Stan Math Library  2.14.0
reverse mode automatic differentiation
logistic_lpdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_LOGISTIC_LPDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_LOGISTIC_LPDF_HPP
3 
4 #include <boost/random/exponential_distribution.hpp>
5 #include <boost/random/variate_generator.hpp>
22 #include <cmath>
23 
24 namespace stan {
25  namespace math {
26 
27  // Logistic(y|mu, sigma) [sigma > 0]
28  template <bool propto,
29  typename T_y, typename T_loc, typename T_scale>
31  logistic_lpdf(const T_y& y, const T_loc& mu, const T_scale& sigma) {
32  static const char* function("logistic_lpdf");
34  T_partials_return;
35 
36  using std::log;
37  using std::exp;
38 
39  if (!(stan::length(y)
40  && stan::length(mu)
41  && stan::length(sigma)))
42  return 0.0;
43 
44  T_partials_return logp(0.0);
45 
46  check_finite(function, "Random variable", y);
47  check_finite(function, "Location parameter", mu);
48  check_positive_finite(function, "Scale parameter", sigma);
49  check_consistent_sizes(function,
50  "Random variable", y,
51  "Location parameter", mu,
52  "Scale parameter", sigma);
53 
55  return 0.0;
56 
58  operands_and_partials(y, mu, sigma);
59 
60  VectorView<const T_y> y_vec(y);
61  VectorView<const T_loc> mu_vec(mu);
62  VectorView<const T_scale> sigma_vec(sigma);
63  size_t N = max_size(y, mu, sigma);
64 
67  T_partials_return, T_scale> log_sigma(length(sigma));
68  for (size_t i = 0; i < length(sigma); i++) {
69  inv_sigma[i] = 1.0 / value_of(sigma_vec[i]);
71  log_sigma[i] = log(value_of(sigma_vec[i]));
72  }
73 
75  T_partials_return, T_loc, T_scale>
76  exp_mu_div_sigma(max_size(mu, sigma));
78  T_partials_return, T_y, T_scale>
79  exp_y_div_sigma(max_size(y, sigma));
81  for (size_t n = 0; n < max_size(mu, sigma); n++)
82  exp_mu_div_sigma[n] = exp(value_of(mu_vec[n])
83  / value_of(sigma_vec[n]));
84  for (size_t n = 0; n < max_size(y, sigma); n++)
85  exp_y_div_sigma[n] = exp(value_of(y_vec[n])
86  / value_of(sigma_vec[n]));
87  }
88 
89  for (size_t n = 0; n < N; n++) {
90  const T_partials_return y_dbl = value_of(y_vec[n]);
91  const T_partials_return mu_dbl = value_of(mu_vec[n]);
92 
93  const T_partials_return y_minus_mu = y_dbl - mu_dbl;
94  const T_partials_return y_minus_mu_div_sigma = y_minus_mu
95  * inv_sigma[n];
96  T_partials_return exp_m_y_minus_mu_div_sigma(0);
98  exp_m_y_minus_mu_div_sigma = exp(-y_minus_mu_div_sigma);
99  T_partials_return inv_1p_exp_y_minus_mu_div_sigma(0);
101  inv_1p_exp_y_minus_mu_div_sigma = 1 / (1 + exp(y_minus_mu_div_sigma));
102 
104  logp -= y_minus_mu_div_sigma;
106  logp -= log_sigma[n];
108  logp -= 2.0 * log1p(exp_m_y_minus_mu_div_sigma);
109 
111  operands_and_partials.d_x1[n]
112  += (2 * inv_1p_exp_y_minus_mu_div_sigma - 1) * inv_sigma[n];
114  operands_and_partials.d_x2[n] +=
115  (1 - 2 * exp_mu_div_sigma[n] / (exp_mu_div_sigma[n]
116  + exp_y_div_sigma[n]))
117  * inv_sigma[n];
119  operands_and_partials.d_x3[n] +=
120  ((1 - 2 * inv_1p_exp_y_minus_mu_div_sigma)
121  *y_minus_mu*inv_sigma[n] - 1) * inv_sigma[n];
122  }
123  return operands_and_partials.value(logp);
124  }
125 
126  template <typename T_y, typename T_loc, typename T_scale>
127  inline
129  logistic_lpdf(const T_y& y, const T_loc& mu, const T_scale& sigma) {
130  return logistic_lpdf<false>(y, mu, sigma);
131  }
132 
133  }
134 }
135 #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
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:14
T_return_type value(double value)
Returns a T_return_type with the value specified with the partial derivatves.
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
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...
void check_positive_finite(const char *function, const char *name, const T_y &y)
Check if y is positive and finite.
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:10
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 logistic_lpdf(const T_y &y, const T_loc &mu, const T_scale &sigma)
VectorBuilder allocates type T1 values to be used as intermediate values.
fvar< T > log1p(const fvar< T > &x)
Definition: log1p.hpp:11
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
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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