Stan Math Library  2.10.0
reverse mode automatic differentiation
inv_gamma_ccdf_log.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_INV_GAMMA_CCDF_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_INV_GAMMA_CCDF_LOG_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 
31  namespace math {
32 
33  template <typename T_y, typename T_shape, typename T_scale>
34  typename return_type<T_y, T_shape, T_scale>::type
35  inv_gamma_ccdf_log(const T_y& y, const T_shape& alpha,
36  const T_scale& beta) {
38  T_partials_return;
39 
40  // Size checks
41  if (!(stan::length(y) && stan::length(alpha) && stan::length(beta)))
42  return 0.0;
43 
44  // Error checks
45  static const char* function("stan::math::inv_gamma_ccdf_log");
46 
54  using boost::math::tools::promote_args;
55  using std::exp;
56 
57  T_partials_return P(0.0);
58 
59  check_positive_finite(function, "Shape parameter", alpha);
60  check_positive_finite(function, "Scale parameter", beta);
61  check_not_nan(function, "Random variable", y);
62  check_nonnegative(function, "Random variable", y);
63  check_consistent_sizes(function,
64  "Random variable", y,
65  "Shape parameter", alpha,
66  "Scale Parameter", beta);
67 
68  // Wrap arguments in vectors
69  VectorView<const T_y> y_vec(y);
70  VectorView<const T_shape> alpha_vec(alpha);
71  VectorView<const T_scale> beta_vec(beta);
72  size_t N = max_size(y, alpha, beta);
73 
75  operands_and_partials(y, alpha, beta);
76 
77  // Explicit return for extreme values
78  // The gradients are technically ill-defined, but treated as zero
79 
80  for (size_t i = 0; i < stan::length(y); i++) {
81  if (value_of(y_vec[i]) == 0)
82  return operands_and_partials.value(0.0);
83  }
84 
85  // Compute ccdf_log and its gradients
86  using stan::math::gamma_q;
87  using stan::math::digamma;
88  using boost::math::tgamma;
89  using std::exp;
90  using std::pow;
91  using std::log;
92 
93  // Cache a few expensive function calls if nu is a parameter
95  T_partials_return, T_shape> gamma_vec(stan::length(alpha));
97  T_partials_return, T_shape>
98  digamma_vec(stan::length(alpha));
99 
101  for (size_t i = 0; i < stan::length(alpha); i++) {
102  const T_partials_return alpha_dbl = value_of(alpha_vec[i]);
103  gamma_vec[i] = tgamma(alpha_dbl);
104  digamma_vec[i] = digamma(alpha_dbl);
105  }
106  }
107 
108  // Compute vectorized ccdf_log and gradient
109  for (size_t n = 0; n < N; n++) {
110  // Explicit results for extreme values
111  // The gradients are technically ill-defined, but treated as zero
112  if (value_of(y_vec[n]) == std::numeric_limits<double>::infinity())
113  return operands_and_partials.value(stan::math::negative_infinity());
114 
115  // Pull out values
116  const T_partials_return y_dbl = value_of(y_vec[n]);
117  const T_partials_return y_inv_dbl = 1.0 / y_dbl;
118  const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
119  const T_partials_return beta_dbl = value_of(beta_vec[n]);
120 
121  // Compute
122  const T_partials_return Pn = 1.0 - gamma_q(alpha_dbl, beta_dbl
123  * y_inv_dbl);
124 
125  P += log(Pn);
126 
128  operands_and_partials.d_x1[n] -= beta_dbl * y_inv_dbl * y_inv_dbl
129  * exp(-beta_dbl * y_inv_dbl) * pow(beta_dbl * y_inv_dbl,
130  alpha_dbl-1)
131  / tgamma(alpha_dbl) / Pn;
133  operands_and_partials.d_x2[n]
134  -= stan::math::grad_reg_inc_gamma(alpha_dbl, beta_dbl
135  * y_inv_dbl, gamma_vec[n],
136  digamma_vec[n]) / Pn;
138  operands_and_partials.d_x3[n] += y_inv_dbl
139  * exp(-beta_dbl * y_inv_dbl)
140  * pow(beta_dbl * y_inv_dbl, alpha_dbl-1)
141  / tgamma(alpha_dbl) / Pn;
142  }
143 
144  return operands_and_partials.value(P);
145  }
146  }
147 }
148 
149 #endif
VectorView< T_return_type, false, true > d_x2
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
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
T grad_reg_inc_gamma(T a, T z, T g, T dig, T precision=1e-6)
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
return_type< T_y, T_shape, T_scale >::type inv_gamma_ccdf_log(const T_y &y, const T_shape &alpha, const T_scale &beta)
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.
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.
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 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:15
bool check_positive_finite(const char *function, const char *name, const T_y &y)
Return true if y is positive and finite.
VectorView< T_return_type, false, true > d_x1
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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