Stan Math Library  2.20.0
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 
9 #include <cmath>
10 
11 namespace stan {
12 namespace math {
13 
28 template <typename T_y, typename T_shape, typename T_scale>
30  const T_y& y, const T_shape& alpha, const T_scale& sigma) {
32  T_partials_return;
33 
34  static const char* function = "weibull_cdf";
35 
36  using std::exp;
37  using std::log;
38 
39  if (size_zero(y, alpha, sigma))
40  return 1.0;
41 
42  T_partials_return cdf(1.0);
43  check_nonnegative(function, "Random variable", y);
44  check_positive_finite(function, "Shape parameter", alpha);
45  check_positive_finite(function, "Scale parameter", sigma);
46 
47  operands_and_partials<T_y, T_shape, T_scale> ops_partials(y, alpha, sigma);
48 
49  scalar_seq_view<T_y> y_vec(y);
50  scalar_seq_view<T_scale> sigma_vec(sigma);
51  scalar_seq_view<T_shape> alpha_vec(alpha);
52  size_t N = max_size(y, sigma, alpha);
53  for (size_t n = 0; n < N; n++) {
54  const T_partials_return y_dbl = value_of(y_vec[n]);
55  const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
56  const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
57  const T_partials_return pow_ = pow(y_dbl / sigma_dbl, alpha_dbl);
58  const T_partials_return exp_ = exp(-pow_);
59  const T_partials_return cdf_ = 1.0 - exp_;
60 
61  cdf *= cdf_;
62 
63  const T_partials_return rep_deriv = exp_ * pow_ / cdf_;
65  ops_partials.edge1_.partials_[n] += rep_deriv * alpha_dbl / y_dbl;
67  ops_partials.edge2_.partials_[n] += rep_deriv * log(y_dbl / sigma_dbl);
69  ops_partials.edge3_.partials_[n] -= rep_deriv * alpha_dbl / sigma_dbl;
70  }
71 
73  for (size_t n = 0; n < stan::length(y); ++n)
74  ops_partials.edge1_.partials_[n] *= cdf;
75  }
77  for (size_t n = 0; n < stan::length(alpha); ++n)
78  ops_partials.edge2_.partials_[n] *= cdf;
79  }
81  for (size_t n = 0; n < stan::length(sigma); ++n)
82  ops_partials.edge3_.partials_[n] *= cdf;
83  }
84  return ops_partials.build(cdf);
85 }
86 
87 } // namespace math
88 } // namespace stan
89 #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
return_type< T_y, T_shape, T_scale >::type weibull_cdf(const T_y &y, const T_shape &alpha, const T_scale &sigma)
Returns the Weibull cumulative distribution function for the given location and scale.
Definition: weibull_cdf.hpp:29
bool size_zero(T &x)
Returns 1 if input is of length 0, returns 0 otherwise.
Definition: size_zero.hpp:18
void check_nonnegative(const char *function, const char *name, const T_y &y)
Check if y is non-negative.
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_
fvar< T > pow(const fvar< T > &x1, const fvar< T > &x2)
Definition: pow.hpp:16
internal::ops_partials_edge< double, Op3 > edge3_
internal::ops_partials_edge< double, Op1 > edge1_

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