Stan Math Library  2.20.0
reverse mode automatic differentiation
inv_gamma_cdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_INV_GAMMA_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_INV_GAMMA_CDF_HPP
3 
15 #include <cmath>
16 #include <limits>
17 
18 namespace stan {
19 namespace math {
20 
37 template <typename T_y, typename T_shape, typename T_scale>
39  const T_y& y, const T_shape& alpha, const T_scale& beta) {
41  T_partials_return;
42 
43  if (size_zero(y, alpha, beta))
44  return 1.0;
45 
46  static const char* function = "inv_gamma_cdf";
47 
48  T_partials_return P(1.0);
49 
50  check_positive_finite(function, "Shape parameter", alpha);
51  check_positive_finite(function, "Scale parameter", beta);
52  check_not_nan(function, "Random variable", y);
53  check_nonnegative(function, "Random variable", y);
54  check_consistent_sizes(function, "Random variable", y, "Shape parameter",
55  alpha, "Scale Parameter", beta);
56 
57  scalar_seq_view<T_y> y_vec(y);
58  scalar_seq_view<T_shape> alpha_vec(alpha);
59  scalar_seq_view<T_scale> beta_vec(beta);
60  size_t N = max_size(y, alpha, beta);
61 
62  operands_and_partials<T_y, T_shape, T_scale> ops_partials(y, alpha, beta);
63 
64  // Explicit return for extreme values
65  // The gradients are technically ill-defined, but treated as zero
66  for (size_t i = 0; i < stan::length(y); i++) {
67  if (value_of(y_vec[i]) == 0)
68  return ops_partials.build(0.0);
69  }
70 
71  using std::exp;
72  using std::pow;
73 
74  VectorBuilder<!is_constant_all<T_shape>::value, T_partials_return, T_shape>
75  gamma_vec(stan::length(alpha));
76  VectorBuilder<!is_constant_all<T_shape>::value, T_partials_return, T_shape>
77  digamma_vec(stan::length(alpha));
78 
80  for (size_t i = 0; i < stan::length(alpha); i++) {
81  const T_partials_return alpha_dbl = value_of(alpha_vec[i]);
82  gamma_vec[i] = tgamma(alpha_dbl);
83  digamma_vec[i] = digamma(alpha_dbl);
84  }
85  }
86 
87  for (size_t n = 0; n < N; n++) {
88  // Explicit results for extreme values
89  // The gradients are technically ill-defined, but treated as zero
90  if (value_of(y_vec[n]) == std::numeric_limits<double>::infinity())
91  continue;
92 
93  const T_partials_return y_dbl = value_of(y_vec[n]);
94  const T_partials_return y_inv_dbl = 1.0 / y_dbl;
95  const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
96  const T_partials_return beta_dbl = value_of(beta_vec[n]);
97 
98  const T_partials_return Pn = gamma_q(alpha_dbl, beta_dbl * y_inv_dbl);
99 
100  P *= Pn;
101 
103  ops_partials.edge1_.partials_[n]
104  += beta_dbl * y_inv_dbl * y_inv_dbl * exp(-beta_dbl * y_inv_dbl)
105  * pow(beta_dbl * y_inv_dbl, alpha_dbl - 1) / tgamma(alpha_dbl)
106  / Pn;
108  ops_partials.edge2_.partials_[n]
109  += grad_reg_inc_gamma(alpha_dbl, beta_dbl * y_inv_dbl, gamma_vec[n],
110  digamma_vec[n])
111  / Pn;
113  ops_partials.edge3_.partials_[n]
114  += -y_inv_dbl * exp(-beta_dbl * y_inv_dbl)
115  * pow(beta_dbl * y_inv_dbl, alpha_dbl - 1) / tgamma(alpha_dbl)
116  / Pn;
117  }
118 
120  for (size_t n = 0; n < stan::length(y); ++n)
121  ops_partials.edge1_.partials_[n] *= P;
122  }
124  for (size_t n = 0; n < stan::length(alpha); ++n)
125  ops_partials.edge2_.partials_[n] *= P;
126  }
128  for (size_t n = 0; n < stan::length(beta); ++n)
129  ops_partials.edge3_.partials_[n] *= P;
130  }
131  return ops_partials.build(P);
132 }
133 
134 } // namespace math
135 } // namespace stan
136 #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.
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.
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
return_type< T_y, T_shape, T_scale >::type inv_gamma_cdf(const T_y &y, const T_shape &alpha, const T_scale &beta)
The CDF of an inverse gamma density for y with the specified shape and scale parameters.
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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