Stan Math Library  2.10.0
reverse mode automatic differentiation
pareto_type_2_ccdf_log.hpp
Go to the documentation of this file.
1 #ifndef STAN_MATH_PRIM_SCAL_PROB_PARETO_TYPE_2_CCDF_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_PARETO_TYPE_2_CCDF_LOG_HPP
3 
18 #include <boost/random/variate_generator.hpp>
19 #include <cmath>
20 
21 namespace stan {
22  namespace math {
23 
24  template <typename T_y, typename T_loc, typename T_scale, typename T_shape>
25  typename return_type<T_y, T_loc, T_scale, T_shape>::type
26  pareto_type_2_ccdf_log(const T_y& y, const T_loc& mu,
27  const T_scale& lambda, const T_shape& alpha) {
28  typedef
30  T_partials_return;
31 
32  // Check sizes
33  // Size checks
34  if ( !( stan::length(y)
35  && stan::length(mu)
36  && stan::length(lambda)
37  && stan::length(alpha) ) )
38  return 0.0;
39 
40  // Check errors
41  static const char* function("stan::math::pareto_type_2_ccdf_log");
42 
50  using std::log;
51 
52  T_partials_return P(0.0);
53 
54  check_greater_or_equal(function, "Random variable", y, mu);
55  check_not_nan(function, "Random variable", y);
56  check_nonnegative(function, "Random variable", y);
57  check_positive_finite(function, "Scale parameter", lambda);
58  check_positive_finite(function, "Shape parameter", alpha);
59  check_consistent_sizes(function,
60  "Random variable", y,
61  "Scale parameter", lambda,
62  "Shape parameter", alpha);
63 
64  // Wrap arguments in vectors
65  VectorView<const T_y> y_vec(y);
66  VectorView<const T_loc> mu_vec(mu);
67  VectorView<const T_scale> lambda_vec(lambda);
68  VectorView<const T_shape> alpha_vec(alpha);
69  size_t N = max_size(y, mu, lambda, alpha);
70 
72  operands_and_partials(y, mu, lambda, alpha);
73 
74  VectorBuilder<true, T_partials_return,
75  T_y, T_loc, T_scale, T_shape>
76  ccdf_log(N);
77 
78  VectorBuilder<contains_nonconstant_struct<T_y, T_loc, T_scale,
79  T_shape>::value,
80  T_partials_return, T_y, T_loc, T_scale, T_shape>
81  a_over_lambda_plus_y(N);
82 
84  T_partials_return, T_y, T_loc, T_scale, T_shape>
85  log_1p_y_over_lambda(N);
86 
87  for (size_t i = 0; i < N; i++) {
88  const T_partials_return y_dbl = value_of(y_vec[i]);
89  const T_partials_return mu_dbl = value_of(mu_vec[i]);
90  const T_partials_return lambda_dbl = value_of(lambda_vec[i]);
91  const T_partials_return alpha_dbl = value_of(alpha_vec[i]);
92  const T_partials_return temp = 1.0 + (y_dbl - mu_dbl) / lambda_dbl;
93  const T_partials_return log_temp = log(temp);
94 
95  ccdf_log[i] = -alpha_dbl * log_temp;
96 
98  a_over_lambda_plus_y[i] = alpha_dbl / (y_dbl - mu_dbl + lambda_dbl);
99 
101  log_1p_y_over_lambda[i] = log_temp;
102  }
103 
104  // Compute vectorized CDF and its gradients
105 
106  for (size_t n = 0; n < N; n++) {
107  // Pull out values
108  const T_partials_return y_dbl = value_of(y_vec[n]);
109  const T_partials_return mu_dbl = value_of(mu_vec[n]);
110  const T_partials_return lambda_dbl = value_of(lambda_vec[n]);
111 
112  // Compute
113  P += ccdf_log[n];
114 
116  operands_and_partials.d_x1[n] -= a_over_lambda_plus_y[n];
118  operands_and_partials.d_x2[n] += a_over_lambda_plus_y[n];
120  operands_and_partials.d_x3[n] += a_over_lambda_plus_y[n]
121  * (y_dbl - mu_dbl) / lambda_dbl;
123  operands_and_partials.d_x4[n] -= log_1p_y_over_lambda[n];
124  }
125 
126  return operands_and_partials.value(P);
127  }
128  }
129 }
130 #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.
return_type< T_y, T_loc, T_scale, T_shape >::type pareto_type_2_ccdf_log(const T_y &y, const T_loc &mu, const T_scale &lambda, const T_shape &alpha)
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:15
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
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.
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

     [ Stan Home Page ] © 2011–2016, Stan Development Team.