Stan Math Library  2.20.0
reverse mode automatic differentiation
cauchy_cdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_CAUCHY_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_CAUCHY_CDF_HPP
3 
12 #include <limits>
13 
14 namespace stan {
15 namespace math {
16 
32 template <typename T_y, typename T_loc, typename T_scale>
34  const T_y& y, const T_loc& mu, const T_scale& sigma) {
36  T_partials_return;
37 
38  if (size_zero(y, mu, sigma))
39  return 1.0;
40 
41  static const char* function = "cauchy_cdf";
42 
43  T_partials_return P(1.0);
44 
45  check_not_nan(function, "Random variable", y);
46  check_finite(function, "Location parameter", mu);
47  check_positive_finite(function, "Scale parameter", sigma);
48  check_consistent_sizes(function, "Random variable", y, "Location parameter",
49  mu, "Scale Parameter", sigma);
50 
51  scalar_seq_view<T_y> y_vec(y);
52  scalar_seq_view<T_loc> mu_vec(mu);
53  scalar_seq_view<T_scale> sigma_vec(sigma);
54  size_t N = max_size(y, mu, sigma);
55 
56  operands_and_partials<T_y, T_loc, T_scale> ops_partials(y, mu, sigma);
57 
58  // Explicit return for extreme values
59  // The gradients are technically ill-defined, but treated as zero
60  for (size_t i = 0; i < stan::length(y); i++) {
61  if (value_of(y_vec[i]) == -std::numeric_limits<double>::infinity())
62  return ops_partials.build(0.0);
63  }
64 
65  using std::atan;
66 
67  for (size_t n = 0; n < N; n++) {
68  // Explicit results for extreme values
69  // The gradients are technically ill-defined, but treated as zero
70  if (value_of(y_vec[n]) == std::numeric_limits<double>::infinity()) {
71  continue;
72  }
73 
74  const T_partials_return y_dbl = value_of(y_vec[n]);
75  const T_partials_return mu_dbl = value_of(mu_vec[n]);
76  const T_partials_return sigma_inv_dbl = 1.0 / value_of(sigma_vec[n]);
77 
78  const T_partials_return z = (y_dbl - mu_dbl) * sigma_inv_dbl;
79 
80  const T_partials_return Pn = atan(z) / pi() + 0.5;
81 
82  P *= Pn;
83 
85  ops_partials.edge1_.partials_[n]
86  += sigma_inv_dbl / (pi() * (1.0 + z * z) * Pn);
88  ops_partials.edge2_.partials_[n]
89  += -sigma_inv_dbl / (pi() * (1.0 + z * z) * Pn);
91  ops_partials.edge3_.partials_[n]
92  += -z * sigma_inv_dbl / (pi() * (1.0 + z * z) * Pn);
93  }
94 
96  for (size_t n = 0; n < stan::length(y); ++n)
97  ops_partials.edge1_.partials_[n] *= P;
98  }
100  for (size_t n = 0; n < stan::length(mu); ++n)
101  ops_partials.edge2_.partials_[n] *= P;
102  }
104  for (size_t n = 0; n < stan::length(sigma); ++n)
105  ops_partials.edge3_.partials_[n] *= P;
106  }
107  return ops_partials.build(P);
108 }
109 
110 } // namespace math
111 } // namespace stan
112 #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.
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
fvar< T > atan(const fvar< T > &x)
Definition: atan.hpp:13
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
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_
return_type< T_y, T_loc, T_scale >::type cauchy_cdf(const T_y &y, const T_loc &mu, const T_scale &sigma)
Returns the cauchy cumulative distribution function for the given location, and scale.
Definition: cauchy_cdf.hpp:33
double pi()
Return the value of pi.
Definition: constants.hpp:80
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.
internal::ops_partials_edge< double, Op3 > edge3_
internal::ops_partials_edge< double, Op1 > edge1_

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