Stan Math Library  2.11.0
reverse mode automatic differentiation
student_t_log.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_STUDENT_T_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_STUDENT_T_LOG_HPP
3 
22 #include <boost/random/student_t_distribution.hpp>
23 #include <boost/random/variate_generator.hpp>
24 #include <cmath>
25 
26 namespace stan {
27 
28  namespace math {
29 
55  template <bool propto, typename T_y, typename T_dof,
56  typename T_loc, typename T_scale>
57  typename return_type<T_y, T_dof, T_loc, T_scale>::type
58  student_t_log(const T_y& y, const T_dof& nu, const T_loc& mu,
59  const T_scale& sigma) {
60  static const char* function("stan::math::student_t_log");
61  typedef typename stan::partials_return_type<T_y, T_dof, T_loc,
62  T_scale>::type
63  T_partials_return;
64 
69 
70  // check if any vectors are zero length
71  if (!(stan::length(y)
72  && stan::length(nu)
73  && stan::length(mu)
74  && stan::length(sigma)))
75  return 0.0;
76 
77  T_partials_return logp(0.0);
78 
79  // validate args (here done over var, which should be OK)
80  check_not_nan(function, "Random variable", y);
81  check_positive_finite(function, "Degrees of freedom parameter", nu);
82  check_finite(function, "Location parameter", mu);
83  check_positive_finite(function, "Scale parameter", sigma);
84  check_consistent_sizes(function,
85  "Random variable", y,
86  "Degrees of freedom parameter", nu,
87  "Location parameter", mu,
88  "Scale parameter", sigma);
89 
90  // check if no variables are involved and prop-to
92  return 0.0;
93 
94  VectorView<const T_y> y_vec(y);
95  VectorView<const T_dof> nu_vec(nu);
96  VectorView<const T_loc> mu_vec(mu);
97  VectorView<const T_scale> sigma_vec(sigma);
98  size_t N = max_size(y, nu, mu, sigma);
99 
100  using std::log;
101  using stan::math::digamma;
102  using stan::math::lgamma;
103  using stan::math::square;
104  using stan::math::value_of;
105  using std::log;
106 
108  T_partials_return, T_dof> half_nu(length(nu));
109  for (size_t i = 0; i < length(nu); i++)
111  half_nu[i] = 0.5 * value_of(nu_vec[i]);
112 
114  T_partials_return, T_dof> lgamma_half_nu(length(nu));
116  T_partials_return, T_dof>
117  lgamma_half_nu_plus_half(length(nu));
119  for (size_t i = 0; i < length(nu); i++) {
120  lgamma_half_nu[i] = lgamma(half_nu[i]);
121  lgamma_half_nu_plus_half[i] = lgamma(half_nu[i] + 0.5);
122  }
123  }
124 
126  T_partials_return, T_dof> digamma_half_nu(length(nu));
128  T_partials_return, T_dof>
129  digamma_half_nu_plus_half(length(nu));
131  for (size_t i = 0; i < length(nu); i++) {
132  digamma_half_nu[i] = digamma(half_nu[i]);
133  digamma_half_nu_plus_half[i] = digamma(half_nu[i] + 0.5);
134  }
135  }
136 
138  T_partials_return, T_dof> log_nu(length(nu));
139  for (size_t i = 0; i < length(nu); i++)
141  log_nu[i] = log(value_of(nu_vec[i]));
142 
144  T_partials_return, T_scale> log_sigma(length(sigma));
145  for (size_t i = 0; i < length(sigma); i++)
147  log_sigma[i] = log(value_of(sigma_vec[i]));
148 
150  T_partials_return, T_y, T_dof, T_loc, T_scale>
151  square_y_minus_mu_over_sigma__over_nu(N);
152 
154  T_partials_return, T_y, T_dof, T_loc, T_scale>
155  log1p_exp(N);
156 
157  for (size_t i = 0; i < N; i++)
159  const T_partials_return y_dbl = value_of(y_vec[i]);
160  const T_partials_return mu_dbl = value_of(mu_vec[i]);
161  const T_partials_return sigma_dbl = value_of(sigma_vec[i]);
162  const T_partials_return nu_dbl = value_of(nu_vec[i]);
163  square_y_minus_mu_over_sigma__over_nu[i]
164  = square((y_dbl - mu_dbl) / sigma_dbl) / nu_dbl;
165  log1p_exp[i] = log1p(square_y_minus_mu_over_sigma__over_nu[i]);
166  }
167 
169  operands_and_partials(y, nu, mu, sigma);
170  for (size_t n = 0; n < N; n++) {
171  const T_partials_return y_dbl = value_of(y_vec[n]);
172  const T_partials_return mu_dbl = value_of(mu_vec[n]);
173  const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
174  const T_partials_return nu_dbl = value_of(nu_vec[n]);
176  logp += NEG_LOG_SQRT_PI;
178  logp += lgamma_half_nu_plus_half[n] - lgamma_half_nu[n]
179  - 0.5 * log_nu[n];
181  logp -= log_sigma[n];
183  logp -= (half_nu[n] + 0.5)
184  * log1p_exp[n];
185 
187  operands_and_partials.d_x1[n]
188  += -(half_nu[n]+0.5)
189  * 1.0 / (1.0 + square_y_minus_mu_over_sigma__over_nu[n])
190  * (2.0 * (y_dbl - mu_dbl) / square(sigma_dbl) / nu_dbl);
191  }
193  const T_partials_return inv_nu = 1.0 / nu_dbl;
194  operands_and_partials.d_x2[n]
195  += 0.5*digamma_half_nu_plus_half[n] - 0.5*digamma_half_nu[n]
196  - 0.5 * inv_nu
197  - 0.5*log1p_exp[n]
198  + (half_nu[n] + 0.5)
199  * (1.0/(1.0 + square_y_minus_mu_over_sigma__over_nu[n])
200  * square_y_minus_mu_over_sigma__over_nu[n] * inv_nu);
201  }
203  operands_and_partials.d_x3[n]
204  -= (half_nu[n] + 0.5)
205  / (1.0 + square_y_minus_mu_over_sigma__over_nu[n])
206  * (2.0 * (mu_dbl - y_dbl) / (sigma_dbl*sigma_dbl*nu_dbl));
207  }
209  const T_partials_return inv_sigma = 1.0 / sigma_dbl;
210  operands_and_partials.d_x4[n]
211  += -inv_sigma
212  + (nu_dbl + 1.0) / (1.0 + square_y_minus_mu_over_sigma__over_nu[n])
213  * (square_y_minus_mu_over_sigma__over_nu[n] * inv_sigma);
214  }
215  }
216  return operands_and_partials.value(logp);
217  }
218 
219  template <typename T_y, typename T_dof, typename T_loc, typename T_scale>
220  inline
222  student_t_log(const T_y& y, const T_dof& nu, const T_loc& mu,
223  const T_scale& sigma) {
224  return student_t_log<false>(y, nu, mu, sigma);
225  }
226  }
227 }
228 #endif
VectorView< T_return_type, false, true > d_x2
fvar< T > lgamma(const fvar< T > &x)
Definition: lgamma.hpp:15
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
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:15
T_return_type value(double value)
Returns a T_return_type with the value specified with the partial derivatves.
const double NEG_LOG_SQRT_PI
Definition: constants.hpp:189
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
fvar< T > square(const fvar< T > &x)
Definition: square.hpp:15
Metaprogram to determine if a type has a base scalar type that can be assigned to type double...
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
bool check_finite(const char *function, const char *name, const T_y &y)
Return true if y is finite.
VectorBuilder allocates type T1 values to be used as intermediate values.
fvar< T > log1p_exp(const fvar< T > &x)
Definition: log1p_exp.hpp:13
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
return_type< T_y, T_dof, T_loc, T_scale >::type student_t_log(const T_y &y, const T_dof &nu, const T_loc &mu, const T_scale &sigma)
The log of the Student-t density for the given y, nu, mean, and scale parameter.
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
bool check_positive_finite(const char *function, const char *name, const T_y &y)
Return true if y is positive and finite.
VectorView< T_return_type, false, true > d_x1
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:16
VectorView< T_return_type, false, true > d_x4

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