Stan Math Library  2.11.0
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 
4 #include <boost/random/exponential_distribution.hpp>
5 #include <boost/random/variate_generator.hpp>
20 #include <cmath>
21 
22 namespace stan {
23 
24  namespace math {
25 
38  template <typename T_y, typename T_inv_scale>
39  typename return_type<T_y, T_inv_scale>::type
40  exponential_cdf(const T_y& y, const T_inv_scale& beta) {
42  T_partials_return;
43 
44  static const char* function("stan::math::exponential_cdf");
45 
49  using boost::math::tools::promote_args;
51  using std::exp;
52 
53  T_partials_return cdf(1.0);
54  // check if any vectors are zero length
55  if (!(stan::length(y)
56  && stan::length(beta)))
57  return cdf;
58 
59  check_not_nan(function, "Random variable", y);
60  check_nonnegative(function, "Random variable", y);
61  check_positive_finite(function, "Inverse scale parameter", beta);
62 
64  operands_and_partials(y, beta);
65 
66  VectorView<const T_y> y_vec(y);
67  VectorView<const T_inv_scale> beta_vec(beta);
68  size_t N = max_size(y, beta);
69  for (size_t n = 0; n < N; n++) {
70  const T_partials_return beta_dbl = value_of(beta_vec[n]);
71  const T_partials_return y_dbl = value_of(y_vec[n]);
72  const T_partials_return one_m_exp = 1.0 - exp(-beta_dbl * y_dbl);
73 
74  // cdf
75  cdf *= one_m_exp;
76  }
77 
78  for (size_t n = 0; n < N; n++) {
79  const T_partials_return beta_dbl = value_of(beta_vec[n]);
80  const T_partials_return y_dbl = value_of(y_vec[n]);
81  const T_partials_return one_m_exp = 1.0 - exp(-beta_dbl * y_dbl);
82 
83  // gradients
84  T_partials_return rep_deriv = exp(-beta_dbl * y_dbl) / one_m_exp;
86  operands_and_partials.d_x1[n] += rep_deriv * beta_dbl * cdf;
88  operands_and_partials.d_x2[n] += rep_deriv * y_dbl * cdf;
89  }
90 
91  return operands_and_partials.value(cdf);
92  }
93  }
94 }
95 
96 #endif
VectorView< T_return_type, false, true > d_x2
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.
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...
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:10
This class builds partial derivatives with respect to a set of operands.
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
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
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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