Stan Math Library  2.20.0
reverse mode automatic differentiation
pareto_type_2_cdf.hpp
Go to the documentation of this file.
1 #ifndef STAN_MATH_PRIM_SCAL_PROB_PARETO_TYPE_2_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_PARETO_TYPE_2_CDF_HPP
3 
12 #include <cmath>
13 
14 namespace stan {
15 namespace math {
16 
17 template <typename T_y, typename T_loc, typename T_scale, typename T_shape>
19  const T_y& y, const T_loc& mu, const T_scale& lambda,
20  const T_shape& alpha) {
21  typedef
23  T_partials_return;
24 
25  if (size_zero(y, mu, lambda, alpha))
26  return 1.0;
27 
28  static const char* function = "pareto_type_2_cdf";
29 
30  using std::log;
31 
32  T_partials_return P(1.0);
33 
34  check_greater_or_equal(function, "Random variable", y, mu);
35  check_not_nan(function, "Random variable", y);
36  check_nonnegative(function, "Random variable", y);
37  check_positive_finite(function, "Scale parameter", lambda);
38  check_positive_finite(function, "Shape parameter", alpha);
39  check_consistent_sizes(function, "Random variable", y, "Scale parameter",
40  lambda, "Shape parameter", alpha);
41 
42  scalar_seq_view<T_y> y_vec(y);
43  scalar_seq_view<T_loc> mu_vec(mu);
44  scalar_seq_view<T_scale> lambda_vec(lambda);
45  scalar_seq_view<T_shape> alpha_vec(alpha);
46  size_t N = max_size(y, mu, lambda, alpha);
47 
49  y, mu, lambda, alpha);
50 
52  p1_pow_alpha(N);
53 
55  T_y, T_loc, T_scale, T_shape>
56  grad_1_2(N);
57 
59  T_loc, T_scale, T_shape>
60  grad_3(N);
61 
62  for (size_t i = 0; i < N; i++) {
63  const T_partials_return lambda_dbl = value_of(lambda_vec[i]);
64  const T_partials_return alpha_dbl = value_of(alpha_vec[i]);
65  const T_partials_return temp
66  = 1 + (value_of(y_vec[i]) - value_of(mu_vec[i])) / lambda_dbl;
67  p1_pow_alpha[i] = pow(temp, -alpha_dbl);
68 
70  grad_1_2[i] = p1_pow_alpha[i] / temp * alpha_dbl / lambda_dbl;
71 
73  grad_3[i] = log(temp) * p1_pow_alpha[i];
74  }
75 
76  for (size_t n = 0; n < N; n++) {
77  const T_partials_return y_dbl = value_of(y_vec[n]);
78  const T_partials_return mu_dbl = value_of(mu_vec[n]);
79  const T_partials_return lambda_dbl = value_of(lambda_vec[n]);
80 
81  const T_partials_return Pn = 1.0 - p1_pow_alpha[n];
82 
83  P *= Pn;
84 
86  ops_partials.edge1_.partials_[n] += grad_1_2[n] / Pn;
88  ops_partials.edge2_.partials_[n] -= grad_1_2[n] / Pn;
90  ops_partials.edge3_.partials_[n]
91  += (mu_dbl - y_dbl) * grad_1_2[n] / lambda_dbl / Pn;
93  ops_partials.edge4_.partials_[n] += grad_3[n] / Pn;
94  }
95 
97  for (size_t n = 0; n < stan::length(y); ++n)
98  ops_partials.edge1_.partials_[n] *= P;
99  }
101  for (size_t n = 0; n < stan::length(mu); ++n)
102  ops_partials.edge2_.partials_[n] *= P;
103  }
105  for (size_t n = 0; n < stan::length(lambda); ++n)
106  ops_partials.edge3_.partials_[n] *= P;
107  }
109  for (size_t n = 0; n < stan::length(alpha); ++n)
110  ops_partials.edge4_.partials_[n] *= P;
111  }
112  return ops_partials.build(P);
113 }
114 
115 } // namespace math
116 } // namespace stan
117 #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
internal::ops_partials_edge< double, Op4 > edge4_
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_loc, T_scale, T_shape >::type pareto_type_2_cdf(const T_y &y, const T_loc &mu, const T_scale &lambda, const T_shape &alpha)
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_greater_or_equal(const char *function, const char *name, const T_y &y, const T_low &low)
Check if y is greater or equal than low.
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
void check_not_nan(const char *function, const char *name, const T_y &y)
Check if y is not NaN.
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.
internal::ops_partials_edge< double, Op3 > edge3_
internal::ops_partials_edge< double, Op1 > edge1_

     [ Stan Home Page ] © 2011–2018, Stan Development Team.