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Stokhos::KL::ExponentialRandomField< value_type, execution_space > Class Template Reference

Class representing a KL expansion of an exponential random field. More...

#include <Stokhos_KL_ExponentialRandomField.hpp>

Public Types

typedef
ExponentialOneDEigenFunction
< value_type > 		one_d_eigen_func_type
 
typedef OneDEigenPair
< one_d_eigen_func_type > 		one_d_eigen_pair_type
 
typedef ProductEigenPair
< one_d_eigen_func_type,
execution_space > 		product_eigen_pair_type
 
typedef Kokkos::View
< one_d_eigen_func_type
**, execution_space > 		eigen_func_array_type
 
typedef Kokkos::View
< value_type
*, execution_space > 		eigen_value_array_type
 

Public Member Functions

 ExponentialRandomField ()
 Default constructor.
 
 ExponentialRandomField (Teuchos::ParameterList &solverParams)
 Constructor.
 
KOKKOS_INLINE_FUNCTION ~ExponentialRandomField ()
 Destructor.
 
KOKKOS_INLINE_FUNCTION int spatialDimension () const
 Return spatial dimension of the field.
 
KOKKOS_INLINE_FUNCTION int stochasticDimension () const
 Return stochastic dimension of the field.
 
template<typename point_type , typename rv_type >
KOKKOS_INLINE_FUNCTION
Teuchos::PromotionTraits
< typename rv_type::value_type,
value_type >::promote 		evaluate (const point_type &point, const rv_type &random_variables) const
 Evaluate random field at a point.
 
template<typename point_type >
KOKKOS_INLINE_FUNCTION value_type evaluate_mean (const point_type &point) const
 Evaluate mean of random field at a point.
 
template<typename point_type >
KOKKOS_INLINE_FUNCTION
Teuchos::PromotionTraits
< typename
point_type::value_type,
value_type >::promote 		evaluate_standard_deviation (const point_type &point) const
 Evaluate standard deviation of random field at a point.
 
template<typename point_type >
KOKKOS_INLINE_FUNCTION
Teuchos::PromotionTraits
< typename
point_type::value_type,
value_type >::promote 		evaluate_eigenfunction (const point_type &point, int i) const
 Evaluate given eigenfunction at a point.
 
value_type KOKKOS_INLINE_FUNCTION eigenvalue (int i) const
 Return eigenvalue.
 
void print (std::ostream &os) const
 Print KL expansion.
 

Protected Attributes

int num_KL
 Number of KL terms.
 
int dim
 Dimension of expansion.
 
value_type mean
 Mean of random field.
 
value_type std_dev
 Standard deviation of random field.
 
eigen_func_array_type product_eigen_funcs
 Product eigenfunctions.
 
eigen_value_array_type product_eigen_values
 Product eigenvalues.
 

Detailed Description

template<typename value_type, typename execution_space = Kokkos::DefaultExecutionSpace>
class Stokhos::KL::ExponentialRandomField< value_type, execution_space >

Class representing a KL expansion of an exponential random field.

This class provides a means for evaluating a random field $a(x,\theta)$, $x\in D$, $\theta\in\Omega$ through the KL expansion

\[ a(x,\theta) \approx a_0 + \sigma\sum_{k=1}^M \sqrt{\lambda_k}b_k(x)\xi_k(\theta) \]

where $D$ is a $d$-dimensional hyper-rectangle, for the case when the covariance function of $a$ is exponential:

\[ \mbox{cov}(x,x') = \sigma\exp(-|x_1-x_1'|/L_1-...-|x_d-x_d'|/L_d). \]

In this case, the covariance function and domain factor into a product 1-dimensional covariance functions over 1-dimensional domains, and thus the eigenfunctions $b_k$ and eigenvalues $\lambda_k$ factor into a product of corresponding 1-dimensional eigenfunctions and values. These are computed by the OneDExponentialCovarianceFunction class For a given value of $M$, the code works by computing the $M$ eigenfunctions for each direction using this class. Then all possible tensor products of these one-dimensional eigenfunctions are formed, with corresponding eigenvalue given by the product of the one-dimensional eigenvalues. These eigenvalues are then sorted in increasing order, and the first $M$ are chosen as the $M$ KL eigenpairs. Then given values for the random variables $\xi_k$, the class provides a routine for evaluating a realization of the random field.

The idea for this approach was provided by Chris Miller.

All data is passed into this class through a Teuchos::ParameterList, which accepts the following parameters:

Additionally parameters for the OneDExponentialCovarianceFunction are also accepted.

The documentation for this class was generated from the following files:
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