Stan Math Library  2.10.0
reverse mode automatic differentiation
scaled_inv_chi_square_cdf_log.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_SCALED_INV_CHI_SQUARE_CDF_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_SCALED_INV_CHI_SQUARE_CDF_LOG_HPP
3 
22 #include <boost/random/chi_squared_distribution.hpp>
23 #include <boost/random/variate_generator.hpp>
24 #include <limits>
25 #include <cmath>
26 
27 
28 namespace stan {
29 
30  namespace math {
31 
32  template <typename T_y, typename T_dof, typename T_scale>
33  typename return_type<T_y, T_dof, T_scale>::type
34  scaled_inv_chi_square_cdf_log(const T_y& y, const T_dof& nu,
35  const T_scale& s) {
37  T_partials_return;
38 
39  // Size checks
40  if (!(stan::length(y) && stan::length(nu) && stan::length(s)))
41  return 0.0;
42 
43  static const char* function("stan::math::scaled_inv_chi_square_cdf_log");
44 
50  using std::exp;
51 
52  T_partials_return P(0.0);
53 
54  check_not_nan(function, "Random variable", y);
55  check_nonnegative(function, "Random variable", y);
56  check_positive_finite(function, "Degrees of freedom parameter", nu);
57  check_positive_finite(function, "Scale parameter", s);
58  check_consistent_sizes(function,
59  "Random variable", y,
60  "Degrees of freedom parameter", nu,
61  "Scale parameter", s);
62 
63  // Wrap arguments in vectors
64  VectorView<const T_y> y_vec(y);
65  VectorView<const T_dof> nu_vec(nu);
67  size_t N = max_size(y, nu, s);
68 
70  operands_and_partials(y, nu, s);
71 
72  // Explicit return for extreme values
73  // The gradients are technically ill-defined, but treated as zero
74  for (size_t i = 0; i < stan::length(y); i++) {
75  if (value_of(y_vec[i]) == 0)
76  return operands_and_partials.value(stan::math::negative_infinity());
77  }
78 
79  // Compute cdf_log and its gradients
80  using stan::math::gamma_q;
81  using stan::math::digamma;
82  using boost::math::tgamma;
83  using std::exp;
84  using std::pow;
85  using std::log;
86 
87  // Cache a few expensive function calls if nu is a parameter
89  T_partials_return, T_dof> gamma_vec(stan::length(nu));
91  T_partials_return, T_dof> digamma_vec(stan::length(nu));
92 
94  for (size_t i = 0; i < stan::length(nu); i++) {
95  const T_partials_return half_nu_dbl = 0.5 * value_of(nu_vec[i]);
96  gamma_vec[i] = tgamma(half_nu_dbl);
97  digamma_vec[i] = digamma(half_nu_dbl);
98  }
99  }
100 
101  // Compute vectorized cdf_log and gradient
102  for (size_t n = 0; n < N; n++) {
103  // Explicit results for extreme values
104  // The gradients are technically ill-defined, but treated as zero
105  if (value_of(y_vec[n]) == std::numeric_limits<double>::infinity()) {
106  continue;
107  }
108 
109  // Pull out values
110  const T_partials_return y_dbl = value_of(y_vec[n]);
111  const T_partials_return y_inv_dbl = 1.0 / y_dbl;
112  const T_partials_return half_nu_dbl = 0.5 * value_of(nu_vec[n]);
113  const T_partials_return s_dbl = value_of(s_vec[n]);
114  const T_partials_return half_s2_overx_dbl = 0.5 * s_dbl * s_dbl
115  * y_inv_dbl;
116  const T_partials_return half_nu_s2_overx_dbl
117  = 2.0 * half_nu_dbl * half_s2_overx_dbl;
118 
119  // Compute
120  const T_partials_return Pn = gamma_q(half_nu_dbl, half_nu_s2_overx_dbl);
121  const T_partials_return gamma_p_deriv = exp(-half_nu_s2_overx_dbl)
122  * pow(half_nu_s2_overx_dbl, half_nu_dbl-1) / tgamma(half_nu_dbl);
123 
124  P += log(Pn);
125 
127  operands_and_partials.d_x1[n] += half_nu_s2_overx_dbl * y_inv_dbl
128  * gamma_p_deriv / Pn;
130  operands_and_partials.d_x2[n]
131  += (0.5 * stan::math::grad_reg_inc_gamma(half_nu_dbl,
132  half_nu_s2_overx_dbl,
133  gamma_vec[n],
134  digamma_vec[n])
135  - half_s2_overx_dbl * gamma_p_deriv)
136  / Pn;
138  operands_and_partials.d_x3[n] += - 2.0 * half_nu_dbl * s_dbl
139  * y_inv_dbl * gamma_p_deriv / Pn;
140  }
141 
142  return operands_and_partials.value(P);
143  }
144  }
145 }
146 #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 > log(const fvar< T > &x)
Definition: log.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
T grad_reg_inc_gamma(T a, T z, T g, T dig, T precision=1e-6)
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
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.
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
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 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
return_type< T_y, T_dof, T_scale >::type scaled_inv_chi_square_cdf_log(const T_y &y, const T_dof &nu, const T_scale &s)
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.
VectorView< T_return_type, false, true > d_x1
double negative_infinity()
Return negative infinity.
Definition: constants.hpp:132
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:16

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