Stan Math Library  2.12.0
reverse mode automatic differentiation
pareto_type_2_log.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_PARETO_TYPE_2_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_PARETO_TYPE_2_LOG_HPP
3 
19 #include <boost/random/variate_generator.hpp>
20 #include <cmath>
21 
22 namespace stan {
23  namespace math {
24 
25  // pareto_type_2(y|lambda, alpha) [y >= 0; lambda > 0; alpha > 0]
26  template <bool propto,
27  typename T_y, typename T_loc, typename T_scale, typename T_shape>
28  typename return_type<T_y, T_loc, T_scale, T_shape>::type
29  pareto_type_2_log(const T_y& y, const T_loc& mu, const T_scale& lambda,
30  const T_shape& alpha) {
31  static const char* function("pareto_type_2_log");
32  typedef
34  T_partials_return;
35 
36  using std::log;
37  using std::log;
38 
39  if (!(stan::length(y)
40  && stan::length(mu)
41  && stan::length(lambda)
42  && stan::length(alpha)))
43  return 0.0;
44 
45  T_partials_return logp(0.0);
46 
47  check_greater_or_equal(function, "Random variable", y, mu);
48  check_not_nan(function, "Random variable", y);
49  check_positive_finite(function, "Scale parameter", lambda);
50  check_positive_finite(function, "Shape parameter", alpha);
51  check_consistent_sizes(function,
52  "Random variable", y,
53  "Scale parameter", lambda,
54  "Shape parameter", alpha);
55 
57  return 0.0;
58 
59  VectorView<const T_y> y_vec(y);
60  VectorView<const T_loc> mu_vec(mu);
61  VectorView<const T_scale> lambda_vec(lambda);
62  VectorView<const T_shape> alpha_vec(alpha);
63  size_t N = max_size(y, mu, lambda, alpha);
64 
66  operands_and_partials(y, mu, lambda, alpha);
67 
69  ::value,
70  T_partials_return, T_y, T_loc, T_scale>
71  log1p_scaled_diff(N);
73  for (size_t n = 0; n < N; n++)
74  log1p_scaled_diff[n] = log1p((value_of(y_vec[n])
75  - value_of(mu_vec[n]))
76  / value_of(lambda_vec[n]));
77  }
78 
80  T_partials_return, T_scale> log_lambda(length(lambda));
82  for (size_t n = 0; n < length(lambda); n++)
83  log_lambda[n] = log(value_of(lambda_vec[n]));
84  }
85 
87  T_partials_return, T_shape> log_alpha(length(alpha));
89  for (size_t n = 0; n < length(alpha); n++)
90  log_alpha[n] = log(value_of(alpha_vec[n]));
91  }
92 
94  T_partials_return, T_shape> inv_alpha(length(alpha));
96  for (size_t n = 0; n < length(alpha); n++)
97  inv_alpha[n] = 1 / value_of(alpha_vec[n]);
98  }
99 
100  for (size_t n = 0; n < N; n++) {
101  const T_partials_return y_dbl = value_of(y_vec[n]);
102  const T_partials_return mu_dbl = value_of(mu_vec[n]);
103  const T_partials_return lambda_dbl = value_of(lambda_vec[n]);
104  const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
105  const T_partials_return sum_dbl = lambda_dbl + y_dbl - mu_dbl;
106  const T_partials_return inv_sum = 1.0 / sum_dbl;
107  const T_partials_return alpha_div_sum = alpha_dbl / sum_dbl;
108  const T_partials_return deriv_1_2 = inv_sum + alpha_div_sum;
109 
111  logp += log_alpha[n];
113  logp -= log_lambda[n];
115  logp -= (alpha_dbl + 1.0) * log1p_scaled_diff[n];
116 
118  operands_and_partials.d_x1[n] -= deriv_1_2;
120  operands_and_partials.d_x2[n] += deriv_1_2;
122  operands_and_partials.d_x3[n] -= alpha_div_sum * (mu_dbl - y_dbl)
123  / lambda_dbl + inv_sum;
125  operands_and_partials.d_x4[n] += inv_alpha[n] - log1p_scaled_diff[n];
126  }
127  return operands_and_partials.value(logp);
128  }
129 
130  template <typename T_y, typename T_loc, typename T_scale, typename T_shape>
131  inline
133  pareto_type_2_log(const T_y& y, const T_loc& mu,
134  const T_scale& lambda, const T_shape& alpha) {
135  return pareto_type_2_log<false>(y, mu, lambda, alpha);
136  }
137 
138  }
139 }
140 #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
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) prob...
boost::math::tools::promote_args< typename scalar_type< T1 >::type, typename scalar_type< T2 >::type, typename scalar_type< T3 >::type, typename scalar_type< T4 >::type, typename scalar_type< T5 >::type, typename scalar_type< T6 >::type >::type type
Definition: return_type.hpp:27
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 > log1p(const fvar< T > &x)
Definition: log1p.hpp:15
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
return_type< T_y, T_loc, T_scale, T_shape >::type pareto_type_2_log(const T_y &y, const T_loc &mu, const T_scale &lambda, const T_shape &alpha)
VectorView< T_return_type, false, true > d_x4

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