Stan Math Library  2.10.0
reverse mode automatic differentiation
skew_normal_log.hpp
Go to the documentation of this file.
1 #ifndef STAN_MATH_PRIM_SCAL_PROB_SKEW_NORMAL_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_SKEW_NORMAL_LOG_HPP
3 
17 #include <boost/random/variate_generator.hpp>
18 #include <boost/math/distributions.hpp>
19 #include <cmath>
20 
21 namespace stan {
22 
23  namespace math {
24 
25  template <bool propto,
26  typename T_y, typename T_loc, typename T_scale, typename T_shape>
27  typename return_type<T_y, T_loc, T_scale, T_shape>::type
28  skew_normal_log(const T_y& y, const T_loc& mu, const T_scale& sigma,
29  const T_shape& alpha) {
30  static const char* function("stan::math::skew_normal_log");
31  typedef typename stan::partials_return_type<T_y, T_loc,
32  T_scale, T_shape>::type
33  T_partials_return;
34 
35  using std::log;
43  using std::exp;
44 
45  // check if any vectors are zero length
46  if (!(stan::length(y)
47  && stan::length(mu)
48  && stan::length(sigma)
49  && stan::length(alpha)))
50  return 0.0;
51 
52  // set up return value accumulator
53  T_partials_return logp(0.0);
54 
55  // validate args (here done over var, which should be OK)
56  check_not_nan(function, "Random variable", y);
57  check_finite(function, "Location parameter", mu);
58  check_finite(function, "Shape parameter", alpha);
59  check_positive(function, "Scale parameter", sigma);
60  check_consistent_sizes(function,
61  "Random variable", y,
62  "Location parameter", mu,
63  "Scale parameter", sigma,
64  "Shape paramter", alpha);
65 
66  // check if no variables are involved and prop-to
68  return 0.0;
69 
70  // set up template expressions wrapping scalars into vector views
72  operands_and_partials(y, mu, sigma, alpha);
73 
74  using boost::math::erfc;
75  using boost::math::erf;
76  using std::log;
77 
78  VectorView<const T_y> y_vec(y);
79  VectorView<const T_loc> mu_vec(mu);
80  VectorView<const T_scale> sigma_vec(sigma);
81  VectorView<const T_shape> alpha_vec(alpha);
82  size_t N = max_size(y, mu, sigma, alpha);
83 
86  T_partials_return, T_scale> log_sigma(length(sigma));
87  for (size_t i = 0; i < length(sigma); i++) {
88  inv_sigma[i] = 1.0 / value_of(sigma_vec[i]);
90  log_sigma[i] = log(value_of(sigma_vec[i]));
91  }
92 
93  for (size_t n = 0; n < N; n++) {
94  // pull out values of arguments
95  const T_partials_return y_dbl = value_of(y_vec[n]);
96  const T_partials_return mu_dbl = value_of(mu_vec[n]);
97  const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
98  const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
99 
100  // reusable subexpression values
101  const T_partials_return y_minus_mu_over_sigma
102  = (y_dbl - mu_dbl) * inv_sigma[n];
103  const double pi_dbl = stan::math::pi();
104 
105  // log probability
107  logp -= 0.5 * log(2.0 * pi_dbl);
109  logp -= log(sigma_dbl);
111  logp -= y_minus_mu_over_sigma * y_minus_mu_over_sigma / 2.0;
113  logp += log(erfc(-alpha_dbl * y_minus_mu_over_sigma
114  / std::sqrt(2.0)));
115 
116  // gradients
117  T_partials_return deriv_logerf
118  = 2.0 / std::sqrt(pi_dbl)
119  * exp(-alpha_dbl * y_minus_mu_over_sigma / std::sqrt(2.0)
120  * alpha_dbl * y_minus_mu_over_sigma / std::sqrt(2.0))
121  / (1 + erf(alpha_dbl * y_minus_mu_over_sigma
122  / std::sqrt(2.0)));
124  operands_and_partials.d_x1[n]
125  += -y_minus_mu_over_sigma / sigma_dbl
126  + deriv_logerf * alpha_dbl / (sigma_dbl * std::sqrt(2.0));
128  operands_and_partials.d_x2[n]
129  += y_minus_mu_over_sigma / sigma_dbl
130  + deriv_logerf * -alpha_dbl / (sigma_dbl * std::sqrt(2.0));
132  operands_and_partials.d_x3[n]
133  += -1.0 / sigma_dbl
134  + y_minus_mu_over_sigma * y_minus_mu_over_sigma / sigma_dbl
135  - deriv_logerf * y_minus_mu_over_sigma * alpha_dbl
136  / (sigma_dbl * std::sqrt(2.0));
138  operands_and_partials.d_x4[n]
139  += deriv_logerf * y_minus_mu_over_sigma / std::sqrt(2.0);
140  }
141  return operands_and_partials.value(logp);
142  }
143 
144  template <typename T_y, typename T_loc, typename T_scale, typename T_shape>
145  inline
147  skew_normal_log(const T_y& y, const T_loc& mu, const T_scale& sigma,
148  const T_shape& alpha) {
149  return skew_normal_log<false>(y, mu, sigma, alpha);
150  }
151  }
152 }
153 #endif
154 
VectorView< T_return_type, false, true > d_x2
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
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
fvar< T > erf(const fvar< T > &x)
Definition: erf.hpp:14
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
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
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.
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 > erfc(const fvar< T > &x)
Definition: erfc.hpp:14
double pi()
Return the value of pi.
Definition: constants.hpp:86
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
VectorView< T_return_type, false, true > d_x1
VectorView< T_return_type, false, true > d_x4

     [ Stan Home Page ] © 2011–2016, Stan Development Team.