Stan Math Library  2.12.0
reverse mode automatic differentiation
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 
17 #include <boost/random/variate_generator.hpp>
18 #include <boost/math/distributions.hpp>
19 #include <cmath>
20 
21 namespace stan {
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("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;
36  using std::exp;
37 
38  if (!(stan::length(y)
39  && stan::length(mu)
40  && stan::length(sigma)
41  && stan::length(alpha)))
42  return 0.0;
43 
44  T_partials_return logp(0.0);
45 
46  check_not_nan(function, "Random variable", y);
47  check_finite(function, "Location parameter", mu);
48  check_finite(function, "Shape parameter", alpha);
49  check_positive(function, "Scale parameter", sigma);
50  check_consistent_sizes(function,
51  "Random variable", y,
52  "Location parameter", mu,
53  "Scale parameter", sigma,
54  "Shape paramter", alpha);
55 
57  return 0.0;
58 
60  operands_and_partials(y, mu, sigma, alpha);
61 
62  using boost::math::erfc;
63  using boost::math::erf;
64  using std::log;
65 
66  VectorView<const T_y> y_vec(y);
67  VectorView<const T_loc> mu_vec(mu);
68  VectorView<const T_scale> sigma_vec(sigma);
69  VectorView<const T_shape> alpha_vec(alpha);
70  size_t N = max_size(y, mu, sigma, alpha);
71 
74  T_partials_return, T_scale> log_sigma(length(sigma));
75  for (size_t i = 0; i < length(sigma); i++) {
76  inv_sigma[i] = 1.0 / value_of(sigma_vec[i]);
78  log_sigma[i] = log(value_of(sigma_vec[i]));
79  }
80 
81  for (size_t n = 0; n < N; n++) {
82  const T_partials_return y_dbl = value_of(y_vec[n]);
83  const T_partials_return mu_dbl = value_of(mu_vec[n]);
84  const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
85  const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
86 
87  const T_partials_return y_minus_mu_over_sigma
88  = (y_dbl - mu_dbl) * inv_sigma[n];
89  const double pi_dbl = pi();
90 
92  logp -= 0.5 * log(2.0 * pi_dbl);
94  logp -= log(sigma_dbl);
96  logp -= y_minus_mu_over_sigma * y_minus_mu_over_sigma / 2.0;
98  logp += log(erfc(-alpha_dbl * y_minus_mu_over_sigma
99  / std::sqrt(2.0)));
100 
101  T_partials_return deriv_logerf
102  = 2.0 / std::sqrt(pi_dbl)
103  * exp(-alpha_dbl * y_minus_mu_over_sigma / std::sqrt(2.0)
104  * alpha_dbl * y_minus_mu_over_sigma / std::sqrt(2.0))
105  / (1 + erf(alpha_dbl * y_minus_mu_over_sigma
106  / std::sqrt(2.0)));
108  operands_and_partials.d_x1[n]
109  += -y_minus_mu_over_sigma / sigma_dbl
110  + deriv_logerf * alpha_dbl / (sigma_dbl * std::sqrt(2.0));
112  operands_and_partials.d_x2[n]
113  += y_minus_mu_over_sigma / sigma_dbl
114  + deriv_logerf * -alpha_dbl / (sigma_dbl * std::sqrt(2.0));
116  operands_and_partials.d_x3[n]
117  += -1.0 / sigma_dbl
118  + y_minus_mu_over_sigma * y_minus_mu_over_sigma / sigma_dbl
119  - deriv_logerf * y_minus_mu_over_sigma * alpha_dbl
120  / (sigma_dbl * std::sqrt(2.0));
122  operands_and_partials.d_x4[n]
123  += deriv_logerf * y_minus_mu_over_sigma / std::sqrt(2.0);
124  }
125  return operands_and_partials.value(logp);
126  }
127 
128  template <typename T_y, typename T_loc, typename T_scale, typename T_shape>
129  inline
131  skew_normal_log(const T_y& y, const T_loc& mu, const T_scale& sigma,
132  const T_shape& alpha) {
133  return skew_normal_log<false>(y, mu, sigma, alpha);
134  }
135 
136  }
137 }
138 #endif
139 
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:14
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:14
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:85
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

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