Stan Math Library  2.9.0
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 
4 #include <boost/random/variate_generator.hpp>
18 #include <cmath>
19 
20 
21 namespace stan {
22  namespace math {
23 
24  // pareto_type_2(y|lambda, alpha) [y >= 0; lambda > 0; alpha > 0]
25  template <bool propto,
26  typename T_y, typename T_loc, typename T_scale, typename T_shape>
27  typename return_type<T_y, T_loc, T_scale, T_shape>::type
28  pareto_type_2_log(const T_y& y, const T_loc& mu, const T_scale& lambda,
29  const T_shape& alpha) {
30  static const char* function("stan::math::pareto_type_2_log");
31  typedef
33  T_partials_return;
34 
35  using std::log;
43  using std::log;
44 
45  // check if any vectors are zero length
46  if (!(stan::length(y)
47  && stan::length(mu)
48  && stan::length(lambda)
49  && stan::length(alpha)))
50  return 0.0;
51 
52  // set up return value accumulator
53  T_partials_return logp(0.0);
54 
55  // validate args (here done over var, which should be OK)
56  check_greater_or_equal(function, "Random variable", y, mu);
57  check_not_nan(function, "Random variable", y);
58  check_positive_finite(function, "Scale parameter", lambda);
59  check_positive_finite(function, "Shape parameter", alpha);
60  check_consistent_sizes(function,
61  "Random variable", y,
62  "Scale parameter", lambda,
63  "Shape parameter", alpha);
64 
65 
66  // check if no variables are involved and prop-to
68  return 0.0;
69 
70  VectorView<const T_y> y_vec(y);
71  VectorView<const T_loc> mu_vec(mu);
72  VectorView<const T_scale> lambda_vec(lambda);
73  VectorView<const T_shape> alpha_vec(alpha);
74  size_t N = max_size(y, mu, lambda, alpha);
75 
76  // set up template expressions wrapping scalars into vector views
78  operands_and_partials(y, mu, lambda, alpha);
79 
81  ::value,
82  T_partials_return, T_y, T_loc, T_scale>
83  log1p_scaled_diff(N);
85  for (size_t n = 0; n < N; n++)
86  log1p_scaled_diff[n] = log1p((value_of(y_vec[n])
87  - value_of(mu_vec[n]))
88  / value_of(lambda_vec[n]));
89  }
90 
92  T_partials_return, T_scale> log_lambda(length(lambda));
94  for (size_t n = 0; n < length(lambda); n++)
95  log_lambda[n] = log(value_of(lambda_vec[n]));
96  }
97 
99  T_partials_return, T_shape> log_alpha(length(alpha));
101  for (size_t n = 0; n < length(alpha); n++)
102  log_alpha[n] = log(value_of(alpha_vec[n]));
103  }
104 
106  T_partials_return, T_shape> inv_alpha(length(alpha));
108  for (size_t n = 0; n < length(alpha); n++)
109  inv_alpha[n] = 1 / value_of(alpha_vec[n]);
110  }
111 
112  for (size_t n = 0; n < N; n++) {
113  const T_partials_return y_dbl = value_of(y_vec[n]);
114  const T_partials_return mu_dbl = value_of(mu_vec[n]);
115  const T_partials_return lambda_dbl = value_of(lambda_vec[n]);
116  const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
117  const T_partials_return sum_dbl = lambda_dbl + y_dbl - mu_dbl;
118  const T_partials_return inv_sum = 1.0 / sum_dbl;
119  const T_partials_return alpha_div_sum = alpha_dbl / sum_dbl;
120  const T_partials_return deriv_1_2 = inv_sum + alpha_div_sum;
121 
122  // // log probability
124  logp += log_alpha[n];
126  logp -= log_lambda[n];
128  logp -= (alpha_dbl + 1.0) * log1p_scaled_diff[n];
129 
130  // gradients
132  operands_and_partials.d_x1[n] -= deriv_1_2;
134  operands_and_partials.d_x2[n] += deriv_1_2;
136  operands_and_partials.d_x3[n] -= alpha_div_sum * (mu_dbl - y_dbl)
137  / lambda_dbl + inv_sum;
139  operands_and_partials.d_x4[n] += inv_alpha[n] - log1p_scaled_diff[n];
140  }
141  return operands_and_partials.to_var(logp, y, mu, lambda, alpha);
142  }
143 
144  template <typename T_y, typename T_loc, typename T_scale, typename T_shape>
145  inline
147  pareto_type_2_log(const T_y& y, const T_loc& mu,
148  const T_scale& lambda, const T_shape& alpha) {
149  return pareto_type_2_log<false>(y, mu, lambda, alpha);
150  }
151  }
152 }
153 #endif
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
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
T_return_type to_var(T_partials_return logp, const T1 &x1=0, const T2 &x2=0, const T3 &x3=0, const T4 &x4=0, const T5 &x5=0, const T6 &x6=0)
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
VectorView< T_partials_return, is_vector< T1 >::value, is_constant_struct< T1 >::value > d_x1
Metaprogram to determine if a type has a base scalar type that can be assigned to type double...
VectorView< T_partials_return, is_vector< T3 >::value, is_constant_struct< T3 >::value > d_x3
VectorView< T_partials_return, is_vector< T4 >::value, is_constant_struct< T4 >::value > d_x4
A variable implementation that stores operands and derivatives with respect to the variable...
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.
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.
VectorView< T_partials_return, is_vector< T2 >::value, is_constant_struct< T2 >::value > d_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 metaprogram that takes its argument and allows it to be used like a vector...
Definition: VectorView.hpp:41
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.
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)

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