Stan Math Library  2.10.0
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 
29  namespace math {
30 
31  template <typename T_y, typename T_dof, typename T_loc, typename T_scale>
32  typename return_type<T_y, T_dof, T_loc, T_scale>::type
33  student_t_ccdf_log(const T_y& y, const T_dof& nu, const T_loc& mu,
34  const T_scale& sigma) {
35  typedef
37  T_partials_return;
38 
39  // Size checks
40  if (!(stan::length(y) && stan::length(nu) && stan::length(mu)
41  && stan::length(sigma)))
42  return 0.0;
43 
44  static const char* function("stan::math::student_t_ccdf_log");
45 
51  using std::exp;
52 
53  T_partials_return P(0.0);
54 
55  check_not_nan(function, "Random variable", y);
56  check_positive_finite(function, "Degrees of freedom parameter", nu);
57  check_finite(function, "Location parameter", mu);
58  check_positive_finite(function, "Scale parameter", sigma);
59 
60  // Wrap arguments in vectors
61  VectorView<const T_y> y_vec(y);
62  VectorView<const T_dof> nu_vec(nu);
63  VectorView<const T_loc> mu_vec(mu);
64  VectorView<const T_scale> sigma_vec(sigma);
65  size_t N = max_size(y, nu, mu, sigma);
66 
68  operands_and_partials(y, nu, mu, sigma);
69 
70  // Explicit return for extreme values
71  // The gradients are technically ill-defined, but treated as zero
72  for (size_t i = 0; i < stan::length(y); i++) {
73  if (value_of(y_vec[i]) == -std::numeric_limits<double>::infinity())
74  return operands_and_partials.value(0.0);
75  }
76 
77  using stan::math::digamma;
78  using stan::math::lbeta;
80  using std::pow;
81  using std::exp;
82  using std::log;
83 
84  // Cache a few expensive function calls if nu is a parameter
85  T_partials_return digammaHalf = 0;
86 
88  T_partials_return, T_dof>
89  digamma_vec(stan::length(nu));
91  T_partials_return, T_dof>
92  digammaNu_vec(stan::length(nu));
94  T_partials_return, T_dof>
95  digammaNuPlusHalf_vec(stan::length(nu));
96 
98  digammaHalf = digamma(0.5);
99 
100  for (size_t i = 0; i < stan::length(nu); i++) {
101  const T_partials_return nu_dbl = value_of(nu_vec[i]);
102 
103  digammaNu_vec[i] = digamma(0.5 * nu_dbl);
104  digammaNuPlusHalf_vec[i] = digamma(0.5 + 0.5 * nu_dbl);
105  }
106  }
107 
108  // Compute vectorized cdf_log and gradient
109  for (size_t n = 0; n < N; n++) {
110  // Explicit results for extreme values
111  // The gradients are technically ill-defined, but treated as zero
112  if (value_of(y_vec[n]) == std::numeric_limits<double>::infinity()) {
113  return operands_and_partials.value(stan::math::negative_infinity());
114  }
115 
116  const T_partials_return sigma_inv = 1.0 / value_of(sigma_vec[n]);
117  const T_partials_return t = (value_of(y_vec[n]) - value_of(mu_vec[n]))
118  * sigma_inv;
119  const T_partials_return nu_dbl = value_of(nu_vec[n]);
120  const T_partials_return q = nu_dbl / (t * t);
121  const T_partials_return r = 1.0 / (1.0 + q);
122  const T_partials_return J = 2 * r * r * q / t;
123  const T_partials_return betaNuHalf = exp(lbeta(0.5, 0.5 * nu_dbl));
124  T_partials_return zJacobian = t > 0 ? - 0.5 : 0.5;
125 
126  if (q < 2) {
127  T_partials_return z = inc_beta(0.5 * nu_dbl, (T_partials_return)0.5,
128  1.0 - r);
129  const T_partials_return Pn = t > 0 ? 0.5 * z : 1.0 - 0.5 * z;
130  const T_partials_return d_ibeta = pow(r, -0.5)
131  * pow(1.0 - r, 0.5*nu_dbl - 1) / betaNuHalf;
132 
133  P += log(Pn);
134 
136  operands_and_partials.d_x1[n]
137  += zJacobian * d_ibeta * J * sigma_inv / Pn;
138 
140  T_partials_return g1 = 0;
141  T_partials_return g2 = 0;
142 
143  stan::math::grad_reg_inc_beta(g1, g2, 0.5 * nu_dbl,
144  (T_partials_return)0.5, 1.0 - r,
145  digammaNu_vec[n], digammaHalf,
146  digammaNuPlusHalf_vec[n],
147  betaNuHalf);
148 
149  operands_and_partials.d_x2[n]
150  -= zJacobian * (d_ibeta * (r / t) * (r / t) + 0.5 * g1) / Pn;
151  }
152 
154  operands_and_partials.d_x3[n]
155  -= zJacobian * d_ibeta * J * sigma_inv / Pn;
157  operands_and_partials.d_x4[n]
158  -= zJacobian * d_ibeta * J * sigma_inv * t / Pn;
159 
160  } else {
161  T_partials_return z = 1.0 - inc_beta((T_partials_return)0.5,
162  0.5*nu_dbl, r);
163  zJacobian *= -1;
164 
165  const T_partials_return Pn = t > 0 ? 0.5 * z : 1.0 - 0.5 * z;
166 
167  T_partials_return d_ibeta = pow(1.0-r, 0.5*nu_dbl-1) * pow(r, -0.5)
168  / betaNuHalf;
169 
170  P += log(Pn);
171 
173  operands_and_partials.d_x1[n]
174  -= zJacobian * d_ibeta * J * sigma_inv / Pn;
175 
177  T_partials_return g1 = 0;
178  T_partials_return g2 = 0;
179 
180  stan::math::grad_reg_inc_beta(g1, g2, (T_partials_return)0.5,
181  0.5 * nu_dbl, r,
182  digammaHalf, digammaNu_vec[n],
183  digammaNuPlusHalf_vec[n],
184  betaNuHalf);
185 
186  operands_and_partials.d_x2[n]
187  -= zJacobian * (- d_ibeta * (r / t) * (r / t) + 0.5 * g2) / Pn;
188  }
189 
191  operands_and_partials.d_x3[n]
192  += zJacobian * d_ibeta * J * sigma_inv / Pn;
194  operands_and_partials.d_x4[n]
195  += zJacobian * d_ibeta * J * sigma_inv * t / Pn;
196  }
197  }
198 
199  return operands_and_partials.value(P);
200  }
201  }
202 }
203 #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: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.
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:20
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.
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 > pow(const fvar< T > &x1, const fvar< T > &x2)
Definition: pow.hpp:18
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:132
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:16
VectorView< T_return_type, false, true > d_x4

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