Stan Math Library  2.20.0
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 
10 #include <cmath>
11 
12 namespace stan {
13 namespace math {
14 
29 template <typename T_y, typename T_loc, typename T_scale>
31  const T_y& y, const T_loc& mu, const T_scale& sigma) {
32  static const char* function = "double_exponential_cdf";
34  T_partials_return;
35 
36  if (size_zero(y, mu, sigma))
37  return 1.0;
38 
39  using std::exp;
40 
41  T_partials_return cdf(1.0);
42 
43  check_not_nan(function, "Random variable", y);
44  check_finite(function, "Location parameter", mu);
45  check_positive_finite(function, "Scale parameter", sigma);
46 
47  operands_and_partials<T_y, T_loc, T_scale> ops_partials(y, mu, sigma);
48 
49  scalar_seq_view<T_y> y_vec(y);
50  scalar_seq_view<T_loc> mu_vec(mu);
51  scalar_seq_view<T_scale> sigma_vec(sigma);
52  size_t N = max_size(y, mu, sigma);
53 
54  for (size_t n = 0; n < N; n++) {
55  const T_partials_return y_dbl = value_of(y_vec[n]);
56  const T_partials_return mu_dbl = value_of(mu_vec[n]);
57  const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
58  const T_partials_return scaled_diff = (y_dbl - mu_dbl) / (sigma_dbl);
59  const T_partials_return exp_scaled_diff = exp(scaled_diff);
60 
61  if (y_dbl < mu_dbl)
62  cdf *= exp_scaled_diff * 0.5;
63  else
64  cdf *= 1.0 - 0.5 / exp_scaled_diff;
65  }
66 
67  for (size_t n = 0; n < N; n++) {
68  const T_partials_return y_dbl = value_of(y_vec[n]);
69  const T_partials_return mu_dbl = value_of(mu_vec[n]);
70  const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
71  const T_partials_return scaled_diff = (y_dbl - mu_dbl) / sigma_dbl;
72  const T_partials_return exp_scaled_diff = exp(scaled_diff);
73  const T_partials_return inv_sigma = 1.0 / sigma_dbl;
74 
75  if (y_dbl < mu_dbl) {
77  ops_partials.edge1_.partials_[n] += inv_sigma * cdf;
79  ops_partials.edge2_.partials_[n] -= inv_sigma * cdf;
81  ops_partials.edge3_.partials_[n] -= scaled_diff * inv_sigma * cdf;
82  } else {
83  const T_partials_return rep_deriv
84  = cdf * inv_sigma / (2.0 * exp_scaled_diff - 1.0);
86  ops_partials.edge1_.partials_[n] += rep_deriv;
88  ops_partials.edge2_.partials_[n] -= rep_deriv;
90  ops_partials.edge3_.partials_[n] -= rep_deriv * scaled_diff;
91  }
92  }
93  return ops_partials.build(cdf);
94 }
95 
96 } // namespace math
97 } // namespace stan
98 #endif
void check_finite(const char *function, const char *name, const T_y &y)
Check if y is finite.
boost::math::tools::promote_args< double, typename partials_type< typename scalar_type< T >::type >::type, typename partials_return_type< T_pack... >::type >::type type
T value_of(const fvar< T > &v)
Return the value of the specified variable.
Definition: value_of.hpp:17
Extends std::true_type when instantiated with zero or more template parameters, all of which extend t...
Definition: conjunction.hpp:14
scalar_seq_view provides a uniform sequence-like wrapper around either a scalar or a sequence of scal...
This template builds partial derivatives with respect to a set of operands.
bool size_zero(T &x)
Returns 1 if input is of length 0, returns 0 otherwise.
Definition: size_zero.hpp:18
return_type< T_y, T_loc, T_scale >::type double_exponential_cdf(const T_y &y, const T_loc &mu, const T_scale &sigma)
Returns the double exponential cumulative density function.
void check_positive_finite(const char *function, const char *name, const T_y &y)
Check if y is positive and finite.
boost::math::tools::promote_args< double, typename scalar_type< T >::type, typename return_type< Types_pack... >::type >::type type
Definition: return_type.hpp:36
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:11
void check_not_nan(const char *function, const char *name, const T_y &y)
Check if y is not NaN.
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
T_return_type build(double value)
Build the node to be stored on the autodiff graph.
internal::ops_partials_edge< double, Op2 > edge2_
internal::ops_partials_edge< double, Op3 > edge3_
internal::ops_partials_edge< double, Op1 > edge1_

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