Stan Math Library  2.15.0
reverse mode automatic differentiation
student_t_lcdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_STUDENT_T_LCDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_STUDENT_T_LCDF_HPP
3 
23 #include <boost/random/student_t_distribution.hpp>
24 #include <boost/random/variate_generator.hpp>
25 #include <limits>
26 #include <cmath>
27 
28 namespace stan {
29  namespace math {
30 
31  template <typename T_y, typename T_dof, typename T_loc, typename T_scale>
33  student_t_lcdf(const T_y& y, const T_dof& nu, const T_loc& mu,
34  const T_scale& sigma) {
35  typedef typename
37  T_partials_return;
38 
39  if (!(stan::length(y) && stan::length(nu) && stan::length(mu)
40  && stan::length(sigma)))
41  return 0.0;
42 
43  static const char* function("student_t_lcdf");
44 
45  using std::exp;
46 
47  T_partials_return P(0.0);
48 
49  check_not_nan(function, "Random variable", y);
50  check_positive_finite(function, "Degrees of freedom parameter", nu);
51  check_finite(function, "Location parameter", mu);
52  check_positive_finite(function, "Scale parameter", sigma);
53 
57  scalar_seq_view<const T_scale> sigma_vec(sigma);
58  size_t N = max_size(y, nu, mu, sigma);
59 
61  operands_and_partials(y, nu, mu, sigma);
62 
63  // Explicit return for extreme values
64  // The gradients are technically ill-defined, but treated as zero
65  for (size_t i = 0; i < stan::length(y); i++) {
66  if (value_of(y_vec[i]) == -std::numeric_limits<double>::infinity())
67  return operands_and_partials.value(negative_infinity());
68  }
69 
70  using std::pow;
71  using std::exp;
72  using std::log;
73 
74  T_partials_return digammaHalf = 0;
75 
77  T_partials_return, T_dof>
78  digamma_vec(stan::length(nu));
80  T_partials_return, T_dof>
81  digammaNu_vec(stan::length(nu));
83  T_partials_return, T_dof>
84  digammaNuPlusHalf_vec(stan::length(nu));
85 
87  digammaHalf = digamma(0.5);
88 
89  for (size_t i = 0; i < stan::length(nu); i++) {
90  const T_partials_return nu_dbl = value_of(nu_vec[i]);
91 
92  digammaNu_vec[i] = digamma(0.5 * nu_dbl);
93  digammaNuPlusHalf_vec[i] = digamma(0.5 + 0.5 * nu_dbl);
94  }
95  }
96 
97  for (size_t n = 0; n < N; n++) {
98  // Explicit results for extreme values
99  // The gradients are technically ill-defined, but treated as zero
100  if (value_of(y_vec[n]) == std::numeric_limits<double>::infinity()) {
101  continue;
102  }
103 
104  const T_partials_return sigma_inv = 1.0 / value_of(sigma_vec[n]);
105  const T_partials_return t = (value_of(y_vec[n]) - value_of(mu_vec[n]))
106  * sigma_inv;
107  const T_partials_return nu_dbl = value_of(nu_vec[n]);
108  const T_partials_return q = nu_dbl / (t * t);
109  const T_partials_return r = 1.0 / (1.0 + q);
110  const T_partials_return J = 2 * r * r * q / t;
111  const T_partials_return betaNuHalf = exp(lbeta(0.5, 0.5 * nu_dbl));
112  T_partials_return zJacobian = t > 0 ? - 0.5 : 0.5;
113 
114  if (q < 2) {
115  T_partials_return z
116  = inc_beta(0.5 * nu_dbl, (T_partials_return)0.5, 1.0 - r);
117  const T_partials_return Pn = t > 0 ? 1.0 - 0.5 * z : 0.5 * z;
118  const T_partials_return d_ibeta = pow(r, -0.5)
119  * pow(1.0 - r, 0.5*nu_dbl - 1) / betaNuHalf;
120 
121  P += log(Pn);
122 
124  operands_and_partials.d_x1[n]
125  += - zJacobian * d_ibeta * J * sigma_inv / Pn;
126 
128  T_partials_return g1 = 0;
129  T_partials_return g2 = 0;
130 
131  grad_reg_inc_beta(g1, g2, 0.5 * nu_dbl,
132  (T_partials_return)0.5, 1.0 - r,
133  digammaNu_vec[n], digammaHalf,
134  digammaNuPlusHalf_vec[n],
135  betaNuHalf);
136 
137  operands_and_partials.d_x2[n]
138  += zJacobian * (d_ibeta * (r / t) * (r / t) + 0.5 * g1) / Pn;
139  }
140 
142  operands_and_partials.d_x3[n]
143  += zJacobian * d_ibeta * J * sigma_inv / Pn;
145  operands_and_partials.d_x4[n]
146  += zJacobian * d_ibeta * J * sigma_inv * t / Pn;
147 
148  } else {
149  T_partials_return z = 1.0 - inc_beta((T_partials_return)0.5,
150  0.5*nu_dbl, r);
151  zJacobian *= -1;
152 
153  const T_partials_return Pn = t > 0 ? 1.0 - 0.5 * z : 0.5 * z;
154 
155  T_partials_return d_ibeta = pow(1.0-r, 0.5*nu_dbl-1) * pow(r, -0.5)
156  / betaNuHalf;
157 
158  P += log(Pn);
159 
161  operands_and_partials.d_x1[n]
162  += zJacobian * d_ibeta * J * sigma_inv / Pn;
163 
165  T_partials_return g1 = 0;
166  T_partials_return g2 = 0;
167 
168  grad_reg_inc_beta(g1, g2, (T_partials_return)0.5,
169  0.5 * nu_dbl, r,
170  digammaHalf, digammaNu_vec[n],
171  digammaNuPlusHalf_vec[n],
172  betaNuHalf);
173 
174  operands_and_partials.d_x2[n]
175  += zJacobian * (- d_ibeta * (r / t) * (r / t) + 0.5 * g2) / Pn;
176  }
177 
179  operands_and_partials.d_x3[n]
180  += - zJacobian * d_ibeta * J * sigma_inv / Pn;
182  operands_and_partials.d_x4[n]
183  += - zJacobian * d_ibeta * J * sigma_inv * t / Pn;
184  }
185  }
186  return operands_and_partials.value(P);
187  }
188 
189  }
190 }
191 #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
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.
scalar_seq_view provides a uniform sequence-like wrapper around either a scalar or a sequence of scal...
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_lcdf(const T_y &y, const T_dof &nu, const T_loc &mu, const T_scale &sigma)
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
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
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
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)
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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