Stan Math Library  2.20.0
reverse mode automatic differentiation
frechet_cdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_FRECHET_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_FRECHET_CDF_HPP
3 
5 #include <boost/random/weibull_distribution.hpp>
6 #include <boost/random/variate_generator.hpp>
17 #include <cmath>
18 
19 namespace stan {
20 namespace math {
21 
22 template <typename T_y, typename T_shape, typename T_scale>
24  const T_y& y, const T_shape& alpha, const T_scale& sigma) {
26  T_partials_return;
27 
28  static const char* function = "frechet_cdf";
29 
30  using boost::math::tools::promote_args;
31  using std::exp;
32  using std::log;
33 
34  if (size_zero(y, alpha, sigma))
35  return 1.0;
36 
37  T_partials_return cdf(1.0);
38  check_positive(function, "Random variable", y);
39  check_positive_finite(function, "Shape parameter", alpha);
40  check_positive_finite(function, "Scale parameter", sigma);
41 
42  operands_and_partials<T_y, T_shape, T_scale> ops_partials(y, alpha, sigma);
43 
44  scalar_seq_view<T_y> y_vec(y);
45  scalar_seq_view<T_scale> sigma_vec(sigma);
46  scalar_seq_view<T_shape> alpha_vec(alpha);
47  size_t N = max_size(y, sigma, alpha);
48  for (size_t n = 0; n < N; n++) {
49  const T_partials_return y_dbl = value_of(y_vec[n]);
50  const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
51  const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
52  const T_partials_return pow_ = pow(sigma_dbl / y_dbl, alpha_dbl);
53  const T_partials_return cdf_ = exp(-pow_);
54 
55  cdf *= cdf_;
56 
58  ops_partials.edge1_.partials_[n] += pow_ * alpha_dbl / y_dbl;
60  ops_partials.edge2_.partials_[n] += pow_ * log(y_dbl / sigma_dbl);
62  ops_partials.edge3_.partials_[n] -= pow_ * alpha_dbl / sigma_dbl;
63  }
64 
66  for (size_t n = 0; n < stan::length(y); ++n)
67  ops_partials.edge1_.partials_[n] *= cdf;
68  }
70  for (size_t n = 0; n < stan::length(alpha); ++n)
71  ops_partials.edge2_.partials_[n] *= cdf;
72  }
74  for (size_t n = 0; n < stan::length(sigma); ++n)
75  ops_partials.edge3_.partials_[n] *= cdf;
76  }
77  return ops_partials.build(cdf);
78 }
79 
80 } // namespace math
81 } // namespace stan
82 #endif
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
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:12
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
void check_positive_finite(const char *function, const char *name, const T_y &y)
Check if y is positive and finite.
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
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.
fvar< T > pow(const fvar< T > &x1, const fvar< T > &x2)
Definition: pow.hpp:16
return_type< T_y, T_shape, T_scale >::type frechet_cdf(const T_y &y, const T_shape &alpha, const T_scale &sigma)
Definition: frechet_cdf.hpp:23
internal::ops_partials_edge< double, Op3 > edge3_
internal::ops_partials_edge< double, Op1 > edge1_

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