Stan Math Library  2.20.0
reverse mode automatic differentiation
cauchy_lpdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_CAUCHY_LPDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_CAUCHY_LPDF_HPP
3 
13 #include <cmath>
14 
15 namespace stan {
16 namespace math {
17 
35 template <bool propto, typename T_y, typename T_loc, typename T_scale>
37  const T_y& y, const T_loc& mu, const T_scale& sigma) {
38  static const char* function = "cauchy_lpdf";
40  T_partials_return;
41 
42  if (size_zero(y, mu, sigma))
43  return 0.0;
44 
45  T_partials_return logp(0.0);
46 
47  check_not_nan(function, "Random variable", y);
48  check_finite(function, "Location parameter", mu);
49  check_positive_finite(function, "Scale parameter", sigma);
50  check_consistent_sizes(function, "Random variable", y, "Location parameter",
51  mu, "Scale parameter", sigma);
52 
54  return 0.0;
55 
56  using std::log;
57 
58  scalar_seq_view<T_y> y_vec(y);
59  scalar_seq_view<T_loc> mu_vec(mu);
60  scalar_seq_view<T_scale> sigma_vec(sigma);
61  size_t N = max_size(y, mu, sigma);
62 
66  T_scale>
67  log_sigma(length(sigma));
68  for (size_t i = 0; i < length(sigma); i++) {
69  const T_partials_return sigma_dbl = value_of(sigma_vec[i]);
70  inv_sigma[i] = 1.0 / sigma_dbl;
71  sigma_squared[i] = sigma_dbl * sigma_dbl;
73  log_sigma[i] = log(sigma_dbl);
74  }
75  }
76 
77  operands_and_partials<T_y, T_loc, T_scale> ops_partials(y, mu, sigma);
78 
79  for (size_t n = 0; n < N; n++) {
80  const T_partials_return y_dbl = value_of(y_vec[n]);
81  const T_partials_return mu_dbl = value_of(mu_vec[n]);
82 
83  const T_partials_return y_minus_mu = y_dbl - mu_dbl;
84  const T_partials_return y_minus_mu_squared = y_minus_mu * y_minus_mu;
85  const T_partials_return y_minus_mu_over_sigma = y_minus_mu * inv_sigma[n];
86  const T_partials_return y_minus_mu_over_sigma_squared
87  = y_minus_mu_over_sigma * y_minus_mu_over_sigma;
88 
90  logp += NEG_LOG_PI;
92  logp -= log_sigma[n];
94  logp -= log1p(y_minus_mu_over_sigma_squared);
95 
97  ops_partials.edge1_.partials_[n]
98  -= 2 * y_minus_mu / (sigma_squared[n] + y_minus_mu_squared);
100  ops_partials.edge2_.partials_[n]
101  += 2 * y_minus_mu / (sigma_squared[n] + y_minus_mu_squared);
103  ops_partials.edge3_.partials_[n]
104  += (y_minus_mu_squared - sigma_squared[n]) * inv_sigma[n]
105  / (sigma_squared[n] + y_minus_mu_squared);
106  }
107  return ops_partials.build(logp);
108 }
109 
110 template <typename T_y, typename T_loc, typename T_scale>
112  const T_y& y, const T_loc& mu, const T_scale& sigma) {
113  return cauchy_lpdf<false>(y, mu, sigma);
114 }
115 
116 } // namespace math
117 } // namespace stan
118 #endif
const double NEG_LOG_PI
Definition: constants.hpp:158
void check_finite(const char *function, const char *name, const T_y &y)
Check if y is finite.
boost::math::tools::promote_args< double, typename partials_type< typename scalar_type< T >::type >::type, typename partials_return_type< T_pack... >::type >::type type
T value_of(const fvar< T > &v)
Return the value of the specified variable.
Definition: value_of.hpp:17
Extends std::true_type when instantiated with zero or more template parameters, all of which extend t...
Definition: conjunction.hpp:14
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:12
scalar_seq_view provides a uniform sequence-like wrapper around either a scalar or a sequence of scal...
This template builds partial derivatives with respect to a set of operands.
size_t length(const std::vector< T > &x)
Returns the length of the provided std::vector.
Definition: length.hpp:16
bool size_zero(T &x)
Returns 1 if input is of length 0, returns 0 otherwise.
Definition: size_zero.hpp:18
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) prob...
void check_positive_finite(const char *function, const char *name, const T_y &y)
Check if y is positive and finite.
boost::math::tools::promote_args< double, typename scalar_type< T >::type, typename return_type< Types_pack... >::type >::type type
Definition: return_type.hpp:36
void check_not_nan(const char *function, const char *name, const T_y &y)
Check if y is not NaN.
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
T_return_type build(double value)
Build the node to be stored on the autodiff graph.
VectorBuilder allocates type T1 values to be used as intermediate values.
internal::ops_partials_edge< double, Op2 > edge2_
fvar< T > log1p(const fvar< T > &x)
Definition: log1p.hpp:12
void check_consistent_sizes(const char *function, const char *name1, const T1 &x1, const char *name2, const T2 &x2)
Check if the dimension of x1 is consistent with x2.
internal::ops_partials_edge< double, Op3 > edge3_
internal::ops_partials_edge< double, Op1 > edge1_
return_type< T_y, T_loc, T_scale >::type cauchy_lpdf(const T_y &y, const T_loc &mu, const T_scale &sigma)
The log of the Cauchy density for the specified scalar(s) given the specified location parameter(s) a...
Definition: cauchy_lpdf.hpp:36

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