Stan Math Library  2.15.0
reverse mode automatic differentiation
weibull_lcdf.hpp
Go to the documentation of this file.
1 #ifndef STAN_MATH_PRIM_SCAL_PROB_WEIBULL_LCDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_WEIBULL_LCDF_HPP
3 
19 #include <boost/random/weibull_distribution.hpp>
20 #include <boost/random/variate_generator.hpp>
21 #include <cmath>
22 
23 namespace stan {
24  namespace math {
25 
40  template <typename T_y, typename T_shape, typename T_scale>
42  weibull_lcdf(const T_y& y, const T_shape& alpha, const T_scale& sigma) {
44  T_partials_return;
45 
46  static const char* function("weibull_lcdf");
47 
48  using boost::math::tools::promote_args;
49  using std::log;
50  using std::exp;
51 
52  if (!(stan::length(y)
53  && stan::length(alpha)
54  && stan::length(sigma)))
55  return 0.0;
56 
57  T_partials_return cdf_log(0.0);
58  check_nonnegative(function, "Random variable", y);
59  check_positive_finite(function, "Shape parameter", alpha);
60  check_positive_finite(function, "Scale parameter", sigma);
61 
63  operands_and_partials(y, alpha, sigma);
64 
66  scalar_seq_view<const T_scale> sigma_vec(sigma);
67  scalar_seq_view<const T_shape> alpha_vec(alpha);
68  size_t N = max_size(y, sigma, alpha);
69  for (size_t n = 0; n < N; n++) {
70  const T_partials_return y_dbl = value_of(y_vec[n]);
71  const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
72  const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
73  const T_partials_return pow_ = pow(y_dbl / sigma_dbl, alpha_dbl);
74  const T_partials_return exp_ = exp(-pow_);
75  const T_partials_return cdf_ = 1.0 - exp_;
76 
77  cdf_log += log(cdf_);
78 
79  const T_partials_return rep_deriv = pow_ / (1.0 / exp_ - 1.0);
81  operands_and_partials.d_x1[n] += rep_deriv * alpha_dbl / y_dbl;
83  operands_and_partials.d_x2[n] += rep_deriv * log(y_dbl / sigma_dbl);
85  operands_and_partials.d_x3[n] -= rep_deriv * alpha_dbl / sigma_dbl;
86  }
87  return operands_and_partials.value(cdf_log);
88  }
89 
90  }
91 }
92 #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.
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
void check_nonnegative(const char *function, const char *name, const T_y &y)
Check if y is non-negative.
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...
void check_positive_finite(const char *function, const char *name, const T_y &y)
Check if y is positive and finite.
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
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
return_type< T_y, T_shape, T_scale >::type weibull_lcdf(const T_y &y, const T_shape &alpha, const T_scale &sigma)
Returns the Weibull log cumulative distribution function for the given location and scale...
fvar< T > pow(const fvar< T > &x1, const fvar< T > &x2)
Definition: pow.hpp:17
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

     [ Stan Home Page ] © 2011–2016, Stan Development Team.