Stan Math Library  2.10.0
reverse mode automatic differentiation
exp_mod_normal_log.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_EXP_MOD_NORMAL_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_EXP_MOD_NORMAL_LOG_HPP
3 
14 #include <boost/random/normal_distribution.hpp>
15 #include <boost/math/special_functions/fpclassify.hpp>
16 #include <boost/random/variate_generator.hpp>
17 #include <cmath>
18 
19 namespace stan {
20 
21  namespace math {
22 
23  template <bool propto,
24  typename T_y, typename T_loc, typename T_scale,
25  typename T_inv_scale>
26  typename return_type<T_y, T_loc, T_scale, T_inv_scale>::type
27  exp_mod_normal_log(const T_y& y, const T_loc& mu, const T_scale& sigma,
28  const T_inv_scale& lambda) {
29  static const char* function("stan::math::exp_mod_normal_log");
30  typedef typename stan::partials_return_type<T_y, T_loc, T_scale,
31  T_inv_scale>::type
32  T_partials_return;
33 
41  using std::log;
42 
43  // check if any vectors are zero length
44  if (!(stan::length(y)
45  && stan::length(mu)
46  && stan::length(sigma)
47  && stan::length(lambda)))
48  return 0.0;
49 
50  // set up return value accumulator
51  T_partials_return logp(0.0);
52 
53  // validate args (here done over var, which should be OK)
54  check_not_nan(function, "Random variable", y);
55  check_finite(function, "Location parameter", mu);
56  check_positive_finite(function, "Inv_scale parameter", lambda);
57  check_positive_finite(function, "Scale parameter", sigma);
58  check_consistent_sizes(function,
59  "Random variable", y,
60  "Location parameter", mu,
61  "Scale parameter", sigma,
62  "Inv_scale paramter", lambda);
63 
64  // check if no variables are involved and prop-to
66  return 0.0;
67 
68  using boost::math::erfc;
69  using std::sqrt;
70  using std::log;
71  using std::exp;
72 
73  // set up template expressions wrapping scalars into vector views
75  operands_and_partials(y, mu, sigma, lambda);
76 
77  VectorView<const T_y> y_vec(y);
78  VectorView<const T_loc> mu_vec(mu);
79  VectorView<const T_scale> sigma_vec(sigma);
80  VectorView<const T_inv_scale> lambda_vec(lambda);
81  size_t N = max_size(y, mu, sigma, lambda);
82 
83  for (size_t n = 0; n < N; n++) {
84  // pull out values of arguments
85  const T_partials_return y_dbl = value_of(y_vec[n]);
86  const T_partials_return mu_dbl = value_of(mu_vec[n]);
87  const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
88  const T_partials_return lambda_dbl = value_of(lambda_vec[n]);
89 
90  const T_partials_return pi_dbl = boost::math::constants::pi<double>();
91 
92  // log probability
94  logp -= log(2.0);
96  logp += log(lambda_dbl);
98  logp += lambda_dbl
99  * (mu_dbl + 0.5 * lambda_dbl * sigma_dbl * sigma_dbl - y_dbl)
100  + log(erfc((mu_dbl + lambda_dbl * sigma_dbl
101  * sigma_dbl - y_dbl)
102  / (sqrt(2.0) * sigma_dbl)));
103 
104  // gradients
105  const T_partials_return deriv_logerfc
106  = -2.0 / sqrt(pi_dbl)
107  * exp(-(mu_dbl + lambda_dbl * sigma_dbl * sigma_dbl - y_dbl)
108  / (std::sqrt(2.0) * sigma_dbl)
109  * (mu_dbl + lambda_dbl * sigma_dbl * sigma_dbl - y_dbl)
110  / (sigma_dbl * std::sqrt(2.0)))
111  / erfc((mu_dbl + lambda_dbl * sigma_dbl * sigma_dbl
112  - y_dbl) / (sigma_dbl * std::sqrt(2.0)));
113 
115  operands_and_partials.d_x1[n]
116  += -lambda_dbl
117  + deriv_logerfc * -1.0 / (sigma_dbl * std::sqrt(2.0));
119  operands_and_partials.d_x2[n]
120  += lambda_dbl
121  + deriv_logerfc / (sigma_dbl * std::sqrt(2.0));
123  operands_and_partials.d_x3[n]
124  += sigma_dbl * lambda_dbl * lambda_dbl
125  + deriv_logerfc
126  * (-mu_dbl / (sigma_dbl * sigma_dbl * std::sqrt(2.0))
127  + lambda_dbl / std::sqrt(2.0)
128  + y_dbl / (sigma_dbl * sigma_dbl * std::sqrt(2.0)));
130  operands_and_partials.d_x4[n]
131  += 1 / lambda_dbl + lambda_dbl * sigma_dbl * sigma_dbl
132  + mu_dbl - y_dbl + deriv_logerfc * sigma_dbl / std::sqrt(2.0);
133  }
134  return operands_and_partials.value(logp);
135  }
136 
137  template <typename T_y, typename T_loc, typename T_scale,
138  typename T_inv_scale>
139  inline
141  exp_mod_normal_log(const T_y& y, const T_loc& mu, const T_scale& sigma,
142  const T_inv_scale& lambda) {
143  return exp_mod_normal_log<false>(y, mu, sigma, lambda);
144  }
145  }
146 }
147 #endif
148 
149 
150 
VectorView< T_return_type, false, true > d_x2
fvar< T > sqrt(const fvar< T > &x)
Definition: sqrt.hpp:15
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
return_type< T_y, T_loc, T_scale, T_inv_scale >::type exp_mod_normal_log(const T_y &y, const T_loc &mu, const T_scale &sigma, const T_inv_scale &lambda)
Metaprogram to determine if a type has a base scalar type that can be assigned to type double...
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:10
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.
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 > erfc(const fvar< T > &x)
Definition: erfc.hpp:14
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
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
VectorView< T_return_type, false, true > d_x4

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