Stan Math Library  2.9.0
reverse mode automatic differentiation
gamma_ccdf_log.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_GAMMA_CCDF_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_GAMMA_CCDF_LOG_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 
31  namespace math {
32 
33  template <typename T_y, typename T_shape, typename T_inv_scale>
34  typename return_type<T_y, T_shape, T_inv_scale>::type
35  gamma_ccdf_log(const T_y& y, const T_shape& alpha,
36  const T_inv_scale& beta) {
37  // Size checks
38  if (!(stan::length(y) && stan::length(alpha) && stan::length(beta)))
39  return 0.0;
40 
41  typedef typename stan::partials_return_type<T_y, T_shape,
42  T_inv_scale>::type
43  T_partials_return;
44 
45  // Error checks
46  static const char* function("stan::math::gamma_ccdf_log");
47 
55  using boost::math::tools::promote_args;
56  using std::exp;
57 
58  T_partials_return P(0.0);
59 
60  check_positive_finite(function, "Shape parameter", alpha);
61  check_positive_finite(function, "Scale parameter", beta);
62  check_not_nan(function, "Random variable", y);
63  check_nonnegative(function, "Random variable", y);
64  check_consistent_sizes(function,
65  "Random variable", y,
66  "Shape parameter", alpha,
67  "Scale Parameter", beta);
68 
69  // Wrap arguments in vectors
70  VectorView<const T_y> y_vec(y);
71  VectorView<const T_shape> alpha_vec(alpha);
72  VectorView<const T_inv_scale> beta_vec(beta);
73  size_t N = max_size(y, alpha, beta);
74 
76  operands_and_partials(y, alpha, beta);
77 
78  // Explicit return for extreme values
79  // The gradients are technically ill-defined, but treated as zero
80 
81  for (size_t i = 0; i < stan::length(y); i++) {
82  if (value_of(y_vec[i]) == 0)
83  return operands_and_partials.to_var(0.0, y, alpha, beta);
84  }
85 
86  // Compute ccdf_log and its gradients
87  using stan::math::gamma_p;
88  using stan::math::digamma;
89  using boost::math::tgamma;
90  using std::exp;
91  using std::pow;
92  using std::log;
93 
94  // Cache a few expensive function calls if nu is a parameter
96  T_partials_return, T_shape> gamma_vec(stan::length(alpha));
98  T_partials_return, T_shape>
99  digamma_vec(stan::length(alpha));
100 
102  for (size_t i = 0; i < stan::length(alpha); i++) {
103  const T_partials_return alpha_dbl = value_of(alpha_vec[i]);
104  gamma_vec[i] = tgamma(alpha_dbl);
105  digamma_vec[i] = digamma(alpha_dbl);
106  }
107  }
108 
109  // Compute vectorized ccdf_log and gradient
110  for (size_t n = 0; n < N; n++) {
111  // Explicit results for extreme values
112  // The gradients are technically ill-defined, but treated as zero
113  if (value_of(y_vec[n]) == std::numeric_limits<double>::infinity())
114  return operands_and_partials.to_var(stan::math::negative_infinity(),
115  y, alpha, beta);
116 
117  // Pull out values
118  const T_partials_return y_dbl = value_of(y_vec[n]);
119  const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
120  const T_partials_return beta_dbl = value_of(beta_vec[n]);
121 
122  // Compute
123  const T_partials_return Pn = 1.0 - gamma_p(alpha_dbl, beta_dbl * y_dbl);
124 
125  P += log(Pn);
126 
128  operands_and_partials.d_x1[n] -= beta_dbl * exp(-beta_dbl * y_dbl)
129  * pow(beta_dbl * y_dbl, alpha_dbl-1) / tgamma(alpha_dbl) / Pn;
131  operands_and_partials.d_x2[n]
132  += stan::math::grad_reg_inc_gamma(alpha_dbl, beta_dbl
133  * y_dbl, gamma_vec[n],
134  digamma_vec[n]) / Pn;
136  operands_and_partials.d_x3[n] -= y_dbl * exp(-beta_dbl * y_dbl)
137  * pow(beta_dbl * y_dbl, alpha_dbl-1) / tgamma(alpha_dbl) / Pn;
138  }
139 
140  return operands_and_partials.to_var(P, y, alpha, beta);
141  }
142  }
143 }
144 
145 #endif
bool check_greater_or_equal(const char *function, const char *name, const T_y &y, const T_low &low)
Return true if y is greater or equal than low.
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
fvar< T > log(const fvar< T > &x)
Definition: log.hpp:15
size_t length(const std::vector< T > &x)
Definition: length.hpp:10
T_return_type to_var(T_partials_return logp, const T1 &x1=0, const T2 &x2=0, const T3 &x3=0, const T4 &x4=0, const T5 &x5=0, const T6 &x6=0)
T grad_reg_inc_gamma(T a, T z, T g, T dig, T precision=1e-6)
VectorView< T_partials_return, is_vector< T1 >::value, is_constant_struct< T1 >::value > d_x1
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
VectorView< T_partials_return, is_vector< T3 >::value, is_constant_struct< T3 >::value > d_x3
A variable implementation that stores operands and derivatives with respect to the variable...
return_type< T_y, T_shape, T_inv_scale >::type gamma_ccdf_log(const T_y &y, const T_shape &alpha, const T_inv_scale &beta)
size_t max_size(const T1 &x1, const T2 &x2)
Definition: max_size.hpp:9
bool check_less_or_equal(const char *function, const char *name, const T_y &y, const T_high &high)
Return true if y is less or equal to high.
fvar< T > gamma_p(const fvar< T > &x1, const fvar< T > &x2)
Definition: gamma_p.hpp:15
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.
VectorView< T_partials_return, is_vector< T2 >::value, is_constant_struct< T2 >::value > d_x2
fvar< T > pow(const fvar< T > &x1, const fvar< T > &x2)
Definition: pow.hpp:18
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:15
VectorView is a template metaprogram that takes its argument and allows it to be used like a vector...
Definition: VectorView.hpp:41
bool check_positive_finite(const char *function, const char *name, const T_y &y)
Return true if y is positive and finite.
double negative_infinity()
Return negative infinity.
Definition: constants.hpp:132
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:16

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