Stan Math Library  2.9.0
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 
4 #include <boost/random/student_t_distribution.hpp>
5 #include <boost/random/variate_generator.hpp>
22 #include <cmath>
23 
24 namespace stan {
25 
26  namespace math {
27 
53  template <bool propto, typename T_y, typename T_dof,
54  typename T_loc, typename T_scale>
55  typename return_type<T_y, T_dof, T_loc, T_scale>::type
56  student_t_log(const T_y& y, const T_dof& nu, const T_loc& mu,
57  const T_scale& sigma) {
58  static const char* function("stan::math::student_t_log");
59  typedef typename stan::partials_return_type<T_y, T_dof, T_loc,
60  T_scale>::type
61  T_partials_return;
62 
67 
68  // check if any vectors are zero length
69  if (!(stan::length(y)
70  && stan::length(nu)
71  && stan::length(mu)
72  && stan::length(sigma)))
73  return 0.0;
74 
75  T_partials_return logp(0.0);
76 
77  // validate args (here done over var, which should be OK)
78  check_not_nan(function, "Random variable", y);
79  check_positive_finite(function, "Degrees of freedom parameter", nu);
80  check_finite(function, "Location parameter", mu);
81  check_positive_finite(function, "Scale parameter", sigma);
82  check_consistent_sizes(function,
83  "Random variable", y,
84  "Degrees of freedom parameter", nu,
85  "Location parameter", mu,
86  "Scale parameter", sigma);
87 
88  // check if no variables are involved and prop-to
90  return 0.0;
91 
92  VectorView<const T_y> y_vec(y);
93  VectorView<const T_dof> nu_vec(nu);
94  VectorView<const T_loc> mu_vec(mu);
95  VectorView<const T_scale> sigma_vec(sigma);
96  size_t N = max_size(y, nu, mu, sigma);
97 
98  using std::log;
99  using stan::math::digamma;
100  using stan::math::lgamma;
101  using stan::math::square;
102  using stan::math::value_of;
103  using std::log;
104 
106  T_partials_return, T_dof> half_nu(length(nu));
107  for (size_t i = 0; i < length(nu); i++)
109  half_nu[i] = 0.5 * value_of(nu_vec[i]);
110 
112  T_partials_return, T_dof> lgamma_half_nu(length(nu));
114  T_partials_return, T_dof>
115  lgamma_half_nu_plus_half(length(nu));
117  for (size_t i = 0; i < length(nu); i++) {
118  lgamma_half_nu[i] = lgamma(half_nu[i]);
119  lgamma_half_nu_plus_half[i] = lgamma(half_nu[i] + 0.5);
120  }
121  }
122 
124  T_partials_return, T_dof> digamma_half_nu(length(nu));
126  T_partials_return, T_dof>
127  digamma_half_nu_plus_half(length(nu));
129  for (size_t i = 0; i < length(nu); i++) {
130  digamma_half_nu[i] = digamma(half_nu[i]);
131  digamma_half_nu_plus_half[i] = digamma(half_nu[i] + 0.5);
132  }
133  }
134 
136  T_partials_return, T_dof> log_nu(length(nu));
137  for (size_t i = 0; i < length(nu); i++)
139  log_nu[i] = log(value_of(nu_vec[i]));
140 
142  T_partials_return, T_scale> log_sigma(length(sigma));
143  for (size_t i = 0; i < length(sigma); i++)
145  log_sigma[i] = log(value_of(sigma_vec[i]));
146 
148  T_partials_return, T_y, T_dof, T_loc, T_scale>
149  square_y_minus_mu_over_sigma__over_nu(N);
150 
152  T_partials_return, T_y, T_dof, T_loc, T_scale>
153  log1p_exp(N);
154 
155  for (size_t i = 0; i < N; i++)
157  const T_partials_return y_dbl = value_of(y_vec[i]);
158  const T_partials_return mu_dbl = value_of(mu_vec[i]);
159  const T_partials_return sigma_dbl = value_of(sigma_vec[i]);
160  const T_partials_return nu_dbl = value_of(nu_vec[i]);
161  square_y_minus_mu_over_sigma__over_nu[i]
162  = square((y_dbl - mu_dbl) / sigma_dbl) / nu_dbl;
163  log1p_exp[i] = log1p(square_y_minus_mu_over_sigma__over_nu[i]);
164  }
165 
167  operands_and_partials(y, nu, mu, sigma);
168  for (size_t n = 0; n < N; n++) {
169  const T_partials_return y_dbl = value_of(y_vec[n]);
170  const T_partials_return mu_dbl = value_of(mu_vec[n]);
171  const T_partials_return sigma_dbl = value_of(sigma_vec[n]);
172  const T_partials_return nu_dbl = value_of(nu_vec[n]);
174  logp += NEG_LOG_SQRT_PI;
176  logp += lgamma_half_nu_plus_half[n] - lgamma_half_nu[n]
177  - 0.5 * log_nu[n];
179  logp -= log_sigma[n];
181  logp -= (half_nu[n] + 0.5)
182  * log1p_exp[n];
183 
185  operands_and_partials.d_x1[n]
186  += -(half_nu[n]+0.5)
187  * 1.0 / (1.0 + square_y_minus_mu_over_sigma__over_nu[n])
188  * (2.0 * (y_dbl - mu_dbl) / square(sigma_dbl) / nu_dbl);
189  }
191  const T_partials_return inv_nu = 1.0 / nu_dbl;
192  operands_and_partials.d_x2[n]
193  += 0.5*digamma_half_nu_plus_half[n] - 0.5*digamma_half_nu[n]
194  - 0.5 * inv_nu
195  - 0.5*log1p_exp[n]
196  + (half_nu[n] + 0.5)
197  * (1.0/(1.0 + square_y_minus_mu_over_sigma__over_nu[n])
198  * square_y_minus_mu_over_sigma__over_nu[n] * inv_nu);
199  }
201  operands_and_partials.d_x3[n]
202  -= (half_nu[n] + 0.5)
203  / (1.0 + square_y_minus_mu_over_sigma__over_nu[n])
204  * (2.0 * (mu_dbl - y_dbl) / (sigma_dbl*sigma_dbl*nu_dbl));
205  }
207  const T_partials_return inv_sigma = 1.0 / sigma_dbl;
208  operands_and_partials.d_x4[n]
209  += -inv_sigma
210  + (nu_dbl + 1.0) / (1.0 + square_y_minus_mu_over_sigma__over_nu[n])
211  * (square_y_minus_mu_over_sigma__over_nu[n] * inv_sigma);
212  }
213  }
214  return operands_and_partials.to_var(logp, y, nu, mu, sigma);
215  }
216 
217  template <typename T_y, typename T_dof, typename T_loc, typename T_scale>
218  inline
220  student_t_log(const T_y& y, const T_dof& nu, const T_loc& mu,
221  const T_scale& sigma) {
222  return student_t_log<false>(y, nu, mu, sigma);
223  }
224  }
225 }
226 #endif
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
const double NEG_LOG_SQRT_PI
Definition: constants.hpp:189
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)
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
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...
VectorView< T_partials_return, is_vector< T3 >::value, is_constant_struct< T3 >::value > d_x3
VectorView< T_partials_return, is_vector< T4 >::value, is_constant_struct< T4 >::value > d_x4
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.
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.
VectorView< T_partials_return, is_vector< T2 >::value, is_constant_struct< T2 >::value > d_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 metaprogram that takes its argument and allows it to be used like a vector...
Definition: VectorView.hpp:41
bool check_positive_finite(const char *function, const char *name, const T_y &y)
Return true if y is positive and finite.
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:16

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