Stan Math Library  2.20.0
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 
15 #include <limits>
16 #include <cmath>
17 
18 namespace stan {
19 namespace math {
20 
34 template <typename T_y, typename T_dof, typename T_scale>
36  const T_y& y, const T_dof& nu, const T_scale& s) {
38  T_partials_return;
39 
40  if (size_zero(y, nu, s))
41  return 1.0;
42 
43  static const char* function = "scaled_inv_chi_square_cdf";
44 
45  T_partials_return P(1.0);
46 
47  check_not_nan(function, "Random variable", y);
48  check_nonnegative(function, "Random variable", y);
49  check_positive_finite(function, "Degrees of freedom parameter", nu);
50  check_positive_finite(function, "Scale parameter", s);
51  check_consistent_sizes(function, "Random variable", y,
52  "Degrees of freedom parameter", nu, "Scale parameter",
53  s);
54 
55  scalar_seq_view<T_y> y_vec(y);
56  scalar_seq_view<T_dof> nu_vec(nu);
57  scalar_seq_view<T_scale> s_vec(s);
58  size_t N = max_size(y, nu, s);
59 
60  operands_and_partials<T_y, T_dof, T_scale> ops_partials(y, nu, s);
61 
62  // Explicit return for extreme values
63  // The gradients are technically ill-defined, but treated as zero
64  for (size_t i = 0; i < stan::length(y); i++) {
65  if (value_of(y_vec[i]) == 0)
66  return ops_partials.build(0.0);
67  }
68 
69  using std::exp;
70  using std::pow;
71 
72  VectorBuilder<!is_constant_all<T_dof>::value, T_partials_return, T_dof>
73  gamma_vec(stan::length(nu));
74  VectorBuilder<!is_constant_all<T_dof>::value, T_partials_return, T_dof>
75  digamma_vec(stan::length(nu));
76 
78  for (size_t i = 0; i < stan::length(nu); i++) {
79  const T_partials_return half_nu_dbl = 0.5 * value_of(nu_vec[i]);
80  gamma_vec[i] = tgamma(half_nu_dbl);
81  digamma_vec[i] = digamma(half_nu_dbl);
82  }
83  }
84 
85  for (size_t n = 0; n < N; n++) {
86  // Explicit results for extreme values
87  // The gradients are technically ill-defined, but treated as zero
88  if (value_of(y_vec[n]) == std::numeric_limits<double>::infinity()) {
89  continue;
90  }
91 
92  const T_partials_return y_dbl = value_of(y_vec[n]);
93  const T_partials_return y_inv_dbl = 1.0 / y_dbl;
94  const T_partials_return half_nu_dbl = 0.5 * value_of(nu_vec[n]);
95  const T_partials_return s_dbl = value_of(s_vec[n]);
96  const T_partials_return half_s2_overx_dbl = 0.5 * s_dbl * s_dbl * y_inv_dbl;
97  const T_partials_return half_nu_s2_overx_dbl
98  = 2.0 * half_nu_dbl * half_s2_overx_dbl;
99 
100  const T_partials_return Pn = gamma_q(half_nu_dbl, half_nu_s2_overx_dbl);
101  const T_partials_return gamma_p_deriv
102  = exp(-half_nu_s2_overx_dbl)
103  * pow(half_nu_s2_overx_dbl, half_nu_dbl - 1) / tgamma(half_nu_dbl);
104 
105  P *= Pn;
106 
108  ops_partials.edge1_.partials_[n]
109  += half_nu_s2_overx_dbl * y_inv_dbl * gamma_p_deriv / Pn;
110 
112  ops_partials.edge2_.partials_[n]
113  += (0.5
114  * grad_reg_inc_gamma(half_nu_dbl, half_nu_s2_overx_dbl,
115  gamma_vec[n], digamma_vec[n])
116  - half_s2_overx_dbl * gamma_p_deriv)
117  / Pn;
118 
120  ops_partials.edge3_.partials_[n]
121  += -2.0 * half_nu_dbl * s_dbl * y_inv_dbl * gamma_p_deriv / Pn;
122  }
123 
125  for (size_t n = 0; n < stan::length(y); ++n)
126  ops_partials.edge1_.partials_[n] *= P;
127  }
129  for (size_t n = 0; n < stan::length(nu); ++n)
130  ops_partials.edge2_.partials_[n] *= P;
131  }
133  for (size_t n = 0; n < stan::length(s); ++n)
134  ops_partials.edge3_.partials_[n] *= P;
135  }
136  return ops_partials.build(P);
137 }
138 
139 } // namespace math
140 } // namespace stan
141 #endif
boost::math::tools::promote_args< double, typename partials_type< typename scalar_type< T >::type >::type, typename partials_return_type< T_pack... >::type >::type type
T value_of(const fvar< T > &v)
Return the value of the specified variable.
Definition: value_of.hpp:17
Extends std::true_type when instantiated with zero or more template parameters, all of which extend t...
Definition: conjunction.hpp:14
scalar_seq_view provides a uniform sequence-like wrapper around either a scalar or a sequence of scal...
This template builds partial derivatives with respect to a set of operands.
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)
Returns the length of the provided std::vector.
Definition: length.hpp:16
bool size_zero(T &x)
Returns 1 if input is of length 0, returns 0 otherwise.
Definition: size_zero.hpp:18
void check_nonnegative(const char *function, const char *name, const T_y &y)
Check if y is non-negative.
void check_positive_finite(const char *function, const char *name, const T_y &y)
Check if y is positive and finite.
return_type< T1, T2 >::type grad_reg_inc_gamma(T1 a, T2 z, T1 g, T1 dig, double precision=1e-6, int max_steps=1e5)
Gradient of the regularized incomplete gamma functions igamma(a, z)
boost::math::tools::promote_args< double, typename scalar_type< T >::type, typename return_type< Types_pack... >::type >::type type
Definition: return_type.hpp:36
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:11
void check_not_nan(const char *function, const char *name, const T_y &y)
Check if y is not NaN.
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
T_return_type build(double value)
Build the node to be stored on the autodiff graph.
VectorBuilder allocates type T1 values to be used as intermediate values.
internal::ops_partials_edge< double, Op2 > edge2_
fvar< T > pow(const fvar< T > &x1, const fvar< T > &x2)
Definition: pow.hpp:16
fvar< T > tgamma(const fvar< T > &x)
Return the result of applying the gamma function to the specified argument.
Definition: tgamma.hpp:21
void check_consistent_sizes(const char *function, const char *name1, const T1 &x1, const char *name2, const T2 &x2)
Check if the dimension of x1 is consistent with x2.
fvar< T > gamma_q(const fvar< T > &x1, const fvar< T > &x2)
Definition: gamma_q.hpp:13
internal::ops_partials_edge< double, Op3 > edge3_
internal::ops_partials_edge< double, Op1 > edge1_
fvar< T > digamma(const fvar< T > &x)
Return the derivative of the log gamma function at the specified argument.
Definition: digamma.hpp:23

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