Stan Math Library  2.15.0
reverse mode automatic differentiation
normal_lccdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_NORMAL_LCCDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_NORMAL_LCCDF_HPP
3 
16 #include <boost/random/normal_distribution.hpp>
17 #include <boost/random/variate_generator.hpp>
18 #include <cmath>
19 #include <limits>
20 
21 namespace stan {
22  namespace math {
23 
24  template <typename T_y, typename T_loc, typename T_scale>
26  normal_lccdf(const T_y& y, const T_loc& mu, const T_scale& sigma) {
27  static const char* function("normal_lccdf");
29  T_partials_return;
30 
31  using std::log;
32  using std::exp;
33 
34  T_partials_return ccdf_log(0.0);
35  if (!(stan::length(y)
36  && stan::length(mu)
37  && stan::length(sigma)))
38  return ccdf_log;
39 
40  check_not_nan(function, "Random variable", y);
41  check_finite(function, "Location parameter", mu);
42  check_not_nan(function, "Scale parameter", sigma);
43  check_positive(function, "Scale parameter", sigma);
44  check_consistent_sizes(function,
45  "Random variable", y,
46  "Location parameter", mu,
47  "Scale parameter", sigma);
48 
50  operands_and_partials(y, mu, sigma);
51 
54  scalar_seq_view<const T_scale> sigma_vec(sigma);
55  size_t N = max_size(y, mu, sigma);
56  double log_half = std::log(0.5);
57 
58  const double SQRT_TWO_OVER_PI = std::sqrt(2.0 / pi());
59  for (size_t n = 0; n < N; n++) {
60  const T_partials_return y_dbl = value_of(y_vec[n]);
61  const T_partials_return mu_dbl = value_of(mu_vec[n]);
62  const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
63 
64  const T_partials_return scaled_diff = (y_dbl - mu_dbl)
65  / (sigma_dbl * SQRT_2);
66 
67  T_partials_return one_m_erf;
68  if (scaled_diff < -37.5 * INV_SQRT_2)
69  one_m_erf = 2.0;
70  else if (scaled_diff < -5.0 * INV_SQRT_2)
71  one_m_erf = 2.0 - erfc(-scaled_diff);
72  else if (scaled_diff > 8.25 * INV_SQRT_2)
73  one_m_erf = 0.0;
74  else
75  one_m_erf = 1.0 - erf(scaled_diff);
76 
77  ccdf_log += log_half + log(one_m_erf);
78 
80  const T_partials_return rep_deriv_div_sigma
81  = scaled_diff > 8.25 * INV_SQRT_2
82  ? std::numeric_limits<double>::infinity()
83  : SQRT_TWO_OVER_PI * exp(-scaled_diff * scaled_diff)
84  / one_m_erf / sigma_dbl;
86  operands_and_partials.d_x1[n] -= rep_deriv_div_sigma;
88  operands_and_partials.d_x2[n] += rep_deriv_div_sigma;
90  operands_and_partials.d_x3[n] += rep_deriv_div_sigma
91  * scaled_diff * SQRT_2;
92  }
93  }
94  return operands_and_partials.value(ccdf_log);
95  }
96 
97  }
98 }
99 #endif
VectorView< T_return_type, false, true > d_x2
void check_finite(const char *function, const char *name, const T_y &y)
Check if y is finite.
fvar< T > sqrt(const fvar< T > &x)
Definition: sqrt.hpp:14
T value_of(const fvar< T > &v)
Return the value of the specified variable.
Definition: value_of.hpp:16
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:14
T_return_type value(double value)
Returns a T_return_type with the value specified with the partial derivatves.
scalar_seq_view provides a uniform sequence-like wrapper around either a scalar or a sequence of scal...
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
fvar< T > erf(const fvar< T > &x)
Definition: erf.hpp:14
boost::math::tools::promote_args< typename scalar_type< T1 >::type, typename scalar_type< T2 >::type, typename scalar_type< T3 >::type, typename scalar_type< T4 >::type, typename scalar_type< T5 >::type, typename scalar_type< T6 >::type >::type type
Definition: return_type.hpp:27
Metaprogram to determine if a type has a base scalar type that can be assigned to type double...
const double SQRT_2
The value of the square root of 2, .
Definition: constants.hpp:20
const double INV_SQRT_2
The value of 1 over the square root of 2, .
Definition: constants.hpp:26
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:10
void check_not_nan(const char *function, const char *name, const T_y &y)
Check if y is not NaN.
This class builds partial derivatives with respect to a set of operands.
VectorView< T_return_type, false, true > d_x3
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
return_type< T_y, T_loc, T_scale >::type normal_lccdf(const T_y &y, const T_loc &mu, const T_scale &sigma)
fvar< T > erfc(const fvar< T > &x)
Definition: erfc.hpp:14
void check_positive(const char *function, const char *name, const T_y &y)
Check if y is positive.
double pi()
Return the value of pi.
Definition: constants.hpp:85
void check_consistent_sizes(const char *function, const char *name1, const T1 &x1, const char *name2, const T2 &x2)
Check if the dimension of x1 is consistent with x2.
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
VectorView< T_return_type, false, true > d_x1

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