Stan Math Library  2.9.0
reverse mode automatic differentiation
inv_gamma_cdf.hpp
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1 #ifndef STAN_MATH_PRIM_SCAL_PROB_INV_GAMMA_CDF_HPP
2 #define STAN_MATH_PRIM_SCAL_PROB_INV_GAMMA_CDF_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 
49  template <typename T_y, typename T_shape, typename T_scale>
50  typename return_type<T_y, T_shape, T_scale>::type
51  inv_gamma_cdf(const T_y& y, const T_shape& alpha, const T_scale& beta) {
53  T_partials_return;
54 
55  // Size checks
56  if (!(stan::length(y) && stan::length(alpha) && stan::length(beta)))
57  return 1.0;
58 
59  // Error checks
60  static const char* function("stan::math::inv_gamma_cdf");
61 
69  using boost::math::tools::promote_args;
70  using std::exp;
71 
72  T_partials_return P(1.0);
73 
74  check_positive_finite(function, "Shape parameter", alpha);
75  check_positive_finite(function, "Scale parameter", beta);
76  check_not_nan(function, "Random variable", y);
77  check_nonnegative(function, "Random variable", y);
78  check_consistent_sizes(function,
79  "Random variable", y,
80  "Shape parameter", alpha,
81  "Scale Parameter", beta);
82 
83  // Wrap arguments in vectors
84  VectorView<const T_y> y_vec(y);
85  VectorView<const T_shape> alpha_vec(alpha);
86  VectorView<const T_scale> beta_vec(beta);
87  size_t N = max_size(y, alpha, beta);
88 
90  operands_and_partials(y, alpha, beta);
91 
92  // Explicit return for extreme values
93  // The gradients are technically ill-defined, but treated as zero
94 
95  for (size_t i = 0; i < stan::length(y); i++) {
96  if (value_of(y_vec[i]) == 0)
97  return operands_and_partials.to_var(0.0, y, alpha, beta);
98  }
99 
100  // Compute CDF and its gradients
101  using stan::math::gamma_q;
102  using stan::math::digamma;
103  using boost::math::tgamma;
104  using std::exp;
105  using std::pow;
106 
107  // Cache a few expensive function calls if nu is a parameter
109  T_partials_return, T_shape>
110  gamma_vec(stan::length(alpha));
112  T_partials_return, T_shape>
113  digamma_vec(stan::length(alpha));
114 
116  for (size_t i = 0; i < stan::length(alpha); i++) {
117  const T_partials_return alpha_dbl = value_of(alpha_vec[i]);
118  gamma_vec[i] = tgamma(alpha_dbl);
119  digamma_vec[i] = digamma(alpha_dbl);
120  }
121  }
122 
123  // Compute vectorized CDF and gradient
124  for (size_t n = 0; n < N; n++) {
125  // Explicit results for extreme values
126  // The gradients are technically ill-defined, but treated as zero
127  if (value_of(y_vec[n]) == std::numeric_limits<double>::infinity())
128  continue;
129 
130  // Pull out values
131  const T_partials_return y_dbl = value_of(y_vec[n]);
132  const T_partials_return y_inv_dbl = 1.0 / y_dbl;
133  const T_partials_return alpha_dbl = value_of(alpha_vec[n]);
134  const T_partials_return beta_dbl = value_of(beta_vec[n]);
135 
136  // Compute
137  const T_partials_return Pn = gamma_q(alpha_dbl, beta_dbl * y_inv_dbl);
138 
139  P *= Pn;
140 
142  operands_and_partials.d_x1[n] += beta_dbl * y_inv_dbl * y_inv_dbl
143  * exp(-beta_dbl * y_inv_dbl) * pow(beta_dbl
144  * y_inv_dbl, alpha_dbl-1)
145  / tgamma(alpha_dbl) / Pn;
147  operands_and_partials.d_x2[n]
148  += stan::math::grad_reg_inc_gamma(alpha_dbl, beta_dbl
149  * y_inv_dbl, gamma_vec[n],
150  digamma_vec[n]) / Pn;
152  operands_and_partials.d_x3[n] += - y_inv_dbl
153  * exp(-beta_dbl * y_inv_dbl)
154  * pow(beta_dbl * y_inv_dbl, alpha_dbl-1)
155  / tgamma(alpha_dbl) / Pn;
156  }
157 
159  for (size_t n = 0; n < stan::length(y); ++n)
160  operands_and_partials.d_x1[n] *= P;
161  }
163  for (size_t n = 0; n < stan::length(alpha); ++n)
164  operands_and_partials.d_x2[n] *= P;
165  }
167  for (size_t n = 0; n < stan::length(beta); ++n)
168  operands_and_partials.d_x3[n] *= P;
169  }
170 
171  return operands_and_partials.to_var(P, y, alpha, beta);
172  }
173  }
174 }
175 
176 #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.
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
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.
return_type< T_y, T_shape, T_scale >::type inv_gamma_cdf(const T_y &y, const T_shape &alpha, const T_scale &beta)
The CDF of an inverse gamma density for y with the specified shape and scale parameters.
fvar< T > digamma(const fvar< T > &x)
Definition: digamma.hpp:16

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