Stan Math Library  2.11.0
reverse mode automatic differentiation
skew_normal_cdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_SKEW_NORMAL_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_SKEW_NORMAL_CDF_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 <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_cdf(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_cdf");
30  typedef typename stan::partials_return_type<T_y, T_loc, T_scale,
31  T_shape>::type
32  T_partials_return;
33 
38  using stan::math::owens_t;
40 
41  T_partials_return cdf(1.0);
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(alpha)))
48  return cdf;
49 
50  check_not_nan(function, "Random variable", y);
51  check_finite(function, "Location parameter", mu);
52  check_not_nan(function, "Scale parameter", sigma);
53  check_positive(function, "Scale parameter", sigma);
54  check_finite(function, "Shape parameter", alpha);
55  check_not_nan(function, "Shape parameter", alpha);
56  check_consistent_sizes(function,
57  "Random variable", y,
58  "Location parameter", mu,
59  "Scale parameter", sigma,
60  "Shape paramter", alpha);
61 
63  operands_and_partials(y, mu, sigma, alpha);
64 
65  using stan::math::SQRT_2;
66  using stan::math::pi;
67  using std::exp;
68 
69  VectorView<const T_y> y_vec(y);
70  VectorView<const T_loc> mu_vec(mu);
71  VectorView<const T_scale> sigma_vec(sigma);
72  VectorView<const T_shape> alpha_vec(alpha);
73  size_t N = max_size(y, mu, sigma, alpha);
74  const double SQRT_TWO_OVER_PI = std::sqrt(2.0 / stan::math::pi());
75 
76  for (size_t n = 0; n < N; n++) {
77  const T_partials_return y_dbl = value_of(y_vec[n]);
78  const T_partials_return mu_dbl = value_of(mu_vec[n]);
79  const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
80  const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
81  const T_partials_return alpha_dbl_sq = alpha_dbl * alpha_dbl;
82  const T_partials_return diff = (y_dbl - mu_dbl) / sigma_dbl;
83  const T_partials_return diff_sq = diff * diff;
84  const T_partials_return scaled_diff = diff / SQRT_2;
85  const T_partials_return scaled_diff_sq = diff_sq * 0.5;
86  const T_partials_return cdf_ = 0.5 * erfc(-scaled_diff) - 2
87  * owens_t(diff, alpha_dbl);
88 
89  // cdf
90  cdf *= cdf_;
91 
92  // gradients
93  const T_partials_return deriv_erfc = SQRT_TWO_OVER_PI * 0.5
94  * exp(-scaled_diff_sq)
95  / sigma_dbl;
96  const T_partials_return deriv_owens = erf(alpha_dbl * scaled_diff)
97  * exp(-scaled_diff_sq) / SQRT_TWO_OVER_PI / (-2.0 * pi()) / sigma_dbl;
98  const T_partials_return rep_deriv = (-2.0 * deriv_owens + deriv_erfc)
99  / cdf_;
100 
102  operands_and_partials.d_x1[n] += rep_deriv;
104  operands_and_partials.d_x2[n] -= rep_deriv;
106  operands_and_partials.d_x3[n] -= rep_deriv * diff;
108  operands_and_partials.d_x4[n] += -2.0 * exp(-0.5 * diff_sq
109  * (1.0 + alpha_dbl_sq))
110  / ((1 + alpha_dbl_sq) * 2.0 * pi()) / cdf_;
111  }
112 
114  for (size_t n = 0; n < stan::length(y); ++n)
115  operands_and_partials.d_x1[n] *= cdf;
116  }
118  for (size_t n = 0; n < stan::length(mu); ++n)
119  operands_and_partials.d_x2[n] *= cdf;
120  }
122  for (size_t n = 0; n < stan::length(sigma); ++n)
123  operands_and_partials.d_x3[n] *= cdf;
124  }
126  for (size_t n = 0; n < stan::length(alpha); ++n)
127  operands_and_partials.d_x4[n] *= cdf;
128  }
129 
130  return operands_and_partials.value(cdf);
131  }
132  }
133 }
134 #endif
135 
VectorView< T_return_type, false, true > d_x2
return_type< T_y, T_loc, T_scale, T_shape >::type skew_normal_cdf(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
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
fvar< T > owens_t(const fvar< T > &x1, const fvar< T > &x2)
Definition: owens_t.hpp:14
Metaprogram to determine if a type has a base scalar type that can be assigned to type double...
const double SQRT_2
The value of the square root of 2, .
Definition: constants.hpp:21
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.
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

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