Stan Math Library  2.11.0
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 
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_cdf(const T_y& y, const T_dof& nu, const T_loc& mu,
34  const T_scale& sigma) {
35  typedef typename stan::partials_return_type<T_y, T_dof, T_loc,
36  T_scale>::type
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 1.0;
43 
44  static const char* function("stan::math::student_t_cdf");
45 
51  using std::exp;
52 
53  T_partials_return P(1.0);
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 
83  // Cache a few expensive function calls if nu is a parameter
84  T_partials_return digammaHalf = 0;
85 
87  T_partials_return, T_dof>
88  digamma_vec(stan::length(nu));
90  T_partials_return, T_dof>
91  digammaNu_vec(stan::length(nu));
93  T_partials_return, T_dof>
94  digammaNuPlusHalf_vec(stan::length(nu));
95 
97  digammaHalf = digamma(0.5);
98 
99  for (size_t i = 0; i < stan::length(nu); i++) {
100  const T_partials_return nu_dbl = value_of(nu_vec[i]);
101 
102  digammaNu_vec[i] = digamma(0.5 * nu_dbl);
103  digammaNuPlusHalf_vec[i] = digamma(0.5 + 0.5 * nu_dbl);
104  }
105  }
106 
107  // Compute vectorized CDF and gradient
108  for (size_t n = 0; n < N; n++) {
109  // Explicit results for extreme values
110  // The gradients are technically ill-defined, but treated as zero
111  if (value_of(y_vec[n]) == std::numeric_limits<double>::infinity()) {
112  continue;
113  }
114 
115  const T_partials_return sigma_inv = 1.0 / value_of(sigma_vec[n]);
116  const T_partials_return t = (value_of(y_vec[n]) - value_of(mu_vec[n]))
117  * sigma_inv;
118  const T_partials_return nu_dbl = value_of(nu_vec[n]);
119  const T_partials_return q = nu_dbl / (t * t);
120  const T_partials_return r = 1.0 / (1.0 + q);
121  const T_partials_return J = 2 * r * r * q / t;
122  const T_partials_return betaNuHalf = exp(lbeta(0.5, 0.5*nu_dbl));
123  double zJacobian = t > 0 ? - 0.5 : 0.5;
124 
125  if (q < 2) {
126  T_partials_return z = inc_beta(0.5 * nu_dbl, (T_partials_return)0.5,
127  1.0 - r);
128  const T_partials_return Pn = t > 0 ? 1.0 - 0.5 * z : 0.5 * z;
129  const T_partials_return d_ibeta = pow(r, -0.5)
130  * pow(1.0 - r, 0.5*nu_dbl - 1) / betaNuHalf;
131 
132  P *= Pn;
133 
135  operands_and_partials.d_x1[n]
136  += - zJacobian * d_ibeta * J * sigma_inv / Pn;
138  T_partials_return g1 = 0;
139  T_partials_return g2 = 0;
140 
141  stan::math::grad_reg_inc_beta(g1, g2, 0.5 * nu_dbl,
142  (T_partials_return)0.5, 1.0 - r,
143  digammaNu_vec[n], digammaHalf,
144  digammaNuPlusHalf_vec[n],
145  betaNuHalf);
146 
147  operands_and_partials.d_x2[n]
148  += zJacobian * (d_ibeta * (r / t) * (r / t) + 0.5 * g1) / Pn;
149  }
150 
152  operands_and_partials.d_x3[n]
153  += zJacobian * d_ibeta * J * sigma_inv / Pn;
155  operands_and_partials.d_x4[n]
156  += zJacobian * d_ibeta * J * sigma_inv * t / Pn;
157 
158  } else {
159  T_partials_return z = 1.0 - inc_beta((T_partials_return)0.5,
160  0.5*nu_dbl, r);
161 
162  zJacobian *= -1;
163 
164  const T_partials_return Pn = t > 0 ? 1.0 - 0.5 * z : 0.5 * z;
165 
166  T_partials_return d_ibeta = pow(1.0-r, 0.5*nu_dbl-1) * pow(r, -0.5)
167  / betaNuHalf;
168 
169  P *= Pn;
170 
172  operands_and_partials.d_x1[n]
173  += zJacobian * d_ibeta * J * sigma_inv / Pn;
175  T_partials_return g1 = 0;
176  T_partials_return g2 = 0;
177 
178  stan::math::grad_reg_inc_beta(g1, g2, (T_partials_return)0.5,
179  0.5 * nu_dbl, r,
180  digammaHalf, digammaNu_vec[n],
181  digammaNuPlusHalf_vec[n],
182  betaNuHalf);
183 
184  operands_and_partials.d_x2[n]
185  += zJacobian * (- d_ibeta * (r / t) * (r / t) + 0.5 * g2) / Pn;
186  }
188  operands_and_partials.d_x3[n]
189  += - zJacobian * d_ibeta * J * sigma_inv / Pn;
191  operands_and_partials.d_x4[n]
192  += - zJacobian * d_ibeta * J * sigma_inv * t / Pn;
193  }
194  }
195 
197  for (size_t n = 0; n < stan::length(y); ++n)
198  operands_and_partials.d_x1[n] *= P;
199  }
201  for (size_t n = 0; n < stan::length(nu); ++n)
202  operands_and_partials.d_x2[n] *= P;
203  }
205  for (size_t n = 0; n < stan::length(mu); ++n)
206  operands_and_partials.d_x3[n] *= P;
207  }
209  for (size_t n = 0; n < stan::length(sigma); ++n)
210  operands_and_partials.d_x4[n] *= P;
211  }
212 
213  return operands_and_partials.value(P);
214  }
215  }
216 }
217 #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
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
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
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)
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
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
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:16
VectorView< T_return_type, false, true > d_x4

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