Stan Math Library  2.8.0
reverse mode automatic differentiation
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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 
27  namespace math {
28 
29  template <typename T_y, typename T_shape, typename T_scale>
30  typename return_type<T_y, T_shape, T_scale>::type
31  frechet_cdf(const T_y& y, const T_shape& alpha, const T_scale& sigma) {
33  T_partials_return;
34 
35  static const char* function("stan::math::frechet_cdf");
36 
40  using boost::math::tools::promote_args;
42  using std::log;
43  using std::exp;
44 
45  // check if any vectors are zero length
46  if (!(stan::length(y)
47  && stan::length(alpha)
48  && stan::length(sigma)))
49  return 1.0;
50 
51  T_partials_return cdf(1.0);
52  check_positive(function, "Random variable", y);
53  check_positive_finite(function, "Shape parameter", alpha);
54  check_positive_finite(function, "Scale parameter", sigma);
55 
57  operands_and_partials(y, alpha, sigma);
58 
59  VectorView<const T_y> y_vec(y);
60  VectorView<const T_scale> sigma_vec(sigma);
61  VectorView<const T_shape> alpha_vec(alpha);
62  size_t N = max_size(y, sigma, alpha);
63  for (size_t n = 0; n < N; n++) {
64  const T_partials_return y_dbl = value_of(y_vec[n]);
65  const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
66  const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
67  const T_partials_return pow_ = pow(sigma_dbl / y_dbl, alpha_dbl);
68  const T_partials_return cdf_ = exp(-pow_);
69 
70  // cdf
71  cdf *= cdf_;
72 
73  // gradients
75  operands_and_partials.d_x1[n] += pow_ * alpha_dbl / y_dbl;
77  operands_and_partials.d_x2[n] += pow_ * log(y_dbl / sigma_dbl);
79  operands_and_partials.d_x3[n] -= pow_ * alpha_dbl / sigma_dbl;
80  }
81 
83  for (size_t n = 0; n < stan::length(y); ++n)
84  operands_and_partials.d_x1[n] *= cdf;
85  }
87  for (size_t n = 0; n < stan::length(alpha); ++n)
88  operands_and_partials.d_x2[n] *= cdf;
89  }
91  for (size_t n = 0; n < stan::length(sigma); ++n)
92  operands_and_partials.d_x3[n] *= cdf;
93  }
94 
95  return operands_and_partials.to_var(cdf, y, alpha, sigma);
96  }
97  }
98 }
99 #endif
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:15
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
T_return_type to_var(T_partials_return logp, const T1 &x1=0, const T2 &x2=0, const T3 &x3=0, const T4 &x4=0, const T5 &x5=0, const T6 &x6=0)
VectorView< T_partials_return, is_vector< T1 >::value, is_constant_struct< T1 >::value > d_x1
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
VectorView< T_partials_return, is_vector< T3 >::value, is_constant_struct< T3 >::value > d_x3
A variable implementation that stores operands and derivatives with respect to the variable...
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
VectorView< T_partials_return, is_vector< T2 >::value, is_constant_struct< T2 >::value > d_x2
fvar< T > pow(const fvar< T > &x1, const fvar< T > &x2)
Definition: pow.hpp:18
bool check_nonnegative(const char *function, const char *name, const T_y &y)
Return true if y is non-negative.
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:31
VectorView is a template metaprogram that takes its argument and allows it to be used like a vector...
Definition: VectorView.hpp:41
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.

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