments and its gradient.
Definition: beta.hpp:51
boost::math::tools::promote_args< double, typename scalar_type< T >::type, typename return_type< Types_pack... >::type >::type type
Definition: return_type.hpp:36
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:11
void check_not_nan(const char *function, const char *name, const T_y &y)
Check if y is not NaN.
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:32
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
T_return_type build(double value)
Build the node to be stored on the autodiff graph.
internal::ops_partials_edge< double, Op2 > edge2_
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.
internal::ops_partials_edge< double, Op3 > edge3_
internal::ops_partials_edge< double, Op1 > edge1_

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