Stan Math Library  2.9.0
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 
4 #include <boost/random/cauchy_distribution.hpp>
5 #include <boost/random/variate_generator.hpp>
16 #include <limits>
17 
18 namespace stan {
19 
20  namespace math {
21 
34  template <typename T_y, typename T_loc, typename T_scale>
35  typename return_type<T_y, T_loc, T_scale>::type
36  cauchy_cdf(const T_y& y, const T_loc& mu, const T_scale& sigma) {
38  T_partials_return;
39 
40  // Size checks
41  if ( !( stan::length(y) && stan::length(mu)
42  && stan::length(sigma) ) )
43  return 1.0;
44 
45  static const char* function("stan::math::cauchy_cdf");
46 
51  using boost::math::tools::promote_args;
53 
54  T_partials_return P(1.0);
55 
56  check_not_nan(function, "Random variable", y);
57  check_finite(function, "Location parameter", mu);
58  check_positive_finite(function, "Scale parameter", sigma);
59  check_consistent_sizes(function,
60  "Random variable", y,
61  "Location parameter", mu,
62  "Scale Parameter", sigma);
63 
64  // Wrap arguments in vectors
65  VectorView<const T_y> y_vec(y);
66  VectorView<const T_loc> mu_vec(mu);
67  VectorView<const T_scale> sigma_vec(sigma);
68  size_t N = max_size(y, mu, sigma);
69 
71  operands_and_partials(y, mu, sigma);
72 
73  // Explicit return for extreme values
74  // The gradients are technically ill-defined, but treated as zero
75  for (size_t i = 0; i < stan::length(y); i++) {
76  if (value_of(y_vec[i]) == -std::numeric_limits<double>::infinity())
77  return operands_and_partials.to_var(0.0, y, mu, sigma);
78  }
79 
80  // Compute CDF and its gradients
81  using std::atan;
82  using stan::math::pi;
83 
84  // Compute vectorized CDF and gradient
85  for (size_t n = 0; n < N; n++) {
86  // Explicit results for extreme values
87  // The gradients are technically ill-defined, but treated as zero
88  if (value_of(y_vec[n]) == std::numeric_limits<double>::infinity()) {
89  continue;
90  }
91 
92  // Pull out values
93  const T_partials_return y_dbl = value_of(y_vec[n]);
94  const T_partials_return mu_dbl = value_of(mu_vec[n]);
95  const T_partials_return sigma_inv_dbl = 1.0 / value_of(sigma_vec[n]);
96 
97  const T_partials_return z = (y_dbl - mu_dbl) * sigma_inv_dbl;
98 
99  // Compute
100  const T_partials_return Pn = atan(z) / pi() + 0.5;
101 
102  P *= Pn;
103 
105  operands_and_partials.d_x1[n]
106  += sigma_inv_dbl / (pi() * (1.0 + z * z) * Pn);
108  operands_and_partials.d_x2[n]
109  += - sigma_inv_dbl / (pi() * (1.0 + z * z) * Pn);
111  operands_and_partials.d_x3[n]
112  += - z * sigma_inv_dbl / (pi() * (1.0 + z * z) * Pn);
113  }
114 
116  for (size_t n = 0; n < stan::length(y); ++n)
117  operands_and_partials.d_x1[n] *= P;
118  }
120  for (size_t n = 0; n < stan::length(mu); ++n)
121  operands_and_partials.d_x2[n] *= P;
122  }
124  for (size_t n = 0; n < stan::length(sigma); ++n)
125  operands_and_partials.d_x3[n] *= P;
126  }
127 
128  return operands_and_partials.to_var(P, y, mu, sigma);
129  }
130  }
131 }
132 #endif
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
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
T_return_type to_var(T_partials_return logp, const T1 &x1=0, const T2 &x2=0, const T3 &x3=0, const T4 &x4=0, const T5 &x5=0, const T6 &x6=0)
fvar< T > atan(const fvar< T > &x)
Definition: atan.hpp:12
VectorView< T_partials_return, is_vector< T1 >::value, is_constant_struct< T1 >::value > d_x1
Metaprogram to determine if a type has a base scalar type that can be assigned to type double...
VectorView< T_partials_return, is_vector< T3 >::value, is_constant_struct< T3 >::value > d_x3
A variable implementation that stores operands and derivatives with respect to the variable...
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
bool check_finite(const char *function, const char *name, const T_y &y)
Return true if y is finite.
bool check_consistent_sizes(const char *function, const char *name1, const T1 &x1, const char *name2, const T2 &x2)
Return true if the dimension of x1 is consistent with x2.
return_type< T_y, T_loc, T_scale >::type cauchy_cdf(const T_y &y, const T_loc &mu, const T_scale &sigma)
Calculates the cauchy cumulative distribution function for the given variate, location, and scale.
Definition: cauchy_cdf.hpp:36
VectorView< T_partials_return, is_vector< T2 >::value, is_constant_struct< T2 >::value > d_x2
double pi()
Return the value of pi.
Definition: constants.hpp:86
VectorView is a template metaprogram that takes its argument and allows it to be used like a vector...
Definition: VectorView.hpp:41
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.

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