Stan Math Library  2.20.0
reverse mode automatic differentiation
lognormal_lccdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_LOGNORMAL_LCCDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_LOGNORMAL_LCCDF_HPP
3 
12 #include <cmath>
13 
14 namespace stan {
15 namespace math {
16 
17 template <typename T_y, typename T_loc, typename T_scale>
19  const T_y& y, const T_loc& mu, const T_scale& sigma) {
20  static const char* function = "lognormal_lccdf";
22  T_partials_return;
23 
24  T_partials_return ccdf_log = 0.0;
25 
26  using std::exp;
27  using std::log;
28 
29  if (size_zero(y, mu, sigma))
30  return ccdf_log;
31 
32  check_not_nan(function, "Random variable", y);
33  check_nonnegative(function, "Random variable", y);
34  check_finite(function, "Location parameter", mu);
35  check_positive_finite(function, "Scale parameter", sigma);
36 
37  operands_and_partials<T_y, T_loc, T_scale> ops_partials(y, mu, sigma);
38 
39  scalar_seq_view<T_y> y_vec(y);
40  scalar_seq_view<T_loc> mu_vec(mu);
41  scalar_seq_view<T_scale> sigma_vec(sigma);
42  size_t N = max_size(y, mu, sigma);
43 
44  const double sqrt_pi = std::sqrt(pi());
45 
46  for (size_t i = 0; i < stan::length(y); i++) {
47  if (value_of(y_vec[i]) == 0.0)
48  return ops_partials.build(0.0);
49  }
50 
51  const double log_half = std::log(0.5);
52 
53  for (size_t n = 0; n < N; n++) {
54  const T_partials_return y_dbl = value_of(y_vec[n]);
55  const T_partials_return mu_dbl = value_of(mu_vec[n]);
56  const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
57  const T_partials_return scaled_diff
58  = (log(y_dbl) - mu_dbl) / (sigma_dbl * SQRT_2);
59  const T_partials_return rep_deriv
60  = SQRT_2 / sqrt_pi * exp(-scaled_diff * scaled_diff) / sigma_dbl;
61 
62  const T_partials_return erfc_calc = erfc(scaled_diff);
63  ccdf_log += log_half + log(erfc_calc);
64 
66  ops_partials.edge1_.partials_[n] -= rep_deriv / erfc_calc / y_dbl;
68  ops_partials.edge2_.partials_[n] += rep_deriv / erfc_calc;
70  ops_partials.edge3_.partials_[n]
71  += rep_deriv * scaled_diff * SQRT_2 / erfc_calc;
72  }
73  return ops_partials.build(ccdf_log);
74 }
75 
76 } // namespace math
77 } // namespace stan
78 #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
fvar< T > sqrt(const fvar< T > &x)
Definition: sqrt.hpp:13
return_type< T_y, T_loc, T_scale >::type lognormal_lccdf(const T_y &y, const T_loc &mu, const T_scale &sigma)
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
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:12
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.
size_t length(const std::vector< T > &x)
Returns the length of the provided std::vector.
Definition: length.hpp:16
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.
const double SQRT_2
The value of the square root of 2, .
Definition: constants.hpp:25
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_
fvar< T > erfc(const fvar< T > &x)
Definition: erfc.hpp:15
double pi()
Return the value of pi.
Definition: constants.hpp:80
internal::ops_partials_edge< double, Op3 > edge3_
internal::ops_partials_edge< double, Op1 > edge1_

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