Stan Math Library  2.12.0
reverse mode automatic differentiation
student_t_ccdf_log.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_STUDENT_T_CCDF_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_STUDENT_T_CCDF_LOG_HPP
3 
22 #include <boost/random/student_t_distribution.hpp>
23 #include <boost/random/variate_generator.hpp>
24 #include <limits>
25 #include <cmath>
26 
27 namespace stan {
28  namespace math {
29 
30  template <typename T_y, typename T_dof, typename T_loc, typename T_scale>
31  typename return_type<T_y, T_dof, T_loc, T_scale>::type
32  student_t_ccdf_log(const T_y& y, const T_dof& nu, const T_loc& mu,
33  const T_scale& sigma) {
34  typedef
36  T_partials_return;
37 
38  if (!(stan::length(y) && stan::length(nu) && stan::length(mu)
39  && stan::length(sigma)))
40  return 0.0;
41 
42  static const char* function("student_t_ccdf_log");
43 
44  using std::exp;
45 
46  T_partials_return P(0.0);
47 
48  check_not_nan(function, "Random variable", y);
49  check_positive_finite(function, "Degrees of freedom parameter", nu);
50  check_finite(function, "Location parameter", mu);
51  check_positive_finite(function, "Scale parameter", sigma);
52 
53  VectorView<const T_y> y_vec(y);
54  VectorView<const T_dof> nu_vec(nu);
55  VectorView<const T_loc> mu_vec(mu);
56  VectorView<const T_scale> sigma_vec(sigma);
57  size_t N = max_size(y, nu, mu, sigma);
58 
60  operands_and_partials(y, nu, mu, sigma);
61 
62  // Explicit return for extreme values
63  // The gradients are technically ill-defined, but treated as zero
64  for (size_t i = 0; i < stan::length(y); i++) {
65  if (value_of(y_vec[i]) == -std::numeric_limits<double>::infinity())
66  return operands_and_partials.value(0.0);
67  }
68 
69  using std::pow;
70  using std::exp;
71  using std::log;
72 
73  T_partials_return digammaHalf = 0;
74 
76  T_partials_return, T_dof>
77  digamma_vec(stan::length(nu));
79  T_partials_return, T_dof>
80  digammaNu_vec(stan::length(nu));
82  T_partials_return, T_dof>
83  digammaNuPlusHalf_vec(stan::length(nu));
84 
86  digammaHalf = digamma(0.5);
87 
88  for (size_t i = 0; i < stan::length(nu); i++) {
89  const T_partials_return nu_dbl = value_of(nu_vec[i]);
90 
91  digammaNu_vec[i] = digamma(0.5 * nu_dbl);
92  digammaNuPlusHalf_vec[i] = digamma(0.5 + 0.5 * nu_dbl);
93  }
94  }
95 
96  for (size_t n = 0; n < N; n++) {
97  // Explicit results for extreme values
98  // The gradients are technically ill-defined, but treated as zero
99  if (value_of(y_vec[n]) == std::numeric_limits<double>::infinity()) {
100  return operands_and_partials.value(negative_infinity());
101  }
102 
103  const T_partials_return sigma_inv = 1.0 / value_of(sigma_vec[n]);
104  const T_partials_return t = (value_of(y_vec[n]) - value_of(mu_vec[n]))
105  * sigma_inv;
106  const T_partials_return nu_dbl = value_of(nu_vec[n]);
107  const T_partials_return q = nu_dbl / (t * t);
108  const T_partials_return r = 1.0 / (1.0 + q);
109  const T_partials_return J = 2 * r * r * q / t;
110  const T_partials_return betaNuHalf = exp(lbeta(0.5, 0.5 * nu_dbl));
111  T_partials_return zJacobian = t > 0 ? - 0.5 : 0.5;
112 
113  if (q < 2) {
114  T_partials_return z = inc_beta(0.5 * nu_dbl, (T_partials_return)0.5,
115  1.0 - r);
116  const T_partials_return Pn = t > 0 ? 0.5 * z : 1.0 - 0.5 * z;
117  const T_partials_return d_ibeta = pow(r, -0.5)
118  * pow(1.0 - r, 0.5*nu_dbl - 1) / betaNuHalf;
119 
120  P += log(Pn);
121 
123  operands_and_partials.d_x1[n]
124  += zJacobian * d_ibeta * J * sigma_inv / Pn;
125 
127  T_partials_return g1 = 0;
128  T_partials_return g2 = 0;
129 
130  grad_reg_inc_beta(g1, g2, 0.5 * nu_dbl,
131  (T_partials_return)0.5, 1.0 - r,
132  digammaNu_vec[n], digammaHalf,
133  digammaNuPlusHalf_vec[n],
134  betaNuHalf);
135 
136  operands_and_partials.d_x2[n]
137  -= zJacobian * (d_ibeta * (r / t) * (r / t) + 0.5 * g1) / Pn;
138  }
139 
141  operands_and_partials.d_x3[n]
142  -= zJacobian * d_ibeta * J * sigma_inv / Pn;
144  operands_and_partials.d_x4[n]
145  -= zJacobian * d_ibeta * J * sigma_inv * t / Pn;
146 
147  } else {
148  T_partials_return z = 1.0 - inc_beta((T_partials_return)0.5,
149  0.5*nu_dbl, r);
150  zJacobian *= -1;
151 
152  const T_partials_return Pn = t > 0 ? 0.5 * z : 1.0 - 0.5 * z;
153 
154  T_partials_return d_ibeta = pow(1.0-r, 0.5*nu_dbl-1) * pow(r, -0.5)
155  / betaNuHalf;
156 
157  P += log(Pn);
158 
160  operands_and_partials.d_x1[n]
161  -= zJacobian * d_ibeta * J * sigma_inv / Pn;
162 
164  T_partials_return g1 = 0;
165  T_partials_return g2 = 0;
166 
167  grad_reg_inc_beta(g1, g2, (T_partials_return)0.5,
168  0.5 * nu_dbl, r,
169  digammaHalf, digammaNu_vec[n],
170  digammaNuPlusHalf_vec[n],
171  betaNuHalf);
172 
173  operands_and_partials.d_x2[n]
174  -= zJacobian * (- d_ibeta * (r / t) * (r / t) + 0.5 * g2) / Pn;
175  }
176 
178  operands_and_partials.d_x3[n]
179  += zJacobian * d_ibeta * J * sigma_inv / Pn;
181  operands_and_partials.d_x4[n]
182  += zJacobian * d_ibeta * J * sigma_inv * t / Pn;
183  }
184  }
185  return operands_and_partials.value(P);
186  }
187 
188  }
189 }
190 #endif
VectorView< T_return_type, false, true > d_x2
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 > lbeta(const fvar< T > &x1, const fvar< T > &x2)
Definition: lbeta.hpp:15
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
return_type< T_y, T_dof, T_loc, T_scale >::type student_t_ccdf_log(const T_y &y, const T_dof &nu, const T_loc &mu, const T_scale &sigma)
Metaprogram to determine if a type has a base scalar type that can be assigned to type double...
fvar< T > inc_beta(const fvar< T > &a, const fvar< T > &b, const fvar< T > &x)
Definition: inc_beta.hpp:19
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
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 > pow(const fvar< T > &x1, const fvar< T > &x2)
Definition: pow.hpp:17
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
void grad_reg_inc_beta(T &g1, T &g2, T a, T b, T z, T digammaA, T digammaB, T digammaSum, T betaAB)
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
double negative_infinity()
Return negative infinity.
Definition: constants.hpp:130
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:15
VectorView< T_return_type, false, true > d_x4

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