Stan Math Library  2.20.0
reverse mode automatic differentiation
inv_gamma_lcdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_INV_GAMMA_LCDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_INV_GAMMA_LCDF_HPP
3 
16 #include <cmath>
17 #include <limits>
18 
19 namespace stan {
20 namespace math {
21 
22 template <typename T_y, typename T_shape, typename T_scale>
24  const T_y& y, const T_shape& alpha, const T_scale& beta) {
26  T_partials_return;
27 
28  if (size_zero(y, alpha, beta))
29  return 0.0;
30 
31  static const char* function = "inv_gamma_lcdf";
32 
33  T_partials_return P(0.0);
34 
35  check_positive_finite(function, "Shape parameter", alpha);
36  check_positive_finite(function, "Scale parameter", beta);
37  check_not_nan(function, "Random variable", y);
38  check_nonnegative(function, "Random variable", y);
39  check_consistent_sizes(function, "Random variable", y, "Shape parameter",
40  alpha, "Scale Parameter", beta);
41 
42  scalar_seq_view<T_y> y_vec(y);
43  scalar_seq_view<T_shape> alpha_vec(alpha);
44  scalar_seq_view<T_scale> beta_vec(beta);
45  size_t N = max_size(y, alpha, beta);
46 
47  operands_and_partials<T_y, T_shape, T_scale> ops_partials(y, alpha, beta);
48 
49  // Explicit return for extreme values
50  // The gradients are technically ill-defined, but treated as zero
51  for (size_t i = 0; i < stan::length(y); i++) {
52  if (value_of(y_vec[i]) == 0)
53  return ops_partials.build(negative_infinity());
54  }
55 
56  using std::exp;
57  using std::log;
58  using std::pow;
59 
60  VectorBuilder<!is_constant_all<T_shape>::value, T_partials_return, T_shape>
61  gamma_vec(stan::length(alpha));
62  VectorBuilder<!is_constant_all<T_shape>::value, T_partials_return, T_shape>
63  digamma_vec(stan::length(alpha));
64 
66  for (size_t i = 0; i < stan::length(alpha); i++) {
67  const T_partials_return alpha_dbl = value_of(alpha_vec[i]);
68  gamma_vec[i] = tgamma(alpha_dbl);
69  digamma_vec[i] = digamma(alpha_dbl);
70  }
71  }
72 
73  for (size_t n = 0; n < N; n++) {
74  // Explicit results for extreme values
75  // The gradients are technically ill-defined, but treated as zero
76  if (value_of(y_vec[n]) == std::numeric_limits<double>::infinity())
77  continue;
78 
79  const T_partials_return y_dbl = value_of(y_vec[n]);
80  const T_partials_return y_inv_dbl = 1.0 / y_dbl;
81  const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
82  const T_partials_return beta_dbl = value_of(beta_vec[n]);
83 
84  const T_partials_return Pn = gamma_q(alpha_dbl, beta_dbl * y_inv_dbl);
85 
86  P += log(Pn);
87 
89  ops_partials.edge1_.partials_[n]
90  += beta_dbl * y_inv_dbl * y_inv_dbl * exp(-beta_dbl * y_inv_dbl)
91  * pow(beta_dbl * y_inv_dbl, alpha_dbl - 1) / tgamma(alpha_dbl)
92  / Pn;
94  ops_partials.edge2_.partials_[n]
95  += grad_reg_inc_gamma(alpha_dbl, beta_dbl * y_inv_dbl, gamma_vec[n],
96  digamma_vec[n])
97  / Pn;
99  ops_partials.edge3_.partials_[n]
100  += -y_inv_dbl * exp(-beta_dbl * y_inv_dbl)
101  * pow(beta_dbl * y_inv_dbl, alpha_dbl - 1) / tgamma(alpha_dbl)
102  / Pn;
103  }
104  return ops_partials.build(P);
105 }
106 
107 } // namespace math
108 } // namespace stan
109 #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
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:12
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.
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.
fvar< T > beta(const fvar< T > &x1, const fvar< T > &x2)
Return fvar with the beta function applied to the specified arguments and its gradient.
Definition: beta.hpp:51
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.
return_type< T_y, T_shape, T_scale >::type inv_gamma_lcdf(const T_y &y, const T_shape &alpha, const T_scale &beta)
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_
double negative_infinity()
Return negative infinity.
Definition: constants.hpp:115
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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