Stokhos Development
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Class representing an exponential covariance function and its KL eigevalues/eigenfunctions. More...
#include <Stokhos_KL_OneDExponentialCovarianceFunction.hpp>
Classes | |
struct | EigFuncCos |
Nonlinear function whose roots define eigenvalues for cos() eigenfunction. More... | |
struct | EigFuncSin |
Nonlinear function whose roots define eigenvalues for sin() eigenfunction. More... | |
Public Types | |
typedef ExponentialOneDEigenFunction< value_type > | eigen_function_type |
typedef OneDEigenPair< eigen_function_type > | eigen_pair_type |
Public Member Functions | |
OneDExponentialCovarianceFunction (int M, const value_type &a, const value_type &b, const value_type &L, const int dim_name, Teuchos::ParameterList &solverParams) | |
Constructor. | |
~OneDExponentialCovarianceFunction () | |
Destructor. | |
value_type | evaluateCovariance (const value_type &x, const value_type &xp) const |
Evaluate covariance. | |
const Teuchos::Array< eigen_pair_type > & | getEigenPairs () const |
Get eigenpairs. | |
Protected Types | |
typedef Teuchos::ScalarTraits< value_type >::magnitudeType | magnitude_type |
Protected Attributes | |
value_type | L |
Correlation length. | |
Teuchos::Array< eigen_pair_type > | eig_pair |
Eigenpairs. | |
Class representing an exponential covariance function and its KL eigevalues/eigenfunctions.
This class provides the exponential covariance function
The corresponding eigenfunctions can be shown to be
and
respectively, where
and the corresponding eigenvalues are given by
and
It is straightforward to show that for each
For a given value of
Data for the root solver is passed through a Teuchos::ParameterList, which accepts the following parameters: