Stan Math Library  2.20.0
reverse mode automatic differentiation
pareto_type_2_lcdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_PARETO_TYPE_2_LCDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_PARETO_TYPE_2_LCDF_HPP
3 
13 #include <cmath>
14 
15 namespace stan {
16 namespace math {
17 
18 template <typename T_y, typename T_loc, typename T_scale, typename T_shape>
20  const T_y& y, const T_loc& mu, const T_scale& lambda,
21  const T_shape& alpha) {
22  typedef
24  T_partials_return;
25 
26  if (size_zero(y, mu, lambda, alpha))
27  return 0.0;
28 
29  static const char* function = "pareto_type_2_lcdf";
30 
31  using std::log;
32 
33  T_partials_return P(0.0);
34 
35  check_greater_or_equal(function, "Random variable", y, mu);
36  check_not_nan(function, "Random variable", y);
37  check_nonnegative(function, "Random variable", y);
38  check_positive_finite(function, "Scale parameter", lambda);
39  check_positive_finite(function, "Shape parameter", alpha);
40  check_consistent_sizes(function, "Random variable", y, "Scale parameter",
41  lambda, "Shape parameter", alpha);
42 
43  scalar_seq_view<T_y> y_vec(y);
44  scalar_seq_view<T_loc> mu_vec(mu);
45  scalar_seq_view<T_scale> lambda_vec(lambda);
46  scalar_seq_view<T_shape> alpha_vec(alpha);
47  size_t N = max_size(y, mu, lambda, alpha);
48 
50  y, mu, lambda, alpha);
51 
53  N);
54 
56  inv_p1_pow_alpha_minus_one(N);
57 
58  VectorBuilder<!is_constant_all<T_shape>::value, T_partials_return, T_y, T_loc,
59  T_scale, T_shape>
60  log_1p_y_over_lambda(N);
61 
62  for (size_t i = 0; i < N; i++) {
63  const T_partials_return temp = 1.0
64  + (value_of(y_vec[i]) - value_of(mu_vec[i]))
65  / value_of(lambda_vec[i]);
66  const T_partials_return p1_pow_alpha = pow(temp, value_of(alpha_vec[i]));
67  cdf_log[i] = log1m(1.0 / p1_pow_alpha);
68 
69  inv_p1_pow_alpha_minus_one[i] = 1.0 / (p1_pow_alpha - 1.0);
70 
72  log_1p_y_over_lambda[i] = log(temp);
73  }
74 
75  for (size_t n = 0; n < N; n++) {
76  const T_partials_return y_dbl = value_of(y_vec[n]);
77  const T_partials_return mu_dbl = value_of(mu_vec[n]);
78  const T_partials_return lambda_dbl = value_of(lambda_vec[n]);
79  const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
80 
81  const T_partials_return grad_1_2 = alpha_dbl * inv_p1_pow_alpha_minus_one[n]
82  / (lambda_dbl - mu_dbl + y_dbl);
83 
84  P += cdf_log[n];
85 
87  ops_partials.edge1_.partials_[n] += grad_1_2;
89  ops_partials.edge2_.partials_[n] -= grad_1_2;
91  ops_partials.edge3_.partials_[n]
92  += (mu_dbl - y_dbl) * grad_1_2 / lambda_dbl;
94  ops_partials.edge4_.partials_[n]
95  += log_1p_y_over_lambda[n] * inv_p1_pow_alpha_minus_one[n];
96  }
97  return ops_partials.build(P);
98 }
99 
100 } // namespace math
101 } // namespace stan
102 #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.
bool size_zero(T &x)
Returns 1 if input is of length 0, returns 0 otherwise.
Definition: size_zero.hpp:18
return_type< T_y, T_loc, T_scale, T_shape >::type pareto_type_2_lcdf(const T_y &y, const T_loc &mu, const T_scale &lambda, const T_shape &alpha)
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.
fvar< T > log1m(const fvar< T > &x)
Definition: log1m.hpp:12
internal::ops_partials_edge< double, Op3 > edge3_
internal::ops_partials_edge< double, Op1 > edge1_

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