Stan Math Library  2.6.3
probability, sampling & optimization
 All Classes Namespaces Files Functions Variables Typedefs Enumerator Friends Macros
scaled_inv_chi_square_cdf.hpp
Go to the documentation of this file.
1 #ifndef STAN_MATH_PRIM_SCAL_PROB_SCALED_INV_CHI_SQUARE_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_SCALED_INV_CHI_SQUARE_CDF_HPP
3 
4 #include <boost/random/chi_squared_distribution.hpp>
5 #include <boost/random/variate_generator.hpp>
22 #include <limits>
23 #include <cmath>
24 
25 
26 namespace stan {
27 
28  namespace math {
29 
44  template <typename T_y, typename T_dof, typename T_scale>
45  typename return_type<T_y, T_dof, T_scale>::type
46  scaled_inv_chi_square_cdf(const T_y& y, const T_dof& nu,
47  const T_scale& s) {
49  T_partials_return;
50 
51  // Size checks
52  if (!(stan::length(y) && stan::length(nu) && stan::length(s)))
53  return 1.0;
54 
55  static const char* function("stan::math::scaled_inv_chi_square_cdf");
56 
62  using std::exp;
63 
64  T_partials_return P(1.0);
65 
66  check_not_nan(function, "Random variable", y);
67  check_nonnegative(function, "Random variable", y);
68  check_positive_finite(function, "Degrees of freedom parameter", nu);
69  check_positive_finite(function, "Scale parameter", s);
70  check_consistent_sizes(function,
71  "Random variable", y,
72  "Degrees of freedom parameter", nu,
73  "Scale parameter", s);
74 
75  // Wrap arguments in vectors
76  VectorView<const T_y> y_vec(y);
77  VectorView<const T_dof> nu_vec(nu);
79  size_t N = max_size(y, nu, s);
80 
82  operands_and_partials(y, nu, s);
83 
84  // Explicit return for extreme values
85  // The gradients are technically ill-defined, but treated as zero
86 
87  for (size_t i = 0; i < stan::length(y); i++) {
88  if (value_of(y_vec[i]) == 0)
89  return operands_and_partials.to_var(0.0, y, nu, s);
90  }
91 
92  // Compute CDF and its gradients
93  using stan::math::gamma_q;
94  using stan::math::digamma;
95  using boost::math::tgamma;
96  using std::exp;
97  using std::pow;
98 
99  // Cache a few expensive function calls if nu is a parameter
101  T_partials_return, T_dof> gamma_vec(stan::length(nu));
103  T_partials_return, T_dof> digamma_vec(stan::length(nu));
104 
106  for (size_t i = 0; i < stan::length(nu); i++) {
107  const T_partials_return half_nu_dbl = 0.5 * value_of(nu_vec[i]);
108  gamma_vec[i] = tgamma(half_nu_dbl);
109  digamma_vec[i] = digamma(half_nu_dbl);
110  }
111  }
112 
113  // Compute vectorized CDF and gradient
114  for (size_t n = 0; n < N; n++) {
115  // Explicit results for extreme values
116  // The gradients are technically ill-defined, but treated as zero
117  if (value_of(y_vec[n]) == std::numeric_limits<double>::infinity()) {
118  continue;
119  }
120 
121  // Pull out values
122  const T_partials_return y_dbl = value_of(y_vec[n]);
123  const T_partials_return y_inv_dbl = 1.0 / y_dbl;
124  const T_partials_return half_nu_dbl = 0.5 * value_of(nu_vec[n]);
125  const T_partials_return s_dbl = value_of(s_vec[n]);
126  const T_partials_return half_s2_overx_dbl = 0.5 * s_dbl * s_dbl
127  * y_inv_dbl;
128  const T_partials_return half_nu_s2_overx_dbl
129  = 2.0 * half_nu_dbl * half_s2_overx_dbl;
130 
131  // Compute
132  const T_partials_return Pn = gamma_q(half_nu_dbl, half_nu_s2_overx_dbl);
133  const T_partials_return gamma_p_deriv = exp(-half_nu_s2_overx_dbl)
134  * pow(half_nu_s2_overx_dbl, half_nu_dbl-1) / tgamma(half_nu_dbl);
135 
136  P *= Pn;
137 
139  operands_and_partials.d_x1[n] += half_nu_s2_overx_dbl * y_inv_dbl
140  * gamma_p_deriv / Pn;
141 
142 
143 
145  operands_and_partials.d_x2[n]
146  += (0.5 * stan::math::grad_reg_inc_gamma(half_nu_dbl,
147  half_nu_s2_overx_dbl,
148  gamma_vec[n],
149  digamma_vec[n])
150  - half_s2_overx_dbl * gamma_p_deriv)
151  / Pn;
152 
154  operands_and_partials.d_x3[n]
155  += - 2.0 * half_nu_dbl * s_dbl * y_inv_dbl
156  * gamma_p_deriv / Pn;
157  }
158 
160  for (size_t n = 0; n < stan::length(y); ++n)
161  operands_and_partials.d_x1[n] *= P;
162  }
164  for (size_t n = 0; n < stan::length(nu); ++n)
165  operands_and_partials.d_x2[n] *= P;
166  }
168  for (size_t n = 0; n < stan::length(s); ++n)
169  operands_and_partials.d_x3[n] *= P;
170  }
171 
172  return operands_and_partials.to_var(P, y, nu, s);
173  }
174  }
175 }
176 #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
return_type< T_y, T_dof, T_scale >::type scaled_inv_chi_square_cdf(const T_y &y, const T_dof &nu, const T_scale &s)
The CDF of a scaled inverse chi-squared density for y with the specified degrees of freedom parameter...
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)
T grad_reg_inc_gamma(T a, T z, T g, T dig, T precision=1e-6)
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 > exp(const fvar< T > &x)
Definition: exp.hpp:10
VectorView< T_partials_return, is_vector< T3 >::value, is_constant_struct< T3 >::value > d_x3
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_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
bool check_nonnegative(const char *function, const char *name, const T_y &y)
Return true if y is non-negative.
fvar< T > tgamma(const fvar< T > &x)
Definition: tgamma.hpp:15
VectorView is a template metaprogram that takes its argument and allows it to be used like a vector...
Definition: VectorView.hpp:41
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
fvar< T > gamma_q(const fvar< T > &x1, const fvar< T > &x2)
Definition: gamma_q.hpp:15
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

     [ Stan Home Page ] © 2011–2015, Stan Development Team.