Stan Math Library  2.20.0
reverse mode automatic differentiation
exponential_cdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_EXPONENTIAL_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_EXPONENTIAL_CDF_HPP
3 
10 #include <cmath>
11 
12 namespace stan {
13 namespace math {
14 
27 template <typename T_y, typename T_inv_scale>
29  const T_y& y, const T_inv_scale& beta) {
31  T_partials_return;
32 
33  static const char* function = "exponential_cdf";
34 
35  using std::exp;
36 
37  T_partials_return cdf(1.0);
38  if (size_zero(y, beta))
39  return cdf;
40 
41  check_not_nan(function, "Random variable", y);
42  check_nonnegative(function, "Random variable", y);
43  check_positive_finite(function, "Inverse scale parameter", beta);
44 
45  operands_and_partials<T_y, T_inv_scale> ops_partials(y, beta);
46 
47  scalar_seq_view<T_y> y_vec(y);
48  scalar_seq_view<T_inv_scale> beta_vec(beta);
49  size_t N = max_size(y, beta);
50  for (size_t n = 0; n < N; n++) {
51  const T_partials_return beta_dbl = value_of(beta_vec[n]);
52  const T_partials_return y_dbl = value_of(y_vec[n]);
53  const T_partials_return one_m_exp = 1.0 - exp(-beta_dbl * y_dbl);
54 
55  cdf *= one_m_exp;
56  }
57 
58  for (size_t n = 0; n < N; n++) {
59  const T_partials_return beta_dbl = value_of(beta_vec[n]);
60  const T_partials_return y_dbl = value_of(y_vec[n]);
61  const T_partials_return one_m_exp = 1.0 - exp(-beta_dbl * y_dbl);
62 
63  T_partials_return rep_deriv = exp(-beta_dbl * y_dbl) / one_m_exp;
65  ops_partials.edge1_.partials_[n] += rep_deriv * beta_dbl * cdf;
67  ops_partials.edge2_.partials_[n] += rep_deriv * y_dbl * cdf;
68  }
69  return ops_partials.build(cdf);
70 }
71 
72 } // namespace math
73 } // namespace stan
74 #endif
return_type< T_y, T_inv_scale >::type exponential_cdf(const T_y &y, const T_inv_scale &beta)
Calculates the exponential cumulative distribution function for the given y and beta.
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
void check_nonnegative(const char *function, const char *name, const T_y &y)
Check if y is non-negative.
fvar< T > beta(const fvar< T > &x1, const fvar< T > &x2)
Return fvar with the beta function applied to the specified arguments and its gradient.
Definition: beta.hpp:51
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, Op1 > edge1_

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