Stan Math Library  2.11.0
reverse mode automatic differentiation
double_exponential_cdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_DOUBLE_EXPONENTIAL_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_DOUBLE_EXPONENTIAL_CDF_HPP
3 
16 #include <boost/random/uniform_01.hpp>
17 #include <boost/random/variate_generator.hpp>
18 #include <cmath>
19 
20 namespace stan {
21 
22  namespace math {
23 
38  template <typename T_y, typename T_loc, typename T_scale>
39  typename return_type<T_y, T_loc, T_scale>::type
40  double_exponential_cdf(const T_y& y,
41  const T_loc& mu, const T_scale& sigma) {
42  static const char* function("stan::math::double_exponential_cdf");
44  T_partials_return;
45 
46  // Size checks
47  if ( !( stan::length(y) && stan::length(mu)
48  && stan::length(sigma) ) )
49  return 1.0;
50 
55  using boost::math::tools::promote_args;
56  using std::exp;
57 
58  T_partials_return cdf(1.0);
59 
60  check_not_nan(function, "Random variable", y);
61  check_finite(function, "Location parameter", mu);
62  check_positive_finite(function, "Scale parameter", sigma);
63 
65  operands_and_partials(y, mu, sigma);
66 
67  VectorView<const T_y> y_vec(y);
68  VectorView<const T_loc> mu_vec(mu);
69  VectorView<const T_scale> sigma_vec(sigma);
70  size_t N = max_size(y, mu, sigma);
71 
72  // cdf
73  for (size_t n = 0; n < N; n++) {
74  const T_partials_return y_dbl = value_of(y_vec[n]);
75  const T_partials_return mu_dbl = value_of(mu_vec[n]);
76  const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
77  const T_partials_return scaled_diff = (y_dbl - mu_dbl) / (sigma_dbl);
78  const T_partials_return exp_scaled_diff = exp(scaled_diff);
79 
80  if (y_dbl < mu_dbl)
81  cdf *= exp_scaled_diff * 0.5;
82  else
83  cdf *= 1.0 - 0.5 / exp_scaled_diff;
84  }
85 
86  // gradients
87  for (size_t n = 0; n < N; n++) {
88  const T_partials_return y_dbl = value_of(y_vec[n]);
89  const T_partials_return mu_dbl = value_of(mu_vec[n]);
90  const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
91  const T_partials_return scaled_diff = (y_dbl - mu_dbl) / sigma_dbl;
92  const T_partials_return exp_scaled_diff = exp(scaled_diff);
93  const T_partials_return inv_sigma = 1.0 / sigma_dbl;
94 
95  if (y_dbl < mu_dbl) {
97  operands_and_partials.d_x1[n] += inv_sigma * cdf;
99  operands_and_partials.d_x2[n] -= inv_sigma * cdf;
101  operands_and_partials.d_x3[n] -= scaled_diff * inv_sigma * cdf;
102  } else {
103  const T_partials_return rep_deriv = cdf * inv_sigma
104  / (2.0 * exp_scaled_diff - 1.0);
106  operands_and_partials.d_x1[n] += rep_deriv;
108  operands_and_partials.d_x2[n] -= rep_deriv;
110  operands_and_partials.d_x3[n] -= rep_deriv * scaled_diff;
111  }
112  }
113  return operands_and_partials.value(cdf);
114  }
115  }
116 }
117 #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
Metaprogram to determine if a type has a base scalar type that can be assigned to type double...
return_type< T_y, T_loc, T_scale >::type double_exponential_cdf(const T_y &y, const T_loc &mu, const T_scale &sigma)
Calculates the double exponential cumulative density function.
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
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.
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
bool check_positive_finite(const char *function, const char *name, const T_y &y)
Return true if y is positive and finite.
VectorView< T_return_type, false, true > d_x1

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