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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 
4 #include <boost/random/student_t_distribution.hpp>
5 #include <boost/random/variate_generator.hpp>
22 #include <limits>
23 #include <cmath>
24 
25 namespace stan {
26 
27  namespace math {
28 
29  template <typename T_y, typename T_dof, typename T_loc, typename T_scale>
30  typename return_type<T_y, T_dof, T_loc, T_scale>::type
31  student_t_cdf(const T_y& y, const T_dof& nu, const T_loc& mu,
32  const T_scale& sigma) {
33  typedef typename stan::partials_return_type<T_y, T_dof, T_loc,
34  T_scale>::type
35  T_partials_return;
36 
37  // Size checks
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("stan::math::student_t_cdf");
43 
49  using std::exp;
50 
51  T_partials_return P(1.0);
52 
53  check_not_nan(function, "Random variable", y);
54  check_positive_finite(function, "Degrees of freedom parameter", nu);
55  check_finite(function, "Location parameter", mu);
56  check_positive_finite(function, "Scale parameter", sigma);
57 
58  // Wrap arguments in vectors
59  VectorView<const T_y> y_vec(y);
60  VectorView<const T_dof> nu_vec(nu);
61  VectorView<const T_loc> mu_vec(mu);
62  VectorView<const T_scale> sigma_vec(sigma);
63  size_t N = max_size(y, nu, mu, sigma);
64 
66  operands_and_partials(y, nu, mu, sigma);
67 
68  // Explicit return for extreme values
69  // The gradients are technically ill-defined, but treated as zero
70  for (size_t i = 0; i < stan::length(y); i++) {
71  if (value_of(y_vec[i]) == -std::numeric_limits<double>::infinity())
72  return operands_and_partials.to_var(0.0, y, nu, mu, sigma);
73  }
74 
75  using stan::math::digamma;
76  using stan::math::lbeta;
78  using std::pow;
79  using std::exp;
80 
81  // Cache a few expensive function calls if nu is a parameter
82  T_partials_return digammaHalf = 0;
83 
85  T_partials_return, T_dof>
86  digamma_vec(stan::length(nu));
88  T_partials_return, T_dof>
89  digammaNu_vec(stan::length(nu));
91  T_partials_return, T_dof>
92  digammaNuPlusHalf_vec(stan::length(nu));
93 
95  digammaHalf = digamma(0.5);
96 
97  for (size_t i = 0; i < stan::length(nu); i++) {
98  const T_partials_return nu_dbl = value_of(nu_vec[i]);
99 
100  digammaNu_vec[i] = digamma(0.5 * nu_dbl);
101  digammaNuPlusHalf_vec[i] = digamma(0.5 + 0.5 * nu_dbl);
102  }
103  }
104 
105  // Compute vectorized CDF and gradient
106  for (size_t n = 0; n < N; n++) {
107  // Explicit results for extreme values
108  // The gradients are technically ill-defined, but treated as zero
109  if (value_of(y_vec[n]) == std::numeric_limits<double>::infinity()) {
110  continue;
111  }
112 
113  const T_partials_return sigma_inv = 1.0 / value_of(sigma_vec[n]);
114  const T_partials_return t = (value_of(y_vec[n]) - value_of(mu_vec[n]))
115  * sigma_inv;
116  const T_partials_return nu_dbl = value_of(nu_vec[n]);
117  const T_partials_return q = nu_dbl / (t * t);
118  const T_partials_return r = 1.0 / (1.0 + q);
119  const T_partials_return J = 2 * r * r * q / t;
120  const T_partials_return betaNuHalf = exp(lbeta(0.5, 0.5*nu_dbl));
121  double zJacobian = t > 0 ? - 0.5 : 0.5;
122 
123  if (q < 2) {
124  T_partials_return z = inc_beta(0.5 * nu_dbl, (T_partials_return)0.5,
125  1.0 - r);
126  const T_partials_return Pn = t > 0 ? 1.0 - 0.5 * z : 0.5 * z;
127  const T_partials_return d_ibeta = pow(r, -0.5)
128  * pow(1.0 - r, 0.5*nu_dbl - 1) / betaNuHalf;
129 
130  P *= Pn;
131 
133  operands_and_partials.d_x1[n]
134  += - zJacobian * d_ibeta * J * sigma_inv / Pn;
136  T_partials_return g1 = 0;
137  T_partials_return g2 = 0;
138 
139  stan::math::grad_reg_inc_beta(g1, g2, 0.5 * nu_dbl,
140  (T_partials_return)0.5, 1.0 - r,
141  digammaNu_vec[n], digammaHalf,
142  digammaNuPlusHalf_vec[n],
143  betaNuHalf);
144 
145  operands_and_partials.d_x2[n]
146  += zJacobian * (d_ibeta * (r / t) * (r / t) + 0.5 * g1) / Pn;
147  }
148 
150  operands_and_partials.d_x3[n]
151  += zJacobian * d_ibeta * J * sigma_inv / Pn;
153  operands_and_partials.d_x4[n]
154  += zJacobian * d_ibeta * J * sigma_inv * t / Pn;
155 
156  } else {
157  T_partials_return z = 1.0 - inc_beta((T_partials_return)0.5,
158  0.5*nu_dbl, r);
159 
160  zJacobian *= -1;
161 
162  const T_partials_return Pn = t > 0 ? 1.0 - 0.5 * z : 0.5 * z;
163 
164  T_partials_return d_ibeta = pow(1.0-r, 0.5*nu_dbl-1) * pow(r, -0.5)
165  / betaNuHalf;
166 
167  P *= Pn;
168 
170  operands_and_partials.d_x1[n]
171  += zJacobian * d_ibeta * J * sigma_inv / Pn;
173  T_partials_return g1 = 0;
174  T_partials_return g2 = 0;
175 
176  stan::math::grad_reg_inc_beta(g1, g2, (T_partials_return)0.5,
177  0.5 * nu_dbl, r,
178  digammaHalf, digammaNu_vec[n],
179  digammaNuPlusHalf_vec[n],
180  betaNuHalf);
181 
182  operands_and_partials.d_x2[n]
183  += zJacobian * (- d_ibeta * (r / t) * (r / t) + 0.5 * g2) / Pn;
184  }
186  operands_and_partials.d_x3[n]
187  += - zJacobian * d_ibeta * J * sigma_inv / Pn;
189  operands_and_partials.d_x4[n]
190  += - zJacobian * d_ibeta * J * sigma_inv * t / Pn;
191  }
192  }
193 
195  for (size_t n = 0; n < stan::length(y); ++n)
196  operands_and_partials.d_x1[n] *= P;
197  }
199  for (size_t n = 0; n < stan::length(nu); ++n)
200  operands_and_partials.d_x2[n] *= P;
201  }
203  for (size_t n = 0; n < stan::length(mu); ++n)
204  operands_and_partials.d_x3[n] *= P;
205  }
207  for (size_t n = 0; n < stan::length(sigma); ++n)
208  operands_and_partials.d_x4[n] *= P;
209  }
210 
211  return operands_and_partials.to_var(P, y, nu, mu, sigma);
212  }
213  }
214 }
215 #endif
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
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
T_return_type to_var(T_partials_return logp, const T1 &x1=0, const T2 &x2=0, const T3 &x3=0, const T4 &x4=0, const T5 &x5=0, const T6 &x6=0)
VectorView< T_partials_return, is_vector< T1 >::value, is_constant_struct< T1 >::value > d_x1
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
VectorView< T_partials_return, is_vector< T3 >::value, is_constant_struct< T3 >::value > d_x3
VectorView< T_partials_return, is_vector< T4 >::value, is_constant_struct< T4 >::value > d_x4
A variable implementation that stores operands and derivatives with respect to the variable...
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.
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.
VectorView< T_partials_return, is_vector< T2 >::value, is_constant_struct< T2 >::value > d_x2
fvar< T > pow(const fvar< T > &x1, const fvar< T > &x2)
Definition: pow.hpp:18
VectorView is a template metaprogram that takes its argument and allows it to be used like a vector...
Definition: VectorView.hpp:41
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.
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:16

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