Stan Math Library  2.15.0
reverse mode automatic differentiation
gamma_lccdf.hpp
Go to the documentation of this file.
1 #ifndef STAN_MATH_PRIM_SCAL_PROB_GAMMA_LCCDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_GAMMA_LCCDF_HPP
3 
24 #include <boost/random/gamma_distribution.hpp>
25 #include <boost/random/variate_generator.hpp>
26 #include <cmath>
27 #include <limits>
28 
29 namespace stan {
30  namespace math {
31 
32  template <typename T_y, typename T_shape, typename T_inv_scale>
34  gamma_lccdf(const T_y& y, const T_shape& alpha,
35  const T_inv_scale& beta) {
36  if (!(stan::length(y) && stan::length(alpha) && stan::length(beta)))
37  return 0.0;
38 
39  typedef typename stan::partials_return_type<T_y, T_shape,
40  T_inv_scale>::type
41  T_partials_return;
42 
43  static const char* function("gamma_lccdf");
44 
45  using boost::math::tools::promote_args;
46  using std::exp;
47 
48  T_partials_return P(0.0);
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,
55  "Random variable", y,
56  "Shape parameter", alpha,
57  "Scale Parameter", beta);
58 
60  scalar_seq_view<const T_shape> alpha_vec(alpha);
62  size_t N = max_size(y, alpha, beta);
63 
65  operands_and_partials(y, alpha, beta);
66 
67  // Explicit return for extreme values
68  // The gradients are technically ill-defined, but treated as zero
69  for (size_t i = 0; i < stan::length(y); i++) {
70  if (value_of(y_vec[i]) == 0)
71  return operands_and_partials.value(0.0);
72  }
73 
74  using boost::math::tgamma;
75  using std::exp;
76  using std::pow;
77  using std::log;
78 
80  T_partials_return, T_shape> gamma_vec(stan::length(alpha));
82  T_partials_return, T_shape>
83  digamma_vec(stan::length(alpha));
84 
86  for (size_t i = 0; i < stan::length(alpha); i++) {
87  const T_partials_return alpha_dbl = value_of(alpha_vec[i]);
88  gamma_vec[i] = tgamma(alpha_dbl);
89  digamma_vec[i] = digamma(alpha_dbl);
90  }
91  }
92 
93  for (size_t n = 0; n < N; n++) {
94  // Explicit results for extreme values
95  // The gradients are technically ill-defined, but treated as zero
96  if (value_of(y_vec[n]) == std::numeric_limits<double>::infinity())
97  return operands_and_partials.value(negative_infinity());
98 
99  const T_partials_return y_dbl = value_of(y_vec[n]);
100  const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
101  const T_partials_return beta_dbl = value_of(beta_vec[n]);
102 
103  const T_partials_return Pn = gamma_q(alpha_dbl, beta_dbl * y_dbl);
104 
105  P += log(Pn);
106 
108  operands_and_partials.d_x1[n] -= beta_dbl * exp(-beta_dbl * y_dbl)
109  * pow(beta_dbl * y_dbl, alpha_dbl-1) / tgamma(alpha_dbl) / Pn;
111  operands_and_partials.d_x2[n]
112  += grad_reg_inc_gamma(alpha_dbl, beta_dbl
113  * y_dbl, gamma_vec[n],
114  digamma_vec[n]) / Pn;
116  operands_and_partials.d_x3[n] -= y_dbl * exp(-beta_dbl * y_dbl)
117  * pow(beta_dbl * y_dbl, alpha_dbl-1) / tgamma(alpha_dbl) / Pn;
118  }
119  return operands_and_partials.value(P);
120  }
121 
122  }
123 }
124 
125 #endif
VectorView< T_return_type, false, true > d_x2
T value_of(const fvar< T > &v)
Return the value of the specified variable.
Definition: value_of.hpp:16
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:14
T_return_type value(double value)
Returns a T_return_type with the value specified with the partial derivatves.
scalar_seq_view provides a uniform sequence-like wrapper around either a scalar or a sequence of scal...
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
void check_nonnegative(const char *function, const char *name, const T_y &y)
Check if y is non-negative.
boost::math::tools::promote_args< typename scalar_type< T1 >::type, typename scalar_type< T2 >::type, typename scalar_type< T3 >::type, typename scalar_type< T4 >::type, typename scalar_type< T5 >::type, typename scalar_type< T6 >::type >::type type
Definition: return_type.hpp:27
Metaprogram to determine if a type has a base scalar type that can be assigned to type double...
void check_positive_finite(const char *function, const char *name, const T_y &y)
Check if y is positive and finite.
fvar< T > exp(const fvar< T > &x)
Definition: exp.hpp:10
void check_not_nan(const char *function, const char *name, const T_y &y)
Check if y is not NaN.
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
T grad_reg_inc_gamma(T a, T z, T g, T dig, double precision=1e-6, int max_steps=1e5)
Gradient of the regularized incomplete gamma functions igamma(a, z)
VectorBuilder allocates type T1 values to be used as intermediate values.
return_type< T_y, T_shape, T_inv_scale >::type gamma_lccdf(const T_y &y, const T_shape &alpha, const T_inv_scale &beta)
Definition: gamma_lccdf.hpp:34
fvar< T > pow(const fvar< T > &x1, const fvar< T > &x2)
Definition: pow.hpp:17
fvar< T > tgamma(const fvar< T > &x)
Return the result of applying the gamma function to the specified argument.
Definition: tgamma.hpp:20
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:14
VectorView< T_return_type, false, true > d_x1
double negative_infinity()
Return negative infinity.
Definition: constants.hpp:130
fvar< T > digamma(const fvar< T > &x)
Return the derivative of the log gamma function at the specified argument.
Definition: digamma.hpp:22

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