Stan Math Library  2.14.0
reverse mode automatic differentiation
gamma_cdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_GAMMA_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_GAMMA_CDF_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 
46  template <typename T_y, typename T_shape, typename T_inv_scale>
48  gamma_cdf(const T_y& y, const T_shape& alpha, const T_inv_scale& beta) {
49  if (!(stan::length(y) && stan::length(alpha) && stan::length(beta)))
50  return 1.0;
51  typedef typename stan::partials_return_type<T_y, T_shape,
52  T_inv_scale>::type
53  T_partials_return;
54 
55  static const char* function("gamma_cdf");
56 
57  using boost::math::tools::promote_args;
58  using std::exp;
59 
60  T_partials_return P(1.0);
61 
62  check_positive_finite(function, "Shape parameter", alpha);
63  check_positive_finite(function, "Scale parameter", beta);
64  check_not_nan(function, "Random variable", y);
65  check_nonnegative(function, "Random variable", y);
66  check_consistent_sizes(function,
67  "Random variable", y,
68  "Shape parameter", alpha,
69  "Scale Parameter", beta);
70 
71  VectorView<const T_y> y_vec(y);
72  VectorView<const T_shape> alpha_vec(alpha);
73  VectorView<const T_inv_scale> beta_vec(beta);
74  size_t N = max_size(y, alpha, beta);
75 
77  operands_and_partials(y, alpha, beta);
78 
79  // Explicit return for extreme values
80  // The gradients are technically ill-defined, but treated as zero
81  for (size_t i = 0; i < stan::length(y); i++) {
82  if (value_of(y_vec[i]) == 0)
83  return operands_and_partials.value(0.0);
84  }
85 
86  using boost::math::tgamma;
87  using std::exp;
88  using std::pow;
89 
91  T_partials_return, T_shape> gamma_vec(stan::length(alpha));
93  T_partials_return, T_shape>
94  digamma_vec(stan::length(alpha));
95 
97  for (size_t i = 0; i < stan::length(alpha); i++) {
98  const T_partials_return alpha_dbl = value_of(alpha_vec[i]);
99  gamma_vec[i] = tgamma(alpha_dbl);
100  digamma_vec[i] = digamma(alpha_dbl);
101  }
102  }
103 
104  for (size_t n = 0; n < N; n++) {
105  // Explicit results for extreme values
106  // The gradients are technically ill-defined, but treated as zero
107  if (value_of(y_vec[n]) == std::numeric_limits<double>::infinity())
108  continue;
109 
110  const T_partials_return y_dbl = value_of(y_vec[n]);
111  const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
112  const T_partials_return beta_dbl = value_of(beta_vec[n]);
113 
114  const T_partials_return Pn = gamma_p(alpha_dbl, beta_dbl * y_dbl);
115 
116  P *= Pn;
117 
119  operands_and_partials.d_x1[n] += beta_dbl * exp(-beta_dbl * y_dbl)
120  * pow(beta_dbl * y_dbl, alpha_dbl-1) / tgamma(alpha_dbl) / Pn;
122  operands_and_partials.d_x2[n]
123  -= grad_reg_inc_gamma(alpha_dbl, beta_dbl
124  * y_dbl, gamma_vec[n],
125  digamma_vec[n]) / Pn;
127  operands_and_partials.d_x3[n] += y_dbl * exp(-beta_dbl * y_dbl)
128  * pow(beta_dbl * y_dbl, alpha_dbl-1) / tgamma(alpha_dbl) / Pn;
129  }
130 
132  for (size_t n = 0; n < stan::length(y); ++n)
133  operands_and_partials.d_x1[n] *= P;
134  }
136  for (size_t n = 0; n < stan::length(alpha); ++n)
137  operands_and_partials.d_x2[n] *= P;
138  }
140  for (size_t n = 0; n < stan::length(beta); ++n)
141  operands_and_partials.d_x3[n] *= P;
142  }
143  return operands_and_partials.value(P);
144  }
145 
146  }
147 }
148 #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
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
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
return_type< T_y, T_shape, T_inv_scale >::type gamma_cdf(const T_y &y, const T_shape &alpha, const T_inv_scale &beta)
The cumulative density function for a gamma distribution for y with the specified shape and inverse s...
Definition: gamma_cdf.hpp:48
fvar< T > gamma_p(const fvar< T > &x1, const fvar< T > &x2)
Definition: gamma_p.hpp:14
VectorBuilder allocates type T1 values to be used as intermediate values.
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
fvar< T > tgamma(const fvar< T > &x)
Return the result of applying the gamma function to the specified argument.
Definition: tgamma.hpp:20
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
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.
VectorView< T_return_type, false, true > d_x1
fvar< T > digamma(const fvar< T > &x)
Return the derivative of the log gamma function at the specified argument.
Definition: digamma.hpp:22

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