Stan Math Library  2.11.0
reverse mode automatic differentiation
bernoulli_logit_log.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_BERNOULLI_LOGIT_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_BERNOULLI_LOGIT_LOG_HPP
3 
16 #include <boost/random/bernoulli_distribution.hpp>
17 #include <boost/random/variate_generator.hpp>
18 #include <cmath>
19 
20 namespace stan {
21 
22  namespace math {
23 
24  // Bernoulli(n|inv_logit(theta)) [0 <= n <= 1; -inf <= theta <= inf]
25  // FIXME: documentation
26  template <bool propto, typename T_n, typename T_prob>
27  typename return_type<T_prob>::type
28  bernoulli_logit_log(const T_n& n, const T_prob& theta) {
29  static const char* function("stan::math::bernoulli_logit_log");
31  T_partials_return;
32 
39  using stan::math::log1p;
41  using std::exp;
42 
43  // check if any vectors are zero length
44  if (!(stan::length(n)
45  && stan::length(theta)))
46  return 0.0;
47 
48  // set up return value accumulator
49  T_partials_return logp(0.0);
50 
51  // validate args (here done over var, which should be OK)
52  check_bounded(function, "n", n, 0, 1);
53  check_not_nan(function, "Logit transformed probability parameter", theta);
54  check_consistent_sizes(function,
55  "Random variable", n,
56  "Probability parameter", theta);
57 
58  // check if no variables are involved and prop-to
60  return 0.0;
61 
62  // set up template expressions wrapping scalars into vector views
63  VectorView<const T_n> n_vec(n);
64  VectorView<const T_prob> theta_vec(theta);
65  size_t N = max_size(n, theta);
66  OperandsAndPartials<T_prob> operands_and_partials(theta);
67 
68  for (size_t n = 0; n < N; n++) {
69  // pull out values of arguments
70  const int n_int = value_of(n_vec[n]);
71  const T_partials_return theta_dbl = value_of(theta_vec[n]);
72 
73  // reusable subexpression values
74  const int sign = 2*n_int-1;
75  const T_partials_return ntheta = sign * theta_dbl;
76  const T_partials_return exp_m_ntheta = exp(-ntheta);
77 
78  // Handle extreme values gracefully using Taylor approximations.
79  static const double cutoff = 20.0;
80  if (ntheta > cutoff)
81  logp -= exp_m_ntheta;
82  else if (ntheta < -cutoff)
83  logp += ntheta;
84  else
85  logp -= log1p(exp_m_ntheta);
86 
87  // gradients
89  static const double cutoff = 20.0;
90  if (ntheta > cutoff)
91  operands_and_partials.d_x1[n] -= exp_m_ntheta;
92  else if (ntheta < -cutoff)
93  operands_and_partials.d_x1[n] += sign;
94  else
95  operands_and_partials.d_x1[n] += sign * exp_m_ntheta
96  / (exp_m_ntheta + 1);
97  }
98  }
99  return operands_and_partials.value(logp);
100  }
101 
102  template <typename T_n,
103  typename T_prob>
104  inline
106  bernoulli_logit_log(const T_n& n,
107  const T_prob& theta) {
108  return bernoulli_logit_log<false>(n, theta);
109  }
110 
111  } // namespace math
112 } // namespace stan
113 #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
int sign(const T &z)
Definition: sign.hpp:9
T_return_type value(double value)
Returns a T_return_type with the value specified with the partial derivatves.
fvar< T > inv_logit(const fvar< T > &x)
Definition: inv_logit.hpp:15
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
bool check_bounded(const char *function, const char *name, const T_y &y, const T_low &low, const T_high &high)
Return true if the value is between the low and high values, inclusively.
return_type< T_prob >::type bernoulli_logit_log(const T_n &n, const T_prob &theta)
Template metaprogram to calculate whether a summand needs to be included in a proportional (log) prob...
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...
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:10
This class builds partial derivatives with respect to a set of operands.
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
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.
fvar< T > log1p(const fvar< T > &x)
Definition: log1p.hpp:16
VectorView is a template expression that is constructed with a container or scalar, which it then allows to be used as an array using operator[].
Definition: VectorView.hpp:48
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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