Stan Math Library  2.11.0
reverse mode automatic differentiation
gamma_cdf_log.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_GAMMA_CDF_LOG_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_GAMMA_CDF_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_inv_scale>
34  typename return_type<T_y, T_shape, T_inv_scale>::type
35  gamma_cdf_log(const T_y& y, const T_shape& alpha, const T_inv_scale& beta) {
36  // Size checks
37  if (!(stan::length(y) && stan::length(alpha) && stan::length(beta)))
38  return 0.0;
39  typedef typename stan::partials_return_type<T_y, T_shape,
40  T_inv_scale>::type
41  T_partials_return;
42 
43  // Error checks
44  static const char* function("stan::math::gamma_cdf_log");
45 
53  using boost::math::tools::promote_args;
54  using std::exp;
55 
56  T_partials_return P(0.0);
57 
58  check_positive_finite(function, "Shape parameter", alpha);
59  check_positive_finite(function, "Scale parameter", beta);
60  check_not_nan(function, "Random variable", y);
61  check_nonnegative(function, "Random variable", y);
62  check_consistent_sizes(function,
63  "Random variable", y,
64  "Shape parameter", alpha,
65  "Scale Parameter", beta);
66 
67  // Wrap arguments in vectors
68  VectorView<const T_y> y_vec(y);
69  VectorView<const T_shape> alpha_vec(alpha);
70  VectorView<const T_inv_scale> beta_vec(beta);
71  size_t N = max_size(y, alpha, beta);
72 
74  operands_and_partials(y, alpha, beta);
75 
76  // Explicit return for extreme values
77  // The gradients are technically ill-defined, but treated as zero
78 
79  for (size_t i = 0; i < stan::length(y); i++) {
80  if (value_of(y_vec[i]) == 0)
81  return operands_and_partials.value(stan::math::negative_infinity());
82  }
83 
84  // Compute cdf_log and its gradients
85  using stan::math::gamma_p;
86  using stan::math::digamma;
87  using boost::math::tgamma;
88  using std::exp;
89  using std::pow;
90  using std::log;
91 
92  // Cache a few expensive function calls if nu is a parameter
94  T_partials_return, T_shape> 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  // Compute vectorized cdf_log and gradient
108  for (size_t n = 0; n < N; n++) {
109  // Explicit results for extreme values
110  // The gradients are technically ill-defined, but treated as zero
111  if (value_of(y_vec[n]) == std::numeric_limits<double>::infinity())
112  return operands_and_partials.value(0.0);
113 
114  // Pull out values
115  const T_partials_return y_dbl = value_of(y_vec[n]);
116  const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
117  const T_partials_return beta_dbl = value_of(beta_vec[n]);
118 
119  // Compute
120  const T_partials_return Pn = gamma_p(alpha_dbl, beta_dbl * y_dbl);
121 
122  P += log(Pn);
123 
125  operands_and_partials.d_x1[n] += beta_dbl * exp(-beta_dbl * y_dbl)
126  * pow(beta_dbl * y_dbl, alpha_dbl-1) / tgamma(alpha_dbl) / Pn;
128  operands_and_partials.d_x2[n]
129  -= stan::math::grad_reg_inc_gamma(alpha_dbl, beta_dbl
130  * y_dbl, gamma_vec[n],
131  digamma_vec[n]) / Pn;
133  operands_and_partials.d_x3[n] += y_dbl * exp(-beta_dbl * y_dbl)
134  * pow(beta_dbl * y_dbl, alpha_dbl-1) / tgamma(alpha_dbl) / Pn;
135  }
136 
137  return operands_and_partials.value(P);
138  }
139  }
140 }
141 
142 #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
return_type< T_y, T_shape, T_inv_scale >::type gamma_cdf_log(const T_y &y, const T_shape &alpha, const T_inv_scale &beta)
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
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
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
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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