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reverse mode automatic differentiation
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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 
4 #include <boost/random/uniform_01.hpp>
5 #include <boost/random/variate_generator.hpp>
16 #include <cmath>
17 
18 namespace stan {
19 
20  namespace math {
21 
36  template <typename T_y, typename T_loc, typename T_scale>
37  typename return_type<T_y, T_loc, T_scale>::type
38  double_exponential_cdf(const T_y& y,
39  const T_loc& mu, const T_scale& sigma) {
40  static const char* function("stan::math::double_exponential_cdf");
42  T_partials_return;
43 
44  // Size checks
45  if ( !( stan::length(y) && stan::length(mu)
46  && stan::length(sigma) ) )
47  return 1.0;
48 
53  using boost::math::tools::promote_args;
54  using std::exp;
55 
56  T_partials_return cdf(1.0);
57 
58  check_not_nan(function, "Random variable", y);
59  check_finite(function, "Location parameter", mu);
60  check_positive_finite(function, "Scale parameter", sigma);
61 
63  operands_and_partials(y, mu, sigma);
64 
65  VectorView<const T_y> y_vec(y);
66  VectorView<const T_loc> mu_vec(mu);
67  VectorView<const T_scale> sigma_vec(sigma);
68  size_t N = max_size(y, mu, sigma);
69 
70  // cdf
71  for (size_t n = 0; n < N; n++) {
72  const T_partials_return y_dbl = value_of(y_vec[n]);
73  const T_partials_return mu_dbl = value_of(mu_vec[n]);
74  const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
75  const T_partials_return scaled_diff = (y_dbl - mu_dbl) / (sigma_dbl);
76  const T_partials_return exp_scaled_diff = exp(scaled_diff);
77 
78  if (y_dbl < mu_dbl)
79  cdf *= exp_scaled_diff * 0.5;
80  else
81  cdf *= 1.0 - 0.5 / exp_scaled_diff;
82  }
83 
84  // gradients
85  for (size_t n = 0; n < N; n++) {
86  const T_partials_return y_dbl = value_of(y_vec[n]);
87  const T_partials_return mu_dbl = value_of(mu_vec[n]);
88  const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
89  const T_partials_return scaled_diff = (y_dbl - mu_dbl) / sigma_dbl;
90  const T_partials_return exp_scaled_diff = exp(scaled_diff);
91  const T_partials_return inv_sigma = 1.0 / sigma_dbl;
92 
93  if (y_dbl < mu_dbl) {
95  operands_and_partials.d_x1[n] += inv_sigma * cdf;
97  operands_and_partials.d_x2[n] -= inv_sigma * cdf;
99  operands_and_partials.d_x3[n] -= scaled_diff * inv_sigma * cdf;
100  } else {
101  const T_partials_return rep_deriv = cdf * inv_sigma
102  / (2.0 * exp_scaled_diff - 1.0);
104  operands_and_partials.d_x1[n] += rep_deriv;
106  operands_and_partials.d_x2[n] -= rep_deriv;
108  operands_and_partials.d_x3[n] -= rep_deriv * scaled_diff;
109  }
110  }
111  return operands_and_partials.to_var(cdf, y, mu, sigma);
112  }
113  }
114 }
115 #endif
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
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
T_return_type to_var(T_partials_return logp, const T1 &x1=0, const T2 &x2=0, const T3 &x3=0, const T4 &x4=0, const T5 &x5=0, const T6 &x6=0)
VectorView< T_partials_return, is_vector< T1 >::value, is_constant_struct< T1 >::value > d_x1
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
VectorView< T_partials_return, is_vector< T3 >::value, is_constant_struct< T3 >::value > d_x3
A variable implementation that stores operands and derivatives with respect to the variable...
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< T_partials_return, is_vector< T2 >::value, is_constant_struct< T2 >::value > d_x2
VectorView is a template metaprogram that takes its argument and allows it to be used like a vector...
Definition: VectorView.hpp:41
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.

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