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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 
4 #include <boost/random/bernoulli_distribution.hpp>
5 #include <boost/random/variate_generator.hpp>
16 #include <cmath>
17 
18 namespace stan {
19 
20  namespace math {
21 
22  // Bernoulli(n|inv_logit(theta)) [0 <= n <= 1; -inf <= theta <= inf]
23  // FIXME: documentation
24  template <bool propto, typename T_n, typename T_prob>
25  typename return_type<T_prob>::type
26  bernoulli_logit_log(const T_n& n, const T_prob& theta) {
27  static const char* function("stan::math::bernoulli_logit_log");
29  T_partials_return;
30 
37  using stan::math::log1p;
39  using std::exp;
40 
41  // check if any vectors are zero length
42  if (!(stan::length(n)
43  && stan::length(theta)))
44  return 0.0;
45 
46  // set up return value accumulator
47  T_partials_return logp(0.0);
48 
49  // validate args (here done over var, which should be OK)
50  check_bounded(function, "n", n, 0, 1);
51  check_not_nan(function, "Logit transformed probability parameter", theta);
52  check_consistent_sizes(function,
53  "Random variable", n,
54  "Probability parameter", theta);
55 
56  // check if no variables are involved and prop-to
58  return 0.0;
59 
60  // set up template expressions wrapping scalars into vector views
61  VectorView<const T_n> n_vec(n);
62  VectorView<const T_prob> theta_vec(theta);
63  size_t N = max_size(n, theta);
64  OperandsAndPartials<T_prob> operands_and_partials(theta);
65 
66  for (size_t n = 0; n < N; n++) {
67  // pull out values of arguments
68  const int n_int = value_of(n_vec[n]);
69  const T_partials_return theta_dbl = value_of(theta_vec[n]);
70 
71  // reusable subexpression values
72  const int sign = 2*n_int-1;
73  const T_partials_return ntheta = sign * theta_dbl;
74  const T_partials_return exp_m_ntheta = exp(-ntheta);
75 
76  // Handle extreme values gracefully using Taylor approximations.
77  static const double cutoff = 20.0;
78  if (ntheta > cutoff)
79  logp -= exp_m_ntheta;
80  else if (ntheta < -cutoff)
81  logp += ntheta;
82  else
83  logp -= log1p(exp_m_ntheta);
84 
85  // gradients
87  static const double cutoff = 20.0;
88  if (ntheta > cutoff)
89  operands_and_partials.d_x1[n] -= exp_m_ntheta;
90  else if (ntheta < -cutoff)
91  operands_and_partials.d_x1[n] += sign;
92  else
93  operands_and_partials.d_x1[n] += sign * exp_m_ntheta
94  / (exp_m_ntheta + 1);
95  }
96  }
97  return operands_and_partials.to_var(logp, theta);
98  }
99 
100  template <typename T_n,
101  typename T_prob>
102  inline
104  bernoulli_logit_log(const T_n& n,
105  const T_prob& theta) {
106  return bernoulli_logit_log<false>(n, theta);
107  }
108 
109  } // namespace math
110 } // namespace stan
111 #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
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)
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)
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
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
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_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 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

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