Stan Math Library  2.10.0
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 
23 namespace stan {
24  namespace math {
25 
26  // pareto_type_2(y|lambda, alpha) [y >= 0; lambda > 0; alpha > 0]
27  template <bool propto,
28  typename T_y, typename T_loc, typename T_scale, typename T_shape>
29  typename return_type<T_y, T_loc, T_scale, T_shape>::type
30  pareto_type_2_log(const T_y& y, const T_loc& mu, const T_scale& lambda,
31  const T_shape& alpha) {
32  static const char* function("stan::math::pareto_type_2_log");
33  typedef
35  T_partials_return;
36 
37  using std::log;
45  using std::log;
46 
47  // check if any vectors are zero length
48  if (!(stan::length(y)
49  && stan::length(mu)
50  && stan::length(lambda)
51  && stan::length(alpha)))
52  return 0.0;
53 
54  // set up return value accumulator
55  T_partials_return logp(0.0);
56 
57  // validate args (here done over var, which should be OK)
58  check_greater_or_equal(function, "Random variable", y, mu);
59  check_not_nan(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 
68  // check if no variables are involved and prop-to
70  return 0.0;
71 
72  VectorView<const T_y> y_vec(y);
73  VectorView<const T_loc> mu_vec(mu);
74  VectorView<const T_scale> lambda_vec(lambda);
75  VectorView<const T_shape> alpha_vec(alpha);
76  size_t N = max_size(y, mu, lambda, alpha);
77 
78  // set up template expressions wrapping scalars into vector views
80  operands_and_partials(y, mu, lambda, alpha);
81 
83  ::value,
84  T_partials_return, T_y, T_loc, T_scale>
85  log1p_scaled_diff(N);
87  for (size_t n = 0; n < N; n++)
88  log1p_scaled_diff[n] = log1p((value_of(y_vec[n])
89  - value_of(mu_vec[n]))
90  / value_of(lambda_vec[n]));
91  }
92 
94  T_partials_return, T_scale> log_lambda(length(lambda));
96  for (size_t n = 0; n < length(lambda); n++)
97  log_lambda[n] = log(value_of(lambda_vec[n]));
98  }
99 
101  T_partials_return, T_shape> log_alpha(length(alpha));
103  for (size_t n = 0; n < length(alpha); n++)
104  log_alpha[n] = log(value_of(alpha_vec[n]));
105  }
106 
108  T_partials_return, T_shape> inv_alpha(length(alpha));
110  for (size_t n = 0; n < length(alpha); n++)
111  inv_alpha[n] = 1 / value_of(alpha_vec[n]);
112  }
113 
114  for (size_t n = 0; n < N; n++) {
115  const T_partials_return y_dbl = value_of(y_vec[n]);
116  const T_partials_return mu_dbl = value_of(mu_vec[n]);
117  const T_partials_return lambda_dbl = value_of(lambda_vec[n]);
118  const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
119  const T_partials_return sum_dbl = lambda_dbl + y_dbl - mu_dbl;
120  const T_partials_return inv_sum = 1.0 / sum_dbl;
121  const T_partials_return alpha_div_sum = alpha_dbl / sum_dbl;
122  const T_partials_return deriv_1_2 = inv_sum + alpha_div_sum;
123 
124  // // log probability
126  logp += log_alpha[n];
128  logp -= log_lambda[n];
130  logp -= (alpha_dbl + 1.0) * log1p_scaled_diff[n];
131 
132  // gradients
134  operands_and_partials.d_x1[n] -= deriv_1_2;
136  operands_and_partials.d_x2[n] += deriv_1_2;
138  operands_and_partials.d_x3[n] -= alpha_div_sum * (mu_dbl - y_dbl)
139  / lambda_dbl + inv_sum;
141  operands_and_partials.d_x4[n] += inv_alpha[n] - log1p_scaled_diff[n];
142  }
143  return operands_and_partials.value(logp);
144  }
145 
146  template <typename T_y, typename T_loc, typename T_scale, typename T_shape>
147  inline
149  pareto_type_2_log(const T_y& y, const T_loc& mu,
150  const T_scale& lambda, const T_shape& alpha) {
151  return pareto_type_2_log<false>(y, mu, lambda, alpha);
152  }
153  }
154 }
155 #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
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
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.
fvar< T > log1p(const fvar< T > &x)
Definition: log1p.hpp:16
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
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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