Stan Math Library  2.15.0
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 
17 #include <boost/random/cauchy_distribution.hpp>
18 #include <boost/random/variate_generator.hpp>
19 #include <limits>
20 
21 namespace stan {
22  namespace math {
23 
39  template <typename T_y, typename T_loc, typename T_scale>
41  cauchy_cdf(const T_y& y, const T_loc& mu, const T_scale& sigma) {
43  T_partials_return;
44 
45  if ( !( stan::length(y) && stan::length(mu)
46  && stan::length(sigma) ) )
47  return 1.0;
48 
49  static const char* function("cauchy_cdf");
50 
51  using boost::math::tools::promote_args;
52 
53  T_partials_return P(1.0);
54 
55  check_not_nan(function, "Random variable", y);
56  check_finite(function, "Location parameter", mu);
57  check_positive_finite(function, "Scale parameter", sigma);
58  check_consistent_sizes(function,
59  "Random variable", y,
60  "Location parameter", mu,
61  "Scale Parameter", sigma);
62 
65  scalar_seq_view<const T_scale> sigma_vec(sigma);
66  size_t N = max_size(y, mu, sigma);
67 
69  operands_and_partials(y, mu, sigma);
70 
71  // Explicit return for extreme values
72  // The gradients are technically ill-defined, but treated as zero
73  for (size_t i = 0; i < stan::length(y); i++) {
74  if (value_of(y_vec[i]) == -std::numeric_limits<double>::infinity())
75  return operands_and_partials.value(0.0);
76  }
77 
78  using std::atan;
79 
80  for (size_t n = 0; n < N; n++) {
81  // Explicit results for extreme values
82  // The gradients are technically ill-defined, but treated as zero
83  if (value_of(y_vec[n]) == std::numeric_limits<double>::infinity()) {
84  continue;
85  }
86 
87  const T_partials_return y_dbl = value_of(y_vec[n]);
88  const T_partials_return mu_dbl = value_of(mu_vec[n]);
89  const T_partials_return sigma_inv_dbl = 1.0 / value_of(sigma_vec[n]);
90 
91  const T_partials_return z = (y_dbl - mu_dbl) * sigma_inv_dbl;
92 
93  const T_partials_return Pn = atan(z) / pi() + 0.5;
94 
95  P *= Pn;
96 
98  operands_and_partials.d_x1[n]
99  += sigma_inv_dbl / (pi() * (1.0 + z * z) * Pn);
101  operands_and_partials.d_x2[n]
102  += - sigma_inv_dbl / (pi() * (1.0 + z * z) * Pn);
104  operands_and_partials.d_x3[n]
105  += - z * sigma_inv_dbl / (pi() * (1.0 + z * z) * Pn);
106  }
107 
109  for (size_t n = 0; n < stan::length(y); ++n)
110  operands_and_partials.d_x1[n] *= P;
111  }
113  for (size_t n = 0; n < stan::length(mu); ++n)
114  operands_and_partials.d_x2[n] *= P;
115  }
117  for (size_t n = 0; n < stan::length(sigma); ++n)
118  operands_and_partials.d_x3[n] *= P;
119  }
120  return operands_and_partials.value(P);
121  }
122 
123  }
124 }
125 #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.
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.
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 > atan(const fvar< T > &x)
Definition: atan.hpp:12
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...
void check_positive_finite(const char *function, const char *name, const T_y &y)
Check if y is positive and finite.
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 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:41
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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