Stan Math Library  2.11.0
reverse mode automatic differentiation
weibull_cdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_WEIBULL_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_WEIBULL_CDF_HPP
3 
19 #include <boost/random/weibull_distribution.hpp>
20 #include <boost/random/variate_generator.hpp>
21 #include <cmath>
22 
23 namespace stan {
24 
25  namespace math {
26 
27  template <typename T_y, typename T_shape, typename T_scale>
28  typename return_type<T_y, T_shape, T_scale>::type
29  weibull_cdf(const T_y& y, const T_shape& alpha, const T_scale& sigma) {
31  T_partials_return;
32 
33  static const char* function("stan::math::weibull_cdf");
34 
37  using boost::math::tools::promote_args;
39  using std::log;
40  using std::exp;
41 
42  // check if any vectors are zero length
43  if (!(stan::length(y)
44  && stan::length(alpha)
45  && stan::length(sigma)))
46  return 1.0;
47 
48  T_partials_return cdf(1.0);
49  check_nonnegative(function, "Random variable", y);
50  check_positive_finite(function, "Shape parameter", alpha);
51  check_positive_finite(function, "Scale parameter", sigma);
52 
54  operands_and_partials(y, alpha, sigma);
55 
56  VectorView<const T_y> y_vec(y);
57  VectorView<const T_scale> sigma_vec(sigma);
58  VectorView<const T_shape> alpha_vec(alpha);
59  size_t N = max_size(y, sigma, alpha);
60  for (size_t n = 0; n < N; n++) {
61  const T_partials_return y_dbl = value_of(y_vec[n]);
62  const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
63  const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
64  const T_partials_return pow_ = pow(y_dbl / sigma_dbl, alpha_dbl);
65  const T_partials_return exp_ = exp(-pow_);
66  const T_partials_return cdf_ = 1.0 - exp_;
67 
68  // cdf
69  cdf *= cdf_;
70 
71  // gradients
72  const T_partials_return rep_deriv = exp_ * pow_ / cdf_;
74  operands_and_partials.d_x1[n] += rep_deriv * alpha_dbl / y_dbl;
76  operands_and_partials.d_x2[n] += rep_deriv * log(y_dbl / sigma_dbl);
78  operands_and_partials.d_x3[n] -= rep_deriv * alpha_dbl / sigma_dbl;
79  }
80 
82  for (size_t n = 0; n < stan::length(y); ++n)
83  operands_and_partials.d_x1[n] *= cdf;
84  }
86  for (size_t n = 0; n < stan::length(alpha); ++n)
87  operands_and_partials.d_x2[n] *= cdf;
88  }
90  for (size_t n = 0; n < stan::length(sigma); ++n)
91  operands_and_partials.d_x3[n] *= cdf;
92  }
93 
94  return operands_and_partials.value(cdf);
95  }
96  }
97 }
98 #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:15
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
return_type< T_y, T_shape, T_scale >::type weibull_cdf(const T_y &y, const T_shape &alpha, const T_scale &sigma)
Definition: weibull_cdf.hpp:29
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
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:18
bool check_nonnegative(const char *function, const char *name, const T_y &y)
Return true if y is non-negative.
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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