Stan Math Library  2.12.0
reverse mode automatic differentiation
pareto_type_2_cdf.hpp
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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 
19 #include <boost/random/variate_generator.hpp>
20 #include <cmath>
21 
22 namespace stan {
23  namespace math {
24 
25  template <typename T_y, typename T_loc, typename T_scale, typename T_shape>
26  typename return_type<T_y, T_loc, T_scale, T_shape>::type
27  pareto_type_2_cdf(const T_y& y, const T_loc& mu,
28  const T_scale& lambda, const T_shape& alpha) {
29  typedef
31  T_partials_return;
32 
33  if ( !( stan::length(y)
34  && stan::length(mu)
35  && stan::length(lambda)
36  && stan::length(alpha) ) )
37  return 1.0;
38 
39  static const char* function("pareto_type_2_cdf");
40 
41  using std::log;
42 
43  T_partials_return P(1.0);
44 
45  check_greater_or_equal(function, "Random variable", y, mu);
46  check_not_nan(function, "Random variable", y);
47  check_nonnegative(function, "Random variable", y);
48  check_positive_finite(function, "Scale parameter", lambda);
49  check_positive_finite(function, "Shape parameter", alpha);
50  check_consistent_sizes(function,
51  "Random variable", y,
52  "Scale parameter", lambda,
53  "Shape parameter", alpha);
54 
55  VectorView<const T_y> y_vec(y);
56  VectorView<const T_loc> mu_vec(mu);
57  VectorView<const T_scale> lambda_vec(lambda);
58  VectorView<const T_shape> alpha_vec(alpha);
59  size_t N = max_size(y, mu, lambda, alpha);
60 
62  operands_and_partials(y, mu, lambda, alpha);
63 
64  VectorBuilder<true, T_partials_return,
65  T_y, T_loc, T_scale, T_shape>
66  p1_pow_alpha(N);
67 
69  T_partials_return, T_y, T_loc, T_scale, T_shape>
70  grad_1_2(N);
71 
73  T_partials_return, T_y, T_loc, T_scale, T_shape>
74  grad_3(N);
75 
76  for (size_t i = 0; i < N; i++) {
77  const T_partials_return lambda_dbl = value_of(lambda_vec[i]);
78  const T_partials_return alpha_dbl = value_of(alpha_vec[i]);
79  const T_partials_return temp = 1 + (value_of(y_vec[i])
80  - value_of(mu_vec[i]))
81  / lambda_dbl;
82  p1_pow_alpha[i] = pow(temp, -alpha_dbl);
83 
85  grad_1_2[i] = p1_pow_alpha[i] / temp * alpha_dbl / lambda_dbl;
86 
88  grad_3[i] = log(temp) * p1_pow_alpha[i];
89  }
90 
91  for (size_t n = 0; n < N; n++) {
92  const T_partials_return y_dbl = value_of(y_vec[n]);
93  const T_partials_return mu_dbl = value_of(mu_vec[n]);
94  const T_partials_return lambda_dbl = value_of(lambda_vec[n]);
95 
96  const T_partials_return Pn = 1.0 - p1_pow_alpha[n];
97 
98  P *= Pn;
99 
101  operands_and_partials.d_x1[n] += grad_1_2[n] / Pn;
103  operands_and_partials.d_x2[n] -= grad_1_2[n] / Pn;
105  operands_and_partials.d_x3[n] += (mu_dbl - y_dbl)
106  * grad_1_2[n] / lambda_dbl / Pn;
108  operands_and_partials.d_x4[n] += grad_3[n] / Pn;
109  }
110 
112  for (size_t n = 0; n < stan::length(y); ++n)
113  operands_and_partials.d_x1[n] *= P;
114  }
116  for (size_t n = 0; n < stan::length(mu); ++n)
117  operands_and_partials.d_x2[n] *= P;
118  }
120  for (size_t n = 0; n < stan::length(lambda); ++n)
121  operands_and_partials.d_x3[n] *= P;
122  }
124  for (size_t n = 0; n < stan::length(alpha); ++n)
125  operands_and_partials.d_x4[n] *= P;
126  }
127  return operands_and_partials.value(P);
128  }
129 
130  }
131 }
132 #endif
VectorView< T_return_type, false, true > d_x2
bool check_greater_or_equal(const char *function, const char *name, const T_y &y, const T_low &low)
Return true if y is greater or equal than low.
bool check_not_nan(const char *function, const char *name, const T_y &y)
Return true if y is not NaN.
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:14
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_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)
Metaprogram to determine if a type has a base scalar type that can be assigned to type double...
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
VectorBuilder allocates type T1 values to be used as intermediate values.
bool check_consistent_sizes(const char *function, const char *name1, const T1 &x1, const char *name2, const T2 &x2)
Return true if the dimension of x1 is consistent with x2.
fvar< T > pow(const fvar< T > &x1, const fvar< T > &x2)
Definition: pow.hpp:17
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
VectorView< T_return_type, false, true > d_x4

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