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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 
4 #include <boost/random/normal_distribution.hpp>
5 #include <boost/math/special_functions/fpclassify.hpp>
6 #include <boost/random/variate_generator.hpp>
15 #include <cmath>
16 
17 namespace stan {
18 
19  namespace math {
20 
21  template <bool propto,
22  typename T_y, typename T_loc, typename T_scale,
23  typename T_inv_scale>
24  typename return_type<T_y, T_loc, T_scale, T_inv_scale>::type
25  exp_mod_normal_log(const T_y& y, const T_loc& mu, const T_scale& sigma,
26  const T_inv_scale& lambda) {
27  static const char* function("stan::math::exp_mod_normal_log");
28  typedef typename stan::partials_return_type<T_y, T_loc, T_scale,
29  T_inv_scale>::type
30  T_partials_return;
31 
39  using std::log;
40 
41  // check if any vectors are zero length
42  if (!(stan::length(y)
43  && stan::length(mu)
44  && stan::length(sigma)
45  && stan::length(lambda)))
46  return 0.0;
47 
48  // set up return value accumulator
49  T_partials_return logp(0.0);
50 
51  // validate args (here done over var, which should be OK)
52  check_not_nan(function, "Random variable", y);
53  check_finite(function, "Location parameter", mu);
54  check_positive_finite(function, "Inv_scale parameter", lambda);
55  check_positive_finite(function, "Scale parameter", sigma);
56  check_consistent_sizes(function,
57  "Random variable", y,
58  "Location parameter", mu,
59  "Scale parameter", sigma,
60  "Inv_scale paramter", lambda);
61 
62  // check if no variables are involved and prop-to
64  return 0.0;
65 
66  using boost::math::erfc;
67  using std::sqrt;
68  using std::log;
69  using std::exp;
70 
71  // set up template expressions wrapping scalars into vector views
73  operands_and_partials(y, mu, sigma, lambda);
74 
75  VectorView<const T_y> y_vec(y);
76  VectorView<const T_loc> mu_vec(mu);
77  VectorView<const T_scale> sigma_vec(sigma);
78  VectorView<const T_inv_scale> lambda_vec(lambda);
79  size_t N = max_size(y, mu, sigma, lambda);
80 
81  for (size_t n = 0; n < N; n++) {
82  // pull out values of arguments
83  const T_partials_return y_dbl = value_of(y_vec[n]);
84  const T_partials_return mu_dbl = value_of(mu_vec[n]);
85  const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
86  const T_partials_return lambda_dbl = value_of(lambda_vec[n]);
87 
88  const T_partials_return pi_dbl = boost::math::constants::pi<double>();
89 
90  // log probability
92  logp -= log(2.0);
94  logp += log(lambda_dbl);
96  logp += lambda_dbl
97  * (mu_dbl + 0.5 * lambda_dbl * sigma_dbl * sigma_dbl - y_dbl)
98  + log(erfc((mu_dbl + lambda_dbl * sigma_dbl
99  * sigma_dbl - y_dbl)
100  / (sqrt(2.0) * sigma_dbl)));
101 
102  // gradients
103  const T_partials_return deriv_logerfc
104  = -2.0 / sqrt(pi_dbl)
105  * exp(-(mu_dbl + lambda_dbl * sigma_dbl * sigma_dbl - y_dbl)
106  / (std::sqrt(2.0) * sigma_dbl)
107  * (mu_dbl + lambda_dbl * sigma_dbl * sigma_dbl - y_dbl)
108  / (sigma_dbl * std::sqrt(2.0)))
109  / erfc((mu_dbl + lambda_dbl * sigma_dbl * sigma_dbl
110  - y_dbl) / (sigma_dbl * std::sqrt(2.0)));
111 
113  operands_and_partials.d_x1[n]
114  += -lambda_dbl
115  + deriv_logerfc * -1.0 / (sigma_dbl * std::sqrt(2.0));
117  operands_and_partials.d_x2[n]
118  += lambda_dbl
119  + deriv_logerfc / (sigma_dbl * std::sqrt(2.0));
121  operands_and_partials.d_x3[n]
122  += sigma_dbl * lambda_dbl * lambda_dbl
123  + deriv_logerfc
124  * (-mu_dbl / (sigma_dbl * sigma_dbl * std::sqrt(2.0))
125  + lambda_dbl / std::sqrt(2.0)
126  + y_dbl / (sigma_dbl * sigma_dbl * std::sqrt(2.0)));
128  operands_and_partials.d_x4[n]
129  += 1 / lambda_dbl + lambda_dbl * sigma_dbl * sigma_dbl
130  + mu_dbl - y_dbl + deriv_logerfc * sigma_dbl / std::sqrt(2.0);
131  }
132  return operands_and_partials.to_var(logp, y, mu, sigma, lambda);
133  }
134 
135  template <typename T_y, typename T_loc, typename T_scale,
136  typename T_inv_scale>
137  inline
139  exp_mod_normal_log(const T_y& y, const T_loc& mu, const T_scale& sigma,
140  const T_inv_scale& lambda) {
141  return exp_mod_normal_log<false>(y, mu, sigma, lambda);
142  }
143  }
144 }
145 #endif
146 
147 
148 
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
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
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)
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...
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:10
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 > erfc(const fvar< T > &x)
Definition: erfc.hpp:14
VectorView is a template metaprogram that takes its argument and allows it to be used like a vector...
Definition: VectorView.hpp:41
bool check_positive_finite(const char *function, const char *name, const T_y &y)
Return true if y is positive and finite.

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