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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 
31  namespace math {
32 
47  template <typename T_y, typename T_shape, typename T_inv_scale>
48  typename return_type<T_y, T_shape, T_inv_scale>::type
49  gamma_cdf(const T_y& y, const T_shape& alpha, const T_inv_scale& beta) {
50  // Size checks
51  if (!(stan::length(y) && stan::length(alpha) && stan::length(beta)))
52  return 1.0;
53  typedef typename stan::partials_return_type<T_y, T_shape,
54  T_inv_scale>::type
55  T_partials_return;
56 
57  // Error checks
58  static const char* function("stan::math::gamma_cdf");
59 
67  using boost::math::tools::promote_args;
68  using std::exp;
69 
70  T_partials_return P(1.0);
71 
72  check_positive_finite(function, "Shape parameter", alpha);
73  check_positive_finite(function, "Scale parameter", beta);
74  check_not_nan(function, "Random variable", y);
75  check_nonnegative(function, "Random variable", y);
76  check_consistent_sizes(function,
77  "Random variable", y,
78  "Shape parameter", alpha,
79  "Scale Parameter", beta);
80 
81  // Wrap arguments in vectors
82  VectorView<const T_y> y_vec(y);
83  VectorView<const T_shape> alpha_vec(alpha);
84  VectorView<const T_inv_scale> beta_vec(beta);
85  size_t N = max_size(y, alpha, beta);
86 
88  operands_and_partials(y, alpha, beta);
89 
90  // Explicit return for extreme values
91  // The gradients are technically ill-defined, but treated as zero
92 
93  for (size_t i = 0; i < stan::length(y); i++) {
94  if (value_of(y_vec[i]) == 0)
95  return operands_and_partials.to_var(0.0, y, alpha, beta);
96  }
97 
98  // Compute CDF and its gradients
99  using stan::math::gamma_p;
100  using stan::math::digamma;
101  using boost::math::tgamma;
102  using std::exp;
103  using std::pow;
104 
105  // Cache a few expensive function calls if nu is a parameter
107  T_partials_return, T_shape> gamma_vec(stan::length(alpha));
109  T_partials_return, T_shape>
110  digamma_vec(stan::length(alpha));
111 
113  for (size_t i = 0; i < stan::length(alpha); i++) {
114  const T_partials_return alpha_dbl = value_of(alpha_vec[i]);
115  gamma_vec[i] = tgamma(alpha_dbl);
116  digamma_vec[i] = digamma(alpha_dbl);
117  }
118  }
119 
120  // Compute vectorized CDF and gradient
121  for (size_t n = 0; n < N; n++) {
122  // Explicit results for extreme values
123  // The gradients are technically ill-defined, but treated as zero
124  if (value_of(y_vec[n]) == std::numeric_limits<double>::infinity())
125  continue;
126 
127  // Pull out values
128  const T_partials_return y_dbl = value_of(y_vec[n]);
129  const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
130  const T_partials_return beta_dbl = value_of(beta_vec[n]);
131 
132  // Compute
133  const T_partials_return Pn = gamma_p(alpha_dbl, beta_dbl * y_dbl);
134 
135  P *= Pn;
136 
138  operands_and_partials.d_x1[n] += beta_dbl * exp(-beta_dbl * y_dbl)
139  * pow(beta_dbl * y_dbl, alpha_dbl-1) / tgamma(alpha_dbl) / Pn;
141  operands_and_partials.d_x2[n]
142  -= stan::math::grad_reg_inc_gamma(alpha_dbl, beta_dbl
143  * y_dbl, gamma_vec[n],
144  digamma_vec[n]) / Pn;
146  operands_and_partials.d_x3[n] += y_dbl * exp(-beta_dbl * y_dbl)
147  * pow(beta_dbl * y_dbl, alpha_dbl-1) / tgamma(alpha_dbl) / Pn;
148  }
149 
151  for (size_t n = 0; n < stan::length(y); ++n)
152  operands_and_partials.d_x1[n] *= P;
153  }
155  for (size_t n = 0; n < stan::length(alpha); ++n)
156  operands_and_partials.d_x2[n] *= P;
157  }
159  for (size_t n = 0; n < stan::length(beta); ++n)
160  operands_and_partials.d_x3[n] *= P;
161  }
162 
163  return operands_and_partials.to_var(P, y, alpha, beta);
164  }
165  }
166 }
167 
168 #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
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...
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.
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:49
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.
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:16

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