Stan Math Library  2.11.0
reverse mode automatic differentiation
cauchy_log.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_CAUCHY_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_CAUCHY_LOG_HPP
3 
17 #include <boost/random/cauchy_distribution.hpp>
18 #include <boost/random/variate_generator.hpp>
19 #include <cmath>
20 
21 namespace stan {
22 
23  namespace math {
24 
42  template <bool propto,
43  typename T_y, typename T_loc, typename T_scale>
44  typename return_type<T_y, T_loc, T_scale>::type
45  cauchy_log(const T_y& y, const T_loc& mu, const T_scale& sigma) {
46  static const char* function("stan::math::cauchy_log");
48  T_partials_return;
49 
56 
57  // check if any vectors are zero length
58  if (!(stan::length(y)
59  && stan::length(mu)
60  && stan::length(sigma)))
61  return 0.0;
62 
63  // set up return value accumulator
64  T_partials_return logp(0.0);
65 
66  // validate args (here done over var, which should be OK)
67  check_not_nan(function, "Random variable", y);
68  check_finite(function, "Location parameter", mu);
69  check_positive_finite(function, "Scale parameter", sigma);
70  check_consistent_sizes(function,
71  "Random variable", y,
72  "Location parameter", mu,
73  "Scale parameter", sigma);
74 
75  // check if no variables are involved and prop-to
77  return 0.0;
78 
79  using stan::math::log1p;
80  using stan::math::square;
81  using std::log;
82 
83  // set up template expressions wrapping scalars into vector views
84  VectorView<const T_y> y_vec(y);
85  VectorView<const T_loc> mu_vec(mu);
86  VectorView<const T_scale> sigma_vec(sigma);
87  size_t N = max_size(y, mu, sigma);
88 
90  VectorBuilder<true, T_partials_return,
91  T_scale> sigma_squared(length(sigma));
93  T_partials_return, T_scale> log_sigma(length(sigma));
94  for (size_t i = 0; i < length(sigma); i++) {
95  const T_partials_return sigma_dbl = value_of(sigma_vec[i]);
96  inv_sigma[i] = 1.0 / sigma_dbl;
97  sigma_squared[i] = sigma_dbl * sigma_dbl;
99  log_sigma[i] = log(sigma_dbl);
100  }
101  }
102 
104  operands_and_partials(y, mu, sigma);
105 
106  for (size_t n = 0; n < N; n++) {
107  // pull out values of arguments
108  const T_partials_return y_dbl = value_of(y_vec[n]);
109  const T_partials_return mu_dbl = value_of(mu_vec[n]);
110 
111  // reusable subexpression values
112  const T_partials_return y_minus_mu
113  = y_dbl - mu_dbl;
114  const T_partials_return y_minus_mu_squared
115  = y_minus_mu * y_minus_mu;
116  const T_partials_return y_minus_mu_over_sigma
117  = y_minus_mu * inv_sigma[n];
118  const T_partials_return y_minus_mu_over_sigma_squared
119  = y_minus_mu_over_sigma * y_minus_mu_over_sigma;
120 
121  // log probability
123  logp += NEG_LOG_PI;
125  logp -= log_sigma[n];
127  logp -= log1p(y_minus_mu_over_sigma_squared);
128 
129  // gradients
131  operands_and_partials.d_x1[n] -= 2 * y_minus_mu
132  / (sigma_squared[n] + y_minus_mu_squared);
134  operands_and_partials.d_x2[n] += 2 * y_minus_mu
135  / (sigma_squared[n] + y_minus_mu_squared);
137  operands_and_partials.d_x3[n]
138  += (y_minus_mu_squared - sigma_squared[n])
139  * inv_sigma[n] / (sigma_squared[n] + y_minus_mu_squared);
140  }
141  return operands_and_partials.value(logp);
142  }
143 
144  template <typename T_y, typename T_loc, typename T_scale>
145  inline
147  cauchy_log(const T_y& y, const T_loc& mu, const T_scale& sigma) {
148  return cauchy_log<false>(y, mu, sigma);
149  }
150 
151 
152  }
153 }
154 #endif
VectorView< T_return_type, false, true > d_x2
const double NEG_LOG_PI
Definition: constants.hpp:186
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
fvar< T > square(const fvar< T > &x)
Definition: square.hpp:15
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
return_type< T_y, T_loc, T_scale >::type cauchy_log(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_log.hpp:45
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
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

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