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skew_normal_log.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_SKEW_NORMAL_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_SKEW_NORMAL_LOG_HPP
3 
4 #include <boost/random/variate_generator.hpp>
5 #include <boost/math/distributions.hpp>
18 #include <cmath>
19 
20 namespace stan {
21 
22  namespace math {
23 
24  template <bool propto,
25  typename T_y, typename T_loc, typename T_scale, typename T_shape>
26  typename return_type<T_y, T_loc, T_scale, T_shape>::type
27  skew_normal_log(const T_y& y, const T_loc& mu, const T_scale& sigma,
28  const T_shape& alpha) {
29  static const char* function("stan::math::skew_normal_log");
30  typedef typename stan::partials_return_type<T_y, T_loc,
31  T_scale, T_shape>::type
32  T_partials_return;
33 
34  using std::log;
42  using std::exp;
43 
44  // check if any vectors are zero length
45  if (!(stan::length(y)
46  && stan::length(mu)
47  && stan::length(sigma)
48  && stan::length(alpha)))
49  return 0.0;
50 
51  // set up return value accumulator
52  T_partials_return logp(0.0);
53 
54  // validate args (here done over var, which should be OK)
55  check_not_nan(function, "Random variable", y);
56  check_finite(function, "Location parameter", mu);
57  check_finite(function, "Shape parameter", alpha);
58  check_positive(function, "Scale parameter", sigma);
59  check_consistent_sizes(function,
60  "Random variable", y,
61  "Location parameter", mu,
62  "Scale parameter", sigma,
63  "Shape paramter", alpha);
64 
65  // check if no variables are involved and prop-to
67  return 0.0;
68 
69  // set up template expressions wrapping scalars into vector views
71  operands_and_partials(y, mu, sigma, alpha);
72 
73  using boost::math::erfc;
74  using boost::math::erf;
75  using std::log;
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_shape> alpha_vec(alpha);
81  size_t N = max_size(y, mu, sigma, alpha);
82 
85  T_partials_return, T_scale> log_sigma(length(sigma));
86  for (size_t i = 0; i < length(sigma); i++) {
87  inv_sigma[i] = 1.0 / value_of(sigma_vec[i]);
89  log_sigma[i] = log(value_of(sigma_vec[i]));
90  }
91 
92  for (size_t n = 0; n < N; n++) {
93  // pull out values of arguments
94  const T_partials_return y_dbl = value_of(y_vec[n]);
95  const T_partials_return mu_dbl = value_of(mu_vec[n]);
96  const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
97  const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
98 
99  // reusable subexpression values
100  const T_partials_return y_minus_mu_over_sigma
101  = (y_dbl - mu_dbl) * inv_sigma[n];
102  const double pi_dbl = stan::math::pi();
103 
104  // log probability
106  logp -= 0.5 * log(2.0 * pi_dbl);
108  logp -= log(sigma_dbl);
110  logp -= y_minus_mu_over_sigma * y_minus_mu_over_sigma / 2.0;
112  logp += log(erfc(-alpha_dbl * y_minus_mu_over_sigma
113  / std::sqrt(2.0)));
114 
115  // gradients
116  T_partials_return deriv_logerf
117  = 2.0 / std::sqrt(pi_dbl)
118  * exp(-alpha_dbl * y_minus_mu_over_sigma / std::sqrt(2.0)
119  * alpha_dbl * y_minus_mu_over_sigma / std::sqrt(2.0))
120  / (1 + erf(alpha_dbl * y_minus_mu_over_sigma
121  / std::sqrt(2.0)));
123  operands_and_partials.d_x1[n]
124  += -y_minus_mu_over_sigma / sigma_dbl
125  + deriv_logerf * alpha_dbl / (sigma_dbl * std::sqrt(2.0));
127  operands_and_partials.d_x2[n]
128  += y_minus_mu_over_sigma / sigma_dbl
129  + deriv_logerf * -alpha_dbl / (sigma_dbl * std::sqrt(2.0));
131  operands_and_partials.d_x3[n]
132  += -1.0 / sigma_dbl
133  + y_minus_mu_over_sigma * y_minus_mu_over_sigma / sigma_dbl
134  - deriv_logerf * y_minus_mu_over_sigma * alpha_dbl
135  / (sigma_dbl * std::sqrt(2.0));
137  operands_and_partials.d_x4[n]
138  += deriv_logerf * y_minus_mu_over_sigma / std::sqrt(2.0);
139  }
140  return operands_and_partials.to_var(logp, y, mu, sigma, alpha);
141  }
142 
143  template <typename T_y, typename T_loc, typename T_scale, typename T_shape>
144  inline
146  skew_normal_log(const T_y& y, const T_loc& mu, const T_scale& sigma,
147  const T_shape& alpha) {
148  return skew_normal_log<false>(y, mu, sigma, alpha);
149  }
150  }
151 }
152 #endif
153 
return_type< T_y, T_loc, T_scale, T_shape >::type skew_normal_log(const T_y &y, const T_loc &mu, const T_scale &sigma, const T_shape &alpha)
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
fvar< T > erf(const fvar< T > &x)
Definition: erf.hpp:14
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...
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...
bool check_positive(const char *function, const char *name, const T_y &y)
Return true if y is positive.
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
double pi()
Return the value of pi.
Definition: constants.hpp:86
VectorView is a template metaprogram that takes its argument and allows it to be used like a vector...
Definition: VectorView.hpp:41

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