Stan Math Library  2.14.0
reverse mode automatic differentiation
student_t_cdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_STUDENT_T_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_STUDENT_T_CDF_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>
32  student_t_cdf(const T_y& y, const T_dof& nu, const T_loc& mu,
33  const T_scale& sigma) {
34  typedef typename stan::partials_return_type<T_y, T_dof, T_loc,
35  T_scale>::type
36  T_partials_return;
37 
38  if (!(stan::length(y) && stan::length(nu) && stan::length(mu)
39  && stan::length(sigma)))
40  return 1.0;
41 
42  static const char* function("student_t_cdf");
43 
44  using std::exp;
45 
46  T_partials_return P(1.0);
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 
72  T_partials_return digammaHalf = 0;
73 
75  T_partials_return, T_dof>
76  digamma_vec(stan::length(nu));
78  T_partials_return, T_dof>
79  digammaNu_vec(stan::length(nu));
81  T_partials_return, T_dof>
82  digammaNuPlusHalf_vec(stan::length(nu));
83 
85  digammaHalf = digamma(0.5);
86 
87  for (size_t i = 0; i < stan::length(nu); i++) {
88  const T_partials_return nu_dbl = value_of(nu_vec[i]);
89 
90  digammaNu_vec[i] = digamma(0.5 * nu_dbl);
91  digammaNuPlusHalf_vec[i] = digamma(0.5 + 0.5 * nu_dbl);
92  }
93  }
94 
95  for (size_t n = 0; n < N; n++) {
96  // Explicit results for extreme values
97  // The gradients are technically ill-defined, but treated as zero
98  if (value_of(y_vec[n]) == std::numeric_limits<double>::infinity()) {
99  continue;
100  }
101 
102  const T_partials_return sigma_inv = 1.0 / value_of(sigma_vec[n]);
103  const T_partials_return t = (value_of(y_vec[n]) - value_of(mu_vec[n]))
104  * sigma_inv;
105  const T_partials_return nu_dbl = value_of(nu_vec[n]);
106  const T_partials_return q = nu_dbl / (t * t);
107  const T_partials_return r = 1.0 / (1.0 + q);
108  const T_partials_return J = 2 * r * r * q / t;
109  const T_partials_return betaNuHalf = exp(lbeta(0.5, 0.5*nu_dbl));
110  double zJacobian = t > 0 ? - 0.5 : 0.5;
111 
112  if (q < 2) {
113  T_partials_return z = inc_beta(0.5 * nu_dbl, (T_partials_return)0.5,
114  1.0 - r);
115  const T_partials_return Pn = t > 0 ? 1.0 - 0.5 * z : 0.5 * z;
116  const T_partials_return d_ibeta = pow(r, -0.5)
117  * pow(1.0 - r, 0.5*nu_dbl - 1) / betaNuHalf;
118 
119  P *= Pn;
120 
122  operands_and_partials.d_x1[n]
123  += - zJacobian * d_ibeta * J * sigma_inv / Pn;
125  T_partials_return g1 = 0;
126  T_partials_return g2 = 0;
127 
128  grad_reg_inc_beta(g1, g2, 0.5 * nu_dbl,
129  (T_partials_return)0.5, 1.0 - r,
130  digammaNu_vec[n], digammaHalf,
131  digammaNuPlusHalf_vec[n],
132  betaNuHalf);
133 
134  operands_and_partials.d_x2[n]
135  += zJacobian * (d_ibeta * (r / t) * (r / t) + 0.5 * g1) / Pn;
136  }
137 
139  operands_and_partials.d_x3[n]
140  += zJacobian * d_ibeta * J * sigma_inv / Pn;
142  operands_and_partials.d_x4[n]
143  += zJacobian * d_ibeta * J * sigma_inv * t / Pn;
144 
145  } else {
146  T_partials_return z = 1.0 - inc_beta((T_partials_return)0.5,
147  0.5*nu_dbl, r);
148 
149  zJacobian *= -1;
150 
151  const T_partials_return Pn = t > 0 ? 1.0 - 0.5 * z : 0.5 * z;
152 
153  T_partials_return d_ibeta = pow(1.0-r, 0.5*nu_dbl-1) * pow(r, -0.5)
154  / betaNuHalf;
155 
156  P *= Pn;
157 
159  operands_and_partials.d_x1[n]
160  += zJacobian * d_ibeta * J * sigma_inv / Pn;
162  T_partials_return g1 = 0;
163  T_partials_return g2 = 0;
164 
165  grad_reg_inc_beta(g1, g2, (T_partials_return)0.5,
166  0.5 * nu_dbl, r,
167  digammaHalf, digammaNu_vec[n],
168  digammaNuPlusHalf_vec[n],
169  betaNuHalf);
170 
171  operands_and_partials.d_x2[n]
172  += zJacobian * (- d_ibeta * (r / t) * (r / t) + 0.5 * g2) / Pn;
173  }
175  operands_and_partials.d_x3[n]
176  += - zJacobian * d_ibeta * J * sigma_inv / Pn;
178  operands_and_partials.d_x4[n]
179  += - zJacobian * d_ibeta * J * sigma_inv * t / Pn;
180  }
181  }
182 
184  for (size_t n = 0; n < stan::length(y); ++n)
185  operands_and_partials.d_x1[n] *= P;
186  }
188  for (size_t n = 0; n < stan::length(nu); ++n)
189  operands_and_partials.d_x2[n] *= P;
190  }
192  for (size_t n = 0; n < stan::length(mu); ++n)
193  operands_and_partials.d_x3[n] *= P;
194  }
196  for (size_t n = 0; n < stan::length(sigma); ++n)
197  operands_and_partials.d_x4[n] *= P;
198  }
199  return operands_and_partials.value(P);
200  }
201 
202  }
203 }
204 #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 > lbeta(const fvar< T > &x1, const fvar< T > &x2)
Definition: lbeta.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
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...
fvar< T > inc_beta(const fvar< T > &a, const fvar< T > &b, const fvar< T > &x)
Definition: inc_beta.hpp:19
return_type< T_y, T_dof, T_loc, T_scale >::type student_t_cdf(const T_y &y, const T_dof &nu, const T_loc &mu, const T_scale &sigma)
void check_positive_finite(const char *function, const char *name, const T_y &y)
Check if y is positive and finite.
void grad_reg_inc_beta(T &g1, T &g2, const T &a, const T &b, const T &z, const T &digammaA, const T &digammaB, const T &digammaSum, const T &betaAB)
Computes the gradients of the regularized incomplete beta function.
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:10
void check_not_nan(const char *function, const char *name, const T_y &y)
Check if y is not NaN.
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
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
VectorView< T_return_type, false, true > d_x1
fvar< T > digamma(const fvar< T > &x)
Return the derivative of the log gamma function at the specified argument.
Definition: digamma.hpp:22
VectorView< T_return_type, false, true > d_x4

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