Stan Math Library  2.10.0
reverse mode automatic differentiation
scaled_inv_chi_square_cdf.hpp
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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 
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 
46  template <typename T_y, typename T_dof, typename T_scale>
47  typename return_type<T_y, T_dof, T_scale>::type
48  scaled_inv_chi_square_cdf(const T_y& y, const T_dof& nu,
49  const T_scale& s) {
51  T_partials_return;
52 
53  // Size checks
54  if (!(stan::length(y) && stan::length(nu) && stan::length(s)))
55  return 1.0;
56 
57  static const char* function("stan::math::scaled_inv_chi_square_cdf");
58 
64  using std::exp;
65 
66  T_partials_return P(1.0);
67 
68  check_not_nan(function, "Random variable", y);
69  check_nonnegative(function, "Random variable", y);
70  check_positive_finite(function, "Degrees of freedom parameter", nu);
71  check_positive_finite(function, "Scale parameter", s);
72  check_consistent_sizes(function,
73  "Random variable", y,
74  "Degrees of freedom parameter", nu,
75  "Scale parameter", s);
76 
77  // Wrap arguments in vectors
78  VectorView<const T_y> y_vec(y);
79  VectorView<const T_dof> nu_vec(nu);
81  size_t N = max_size(y, nu, s);
82 
84  operands_and_partials(y, nu, s);
85 
86  // Explicit return for extreme values
87  // The gradients are technically ill-defined, but treated as zero
88 
89  for (size_t i = 0; i < stan::length(y); i++) {
90  if (value_of(y_vec[i]) == 0)
91  return operands_and_partials.value(0.0);
92  }
93 
94  // Compute CDF and its gradients
95  using stan::math::gamma_q;
96  using stan::math::digamma;
97  using boost::math::tgamma;
98  using std::exp;
99  using std::pow;
100 
101  // Cache a few expensive function calls if nu is a parameter
103  T_partials_return, T_dof> gamma_vec(stan::length(nu));
105  T_partials_return, T_dof> digamma_vec(stan::length(nu));
106 
108  for (size_t i = 0; i < stan::length(nu); i++) {
109  const T_partials_return half_nu_dbl = 0.5 * value_of(nu_vec[i]);
110  gamma_vec[i] = tgamma(half_nu_dbl);
111  digamma_vec[i] = digamma(half_nu_dbl);
112  }
113  }
114 
115  // Compute vectorized CDF and gradient
116  for (size_t n = 0; n < N; n++) {
117  // Explicit results for extreme values
118  // The gradients are technically ill-defined, but treated as zero
119  if (value_of(y_vec[n]) == std::numeric_limits<double>::infinity()) {
120  continue;
121  }
122 
123  // Pull out values
124  const T_partials_return y_dbl = value_of(y_vec[n]);
125  const T_partials_return y_inv_dbl = 1.0 / y_dbl;
126  const T_partials_return half_nu_dbl = 0.5 * value_of(nu_vec[n]);
127  const T_partials_return s_dbl = value_of(s_vec[n]);
128  const T_partials_return half_s2_overx_dbl = 0.5 * s_dbl * s_dbl
129  * y_inv_dbl;
130  const T_partials_return half_nu_s2_overx_dbl
131  = 2.0 * half_nu_dbl * half_s2_overx_dbl;
132 
133  // Compute
134  const T_partials_return Pn = gamma_q(half_nu_dbl, half_nu_s2_overx_dbl);
135  const T_partials_return gamma_p_deriv = exp(-half_nu_s2_overx_dbl)
136  * pow(half_nu_s2_overx_dbl, half_nu_dbl-1) / tgamma(half_nu_dbl);
137 
138  P *= Pn;
139 
141  operands_and_partials.d_x1[n] += half_nu_s2_overx_dbl * y_inv_dbl
142  * gamma_p_deriv / Pn;
143 
144 
145 
147  operands_and_partials.d_x2[n]
148  += (0.5 * stan::math::grad_reg_inc_gamma(half_nu_dbl,
149  half_nu_s2_overx_dbl,
150  gamma_vec[n],
151  digamma_vec[n])
152  - half_s2_overx_dbl * gamma_p_deriv)
153  / Pn;
154 
156  operands_and_partials.d_x3[n]
157  += - 2.0 * half_nu_dbl * s_dbl * y_inv_dbl
158  * gamma_p_deriv / Pn;
159  }
160 
162  for (size_t n = 0; n < stan::length(y); ++n)
163  operands_and_partials.d_x1[n] *= P;
164  }
166  for (size_t n = 0; n < stan::length(nu); ++n)
167  operands_and_partials.d_x2[n] *= P;
168  }
170  for (size_t n = 0; n < stan::length(s); ++n)
171  operands_and_partials.d_x3[n] *= P;
172  }
173 
174  return operands_and_partials.value(P);
175  }
176  }
177 }
178 #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
T_return_type value(double value)
Returns a T_return_type with the value specified with the partial derivatves.
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 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
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
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:16

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