Stan Math Library  2.11.0
reverse mode automatic differentiation
rayleigh_cdf.hpp
Go to the documentation of this file.
1 #ifndef STAN_MATH_PRIM_SCAL_PROB_RAYLEIGH_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_RAYLEIGH_CDF_HPP
3 
4 #include <boost/random/uniform_real_distribution.hpp>
5 #include <boost/random/variate_generator.hpp>
20 #include <cmath>
21 
22 namespace stan {
23 
24  namespace math {
25 
26  template <typename T_y, typename T_scale>
27  typename return_type<T_y, T_scale>::type
28  rayleigh_cdf(const T_y& y, const T_scale& sigma) {
29  static const char* function("stan::math::rayleigh_cdf");
31  T_partials_return;
32 
39  using stan::math::square;
41  using std::exp;
42 
43  T_partials_return cdf(1.0);
44 
45  // check if any vectors are zero length
46  if (!(stan::length(y) && stan::length(sigma)))
47  return cdf;
48 
49  check_not_nan(function, "Random variable", y);
50  check_nonnegative(function, "Random variable", y);
51  check_not_nan(function, "Scale parameter", sigma);
52  check_positive(function, "Scale parameter", sigma);
53  check_consistent_sizes(function,
54  "Random variable", y,
55  "Scale parameter", sigma);
56 
57 
58  // set up template expressions wrapping scalars into vector views
59  OperandsAndPartials<T_y, T_scale> operands_and_partials(y, sigma);
60 
61  VectorView<const T_y> y_vec(y);
62  VectorView<const T_scale> sigma_vec(sigma);
63  size_t N = max_size(y, sigma);
64 
66  for (size_t i = 0; i < length(sigma); i++) {
67  inv_sigma[i] = 1.0 / value_of(sigma_vec[i]);
68  }
69 
70  for (size_t n = 0; n < N; n++) {
71  const T_partials_return y_dbl = value_of(y_vec[n]);
72  const T_partials_return y_sqr = y_dbl * y_dbl;
73  const T_partials_return inv_sigma_sqr = inv_sigma[n] * inv_sigma[n];
74  const T_partials_return exp_val = exp(-0.5 * y_sqr * inv_sigma_sqr);
75 
77  cdf *= (1.0 - exp_val);
78  }
79 
80  // gradients
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 y_sqr = square(y_dbl);
84  const T_partials_return inv_sigma_sqr = square(inv_sigma[n]);
85  const T_partials_return exp_val = exp(-0.5 * y_sqr * inv_sigma_sqr);
86  const T_partials_return exp_div_1m_exp = exp_val / (1.0 - exp_val);
87 
89  operands_and_partials.d_x1[n] += y_dbl * inv_sigma_sqr
90  * exp_div_1m_exp * cdf;
92  operands_and_partials.d_x2[n] -= y_sqr * inv_sigma_sqr
93  * inv_sigma[n] * exp_div_1m_exp * cdf;
94  }
95 
96  return operands_and_partials.value(cdf);
97  }
98  }
99 }
100 #endif
VectorView< T_return_type, false, true > d_x2
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
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) prob...
fvar< T > square(const fvar< T > &x)
Definition: square.hpp:15
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.
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
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.
bool check_nonnegative(const char *function, const char *name, const T_y &y)
Return true if y is non-negative.
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
boost::math::tools::promote_args< typename partials_type< typename scalar_type< T1 >::type >::type, typename partials_type< typename scalar_type< T2 >::type >::type, typename partials_type< typename scalar_type< T3 >::type >::type, typename partials_type< typename scalar_type< T4 >::type >::type, typename partials_type< typename scalar_type< T5 >::type >::type, typename partials_type< typename scalar_type< T6 >::type >::type >::type type
return_type< T_y, T_scale >::type rayleigh_cdf(const T_y &y, const T_scale &sigma)
VectorView< T_return_type, false, true > d_x1

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