Stan Math Library  2.9.0
reverse mode automatic differentiation
logistic_cdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_LOGISTIC_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_LOGISTIC_CDF_HPP
3 
4 #include <boost/random/exponential_distribution.hpp>
5 #include <boost/random/variate_generator.hpp>
22 #include <cmath>
23 #include <limits>
24 
25 namespace stan {
26  namespace math {
27 
28  // Logistic(y|mu, sigma) [sigma > 0]
29  template <typename T_y, typename T_loc, typename T_scale>
30  typename return_type<T_y, T_loc, T_scale>::type
31  logistic_cdf(const T_y& y, const T_loc& mu, const T_scale& sigma) {
33  T_partials_return;
34 
35  // Size checks
36  if ( !( stan::length(y) && stan::length(mu)
37  && stan::length(sigma) ) )
38  return 1.0;
39 
40  // Error checks
41  static const char* function("stan::math::logistic_cdf");
42 
48  using boost::math::tools::promote_args;
49  using std::exp;
50 
51  T_partials_return P(1.0);
52 
53  check_not_nan(function, "Random variable", y);
54  check_finite(function, "Location parameter", mu);
55  check_positive_finite(function, "Scale parameter", sigma);
56  check_consistent_sizes(function,
57  "Random variable", y,
58  "Location parameter", mu,
59  "Scale parameter", sigma);
60 
61  // Wrap arguments in vectors
62  VectorView<const T_y> y_vec(y);
63  VectorView<const T_loc> mu_vec(mu);
64  VectorView<const T_scale> sigma_vec(sigma);
65  size_t N = max_size(y, mu, sigma);
66 
68  operands_and_partials(y, mu, sigma);
69 
70  // Explicit return for extreme values
71  // The gradients are technically ill-defined, but treated as zero
72 
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.to_var(0.0, y, mu, sigma);
76  }
77 
78  // Compute vectorized CDF and its gradients
79  for (size_t n = 0; n < N; n++) {
80  // Explicit results for extreme values
81  // The gradients are technically ill-defined, but treated as zero
82  if (value_of(y_vec[n]) == std::numeric_limits<double>::infinity()) {
83  continue;
84  }
85 
86  // Pull out values
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_dbl = value_of(sigma_vec[n]);
90  const T_partials_return sigma_inv_vec = 1.0 / value_of(sigma_vec[n]);
91 
92  // Compute
93  const T_partials_return Pn = 1.0 / (1.0 + exp(-(y_dbl - mu_dbl)
94  * sigma_inv_vec));
95 
96  P *= Pn;
97 
99  operands_and_partials.d_x1[n]
100  += exp(logistic_log(y_dbl, mu_dbl, sigma_dbl)) / Pn;
102  operands_and_partials.d_x2[n]
103  += - exp(logistic_log(y_dbl, mu_dbl, sigma_dbl)) / Pn;
105  operands_and_partials.d_x3[n] += - (y_dbl - mu_dbl) * sigma_inv_vec
106  * exp(logistic_log(y_dbl, mu_dbl, sigma_dbl)) / Pn;
107  }
108 
110  for (size_t n = 0; n < stan::length(y); ++n)
111  operands_and_partials.d_x1[n] *= P;
112  }
114  for (size_t n = 0; n < stan::length(mu); ++n)
115  operands_and_partials.d_x2[n] *= P;
116  }
118  for (size_t n = 0; n < stan::length(sigma); ++n)
119  operands_and_partials.d_x3[n] *= P;
120  }
121 
122  return operands_and_partials.to_var(P, y, mu, sigma);
123  }
124  }
125 }
126 #endif
return_type< T_y, T_loc, T_scale >::type logistic_cdf(const T_y &y, const T_loc &mu, const T_scale &sigma)
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)
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...
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:10
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.
return_type< T_y, T_loc, T_scale >::type logistic_log(const T_y &y, const T_loc &mu, const T_scale &sigma)
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.
VectorView< T_partials_return, is_vector< T2 >::value, is_constant_struct< T2 >::value > d_x2
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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