Stan Math Library  2.12.0
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 
4 #include <boost/random/weibull_distribution.hpp>
5 #include <boost/random/variate_generator.hpp>
23 #include <cmath>
24 
25 namespace stan {
26  namespace math {
27 
28  template <typename T_y, typename T_shape, typename T_scale>
29  typename return_type<T_y, T_shape, T_scale>::type
30  frechet_cdf(const T_y& y, const T_shape& alpha, const T_scale& sigma) {
32  T_partials_return;
33 
34  static const char* function("frechet_cdf");
35 
36  using boost::math::tools::promote_args;
37  using std::log;
38  using std::exp;
39 
40  if (!(stan::length(y)
41  && stan::length(alpha)
42  && stan::length(sigma)))
43  return 1.0;
44 
45  T_partials_return cdf(1.0);
46  check_positive(function, "Random variable", y);
47  check_positive_finite(function, "Shape parameter", alpha);
48  check_positive_finite(function, "Scale parameter", sigma);
49 
51  operands_and_partials(y, alpha, sigma);
52 
53  VectorView<const T_y> y_vec(y);
54  VectorView<const T_scale> sigma_vec(sigma);
55  VectorView<const T_shape> alpha_vec(alpha);
56  size_t N = max_size(y, sigma, alpha);
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 sigma_dbl = value_of(sigma_vec[n]);
60  const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
61  const T_partials_return pow_ = pow(sigma_dbl / y_dbl, alpha_dbl);
62  const T_partials_return cdf_ = exp(-pow_);
63 
64  cdf *= cdf_;
65 
67  operands_and_partials.d_x1[n] += pow_ * alpha_dbl / y_dbl;
69  operands_and_partials.d_x2[n] += pow_ * log(y_dbl / sigma_dbl);
71  operands_and_partials.d_x3[n] -= pow_ * alpha_dbl / sigma_dbl;
72  }
73 
75  for (size_t n = 0; n < stan::length(y); ++n)
76  operands_and_partials.d_x1[n] *= cdf;
77  }
79  for (size_t n = 0; n < stan::length(alpha); ++n)
80  operands_and_partials.d_x2[n] *= cdf;
81  }
83  for (size_t n = 0; n < stan::length(sigma); ++n)
84  operands_and_partials.d_x3[n] *= cdf;
85  }
86  return operands_and_partials.value(cdf);
87  }
88 
89  }
90 }
91 #endif
VectorView< T_return_type, false, true > d_x2
T value_of(const fvar< T > &v)
Return the value of the specified variable.
Definition: value_of.hpp:16
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:14
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
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
This class builds partial derivatives with respect to a set of operands.
VectorView< T_return_type, false, true > d_x3
bool check_positive(const char *function, const char *name, const T_y &y)
Return true if y is positive.
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
fvar< T > pow(const fvar< T > &x1, const fvar< T > &x2)
Definition: pow.hpp:17
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:30
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
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
bool check_positive_finite(const char *function, const char *name, const T_y &y)
Return true if y is positive and finite.
VectorView< T_return_type, false, true > d_x1

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