Stan Math Library  2.12.0
reverse mode automatic differentiation
inv_gamma_cdf.hpp
Go to the documentation of this file.
1 #ifndef STAN_MATH_PRIM_SCAL_PROB_INV_GAMMA_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_INV_GAMMA_CDF_HPP
3 
4 #include <boost/random/gamma_distribution.hpp>
5 #include <boost/random/variate_generator.hpp>
26 #include <cmath>
27 #include <limits>
28 
29 namespace stan {
30  namespace math {
31 
48  template <typename T_y, typename T_shape, typename T_scale>
49  typename return_type<T_y, T_shape, T_scale>::type
50  inv_gamma_cdf(const T_y& y, const T_shape& alpha, const T_scale& beta) {
52  T_partials_return;
53 
54  if (!(stan::length(y) && stan::length(alpha) && stan::length(beta)))
55  return 1.0;
56 
57  static const char* function("inv_gamma_cdf");
58 
59  using boost::math::tools::promote_args;
60  using std::exp;
61 
62  T_partials_return P(1.0);
63 
64  check_positive_finite(function, "Shape parameter", alpha);
65  check_positive_finite(function, "Scale parameter", beta);
66  check_not_nan(function, "Random variable", y);
67  check_nonnegative(function, "Random variable", y);
68  check_consistent_sizes(function,
69  "Random variable", y,
70  "Shape parameter", alpha,
71  "Scale Parameter", beta);
72 
73  VectorView<const T_y> y_vec(y);
74  VectorView<const T_shape> alpha_vec(alpha);
75  VectorView<const T_scale> beta_vec(beta);
76  size_t N = max_size(y, alpha, beta);
77 
79  operands_and_partials(y, alpha, beta);
80 
81  // Explicit return for extreme values
82  // The gradients are technically ill-defined, but treated as zero
83  for (size_t i = 0; i < stan::length(y); i++) {
84  if (value_of(y_vec[i]) == 0)
85  return operands_and_partials.value(0.0);
86  }
87 
88  using boost::math::tgamma;
89  using std::exp;
90  using std::pow;
91 
93  T_partials_return, T_shape>
94  gamma_vec(stan::length(alpha));
96  T_partials_return, T_shape>
97  digamma_vec(stan::length(alpha));
98 
100  for (size_t i = 0; i < stan::length(alpha); i++) {
101  const T_partials_return alpha_dbl = value_of(alpha_vec[i]);
102  gamma_vec[i] = tgamma(alpha_dbl);
103  digamma_vec[i] = digamma(alpha_dbl);
104  }
105  }
106 
107  for (size_t n = 0; n < N; n++) {
108  // Explicit results for extreme values
109  // The gradients are technically ill-defined, but treated as zero
110  if (value_of(y_vec[n]) == std::numeric_limits<double>::infinity())
111  continue;
112 
113  const T_partials_return y_dbl = value_of(y_vec[n]);
114  const T_partials_return y_inv_dbl = 1.0 / y_dbl;
115  const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
116  const T_partials_return beta_dbl = value_of(beta_vec[n]);
117 
118  const T_partials_return Pn = gamma_q(alpha_dbl, beta_dbl * y_inv_dbl);
119 
120  P *= Pn;
121 
123  operands_and_partials.d_x1[n] += beta_dbl * y_inv_dbl * y_inv_dbl
124  * exp(-beta_dbl * y_inv_dbl) * pow(beta_dbl
125  * y_inv_dbl, alpha_dbl-1)
126  / tgamma(alpha_dbl) / Pn;
128  operands_and_partials.d_x2[n]
129  += grad_reg_inc_gamma(alpha_dbl, beta_dbl
130  * y_inv_dbl, gamma_vec[n],
131  digamma_vec[n]) / Pn;
133  operands_and_partials.d_x3[n] += - y_inv_dbl
134  * exp(-beta_dbl * y_inv_dbl)
135  * pow(beta_dbl * y_inv_dbl, alpha_dbl-1)
136  / tgamma(alpha_dbl) / Pn;
137  }
138 
140  for (size_t n = 0; n < stan::length(y); ++n)
141  operands_and_partials.d_x1[n] *= P;
142  }
144  for (size_t n = 0; n < stan::length(alpha); ++n)
145  operands_and_partials.d_x2[n] *= P;
146  }
148  for (size_t n = 0; n < stan::length(beta); ++n)
149  operands_and_partials.d_x3[n] *= P;
150  }
151  return operands_and_partials.value(P);
152  }
153 
154  }
155 }
156 #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.
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
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.
T grad_reg_inc_gamma(T a, T z, T g, T dig, double precision=1e-6)
Gradient of the regularized incomplete gamma functions igamma(a, z)
fvar< T > pow(const fvar< T > &x1, const fvar< T > &x2)
Definition: pow.hpp:17
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:14
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:14
bool check_positive_finite(const char *function, const char *name, const T_y &y)
Return true if y is positive and finite.
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.
VectorView< T_return_type, false, true > d_x1
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:15

     [ Stan Home Page ] © 2011–2016, Stan Development Team.