Stan Math Library  2.11.0
reverse mode automatic differentiation
pareto_type_2_cdf_log.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_PARETO_TYPE_2_CDF_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_PARETO_TYPE_2_CDF_LOG_HPP
3 
18 #include <boost/random/variate_generator.hpp>
19 #include <cmath>
20 
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_log(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  // Check sizes
34  // Size checks
35  if ( !( stan::length(y)
36  && stan::length(mu)
37  && stan::length(lambda)
38  && stan::length(alpha) ) )
39  return 0.0;
40 
41  // Check errors
42  static const char* function("stan::math::pareto_type_2_cdf_log");
43 
52  using stan::math::log1m;
53  using std::log;
54 
55  T_partials_return P(0.0);
56 
57  check_greater_or_equal(function, "Random variable", y, mu);
58  check_not_nan(function, "Random variable", y);
59  check_nonnegative(function, "Random variable", y);
60  check_positive_finite(function, "Scale parameter", lambda);
61  check_positive_finite(function, "Shape parameter", alpha);
62  check_consistent_sizes(function,
63  "Random variable", y,
64  "Scale parameter", lambda,
65  "Shape parameter", alpha);
66 
67  // Wrap arguments in vectors
68  VectorView<const T_y> y_vec(y);
69  VectorView<const T_loc> mu_vec(mu);
70  VectorView<const T_scale> lambda_vec(lambda);
71  VectorView<const T_shape> alpha_vec(alpha);
72  size_t N = max_size(y, mu, lambda, alpha);
73 
75  operands_and_partials(y, mu, lambda, alpha);
76 
77  VectorBuilder<true, T_partials_return,
78  T_y, T_loc, T_scale, T_shape>
79  cdf_log(N);
80 
81  VectorBuilder<true, T_partials_return,
82  T_y, T_loc, T_scale, T_shape>
83  inv_p1_pow_alpha_minus_one(N);
84 
86  T_partials_return, T_y, T_loc, T_scale, T_shape>
87  log_1p_y_over_lambda(N);
88 
89  for (size_t i = 0; i < N; i++) {
90  const T_partials_return temp = 1.0 + (value_of(y_vec[i])
91  - value_of(mu_vec[i]))
92  / value_of(lambda_vec[i]);
93  const T_partials_return p1_pow_alpha
94  = pow(temp, value_of(alpha_vec[i]));
95  cdf_log[i] = log1m(1.0 / p1_pow_alpha);
96 
97  inv_p1_pow_alpha_minus_one[i] = 1.0 / (p1_pow_alpha - 1.0);
98 
100  log_1p_y_over_lambda[i] = log(temp);
101  }
102 
103  // Compute vectorized CDF and its gradients
104 
105  for (size_t n = 0; n < N; n++) {
106  // Pull out values
107  const T_partials_return y_dbl = value_of(y_vec[n]);
108  const T_partials_return mu_dbl = value_of(mu_vec[n]);
109  const T_partials_return lambda_dbl = value_of(lambda_vec[n]);
110  const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
111 
112  const T_partials_return grad_1_2 = alpha_dbl
113  * inv_p1_pow_alpha_minus_one[n] / (lambda_dbl - mu_dbl + y_dbl);
114 
115  // Compute
116  P += cdf_log[n];
117 
119  operands_and_partials.d_x1[n] += grad_1_2;
121  operands_and_partials.d_x2[n] -= grad_1_2;
123  operands_and_partials.d_x3[n] += (mu_dbl - y_dbl) * grad_1_2
124  / lambda_dbl;
126  operands_and_partials.d_x4[n] += log_1p_y_over_lambda[n]
127  * inv_p1_pow_alpha_minus_one[n];
128  }
129 
130  return operands_and_partials.value(P);
131  }
132  }
133 }
134 #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: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
bool check_finite(const char *function, const char *name, const T_y &y)
Return true if y is finite.
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.
return_type< T_y, T_loc, T_scale, T_shape >::type pareto_type_2_cdf_log(const T_y &y, const T_loc &mu, const T_scale &lambda, const T_shape &alpha)
fvar< T > pow(const fvar< T > &x1, const fvar< T > &x2)
Definition: pow.hpp:18
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.
fvar< T > log1m(const fvar< T > &x)
Definition: log1m.hpp:16
VectorView< T_return_type, false, true > d_x1
VectorView< T_return_type, false, true > d_x4

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