Stan Math Library  2.20.0
reverse mode automatic differentiation
weibull_lpdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_WEIBULL_LPDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_WEIBULL_LPDF_HPP
3 
11 #include <cmath>
12 
13 namespace stan {
14 namespace math {
15 
30 template <bool propto, typename T_y, typename T_shape, typename T_scale>
32  const T_y& y, const T_shape& alpha, const T_scale& sigma) {
33  static const char* function = "weibull_lpdf";
35  T_partials_return;
36 
37  using std::log;
38  check_finite(function, "Random variable", y);
39  check_positive_finite(function, "Shape parameter", alpha);
40  check_positive_finite(function, "Scale parameter", sigma);
41  check_consistent_sizes(function, "Random variable", y, "Shape parameter",
42  alpha, "Scale parameter", sigma);
43  if (size_zero(y, alpha, sigma))
44  return 0;
46  return 0;
47 
48  T_partials_return logp(0);
49  scalar_seq_view<T_y> y_vec(y);
50  scalar_seq_view<T_shape> alpha_vec(alpha);
51  scalar_seq_view<T_scale> sigma_vec(sigma);
52  size_t N = max_size(y, alpha, sigma);
53 
54  for (size_t n = 0; n < N; n++) {
55  const T_partials_return y_dbl = value_of(y_vec[n]);
56  if (y_dbl < 0)
57  return LOG_ZERO;
58  }
59 
61  T_shape>
62  log_alpha(length(alpha));
63  for (size_t i = 0; i < length(alpha); i++)
65  log_alpha[i] = log(value_of(alpha_vec[i]));
66 
68  T_y>
69  log_y(length(y));
70  for (size_t i = 0; i < length(y); i++)
72  log_y[i] = log(value_of(y_vec[i]));
73 
75  T_partials_return, T_scale>
76  log_sigma(length(sigma));
77  for (size_t i = 0; i < length(sigma); i++)
79  log_sigma[i] = log(value_of(sigma_vec[i]));
80 
82  T_partials_return, T_scale>
83  inv_sigma(length(sigma));
84  for (size_t i = 0; i < length(sigma); i++)
86  inv_sigma[i] = 1.0 / value_of(sigma_vec[i]);
87 
89  T_partials_return, T_y, T_shape, T_scale>
90  y_div_sigma_pow_alpha(N);
91  for (size_t i = 0; i < N; i++)
93  const T_partials_return y_dbl = value_of(y_vec[i]);
94  const T_partials_return alpha_dbl = value_of(alpha_vec[i]);
95  y_div_sigma_pow_alpha[i] = pow(y_dbl * inv_sigma[i], alpha_dbl);
96  }
97 
98  operands_and_partials<T_y, T_shape, T_scale> ops_partials(y, alpha, sigma);
99  for (size_t n = 0; n < N; n++) {
100  const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
102  logp += log_alpha[n];
104  logp += (alpha_dbl - 1.0) * log_y[n];
106  logp -= alpha_dbl * log_sigma[n];
108  logp -= y_div_sigma_pow_alpha[n];
109 
111  const T_partials_return inv_y = 1.0 / value_of(y_vec[n]);
112  ops_partials.edge1_.partials_[n]
113  += (alpha_dbl - 1.0) * inv_y
114  - alpha_dbl * y_div_sigma_pow_alpha[n] * inv_y;
115  }
117  ops_partials.edge2_.partials_[n]
118  += 1.0 / alpha_dbl
119  + (1.0 - y_div_sigma_pow_alpha[n]) * (log_y[n] - log_sigma[n]);
121  ops_partials.edge3_.partials_[n]
122  += alpha_dbl * inv_sigma[n] * (y_div_sigma_pow_alpha[n] - 1.0);
123  }
124  return ops_partials.build(logp);
125 }
126 
127 template <typename T_y, typename T_shape, typename T_scale>
129  const T_y& y, const T_shape& alpha, const T_scale& sigma) {
130  return weibull_lpdf<false>(y, alpha, sigma);
131 }
132 
133 } // namespace math
134 } // namespace stan
135 #endif
void check_finite(const char *function, const char *name, const T_y &y)
Check if y is finite.
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
bool size_zero(T &x)
Returns 1 if input is of length 0, returns 0 otherwise.
Definition: size_zero.hpp:18
const double LOG_ZERO
Definition: constants.hpp:150
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) prob...
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
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.
VectorBuilder allocates type T1 values to be used as intermediate values.
internal::ops_partials_edge< double, Op2 > edge2_
fvar< T > pow(const fvar< T > &x1, const fvar< T > &x2)
Definition: pow.hpp:16
void check_consistent_sizes(const char *function, const char *name1, const T1 &x1, const char *name2, const T2 &x2)
Check if the dimension of x1 is consistent with x2.
return_type< T_y, T_shape, T_scale >::type weibull_lpdf(const T_y &y, const T_shape &alpha, const T_scale &sigma)
Returns the Weibull log probability density for the given location and scale.
internal::ops_partials_edge< double, Op3 > edge3_
internal::ops_partials_edge< double, Op1 > edge1_

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