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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 Member Functions | |
template<class Func > | |
value_type | newton (const Func &func, const value_type &a, const value_type &b, magnitude_type tol, int max_num_its) |
A basic root finder based on Newton's method. | |
template<class Func > | |
value_type | bisection (const Func &func, const value_type &a, const value_type &b, magnitude_type tol, int max_num_its) |
A basic root finder based on bisection. | |
Protected Attributes | |
value_type | L |
Correlation length. | |
Teuchos::Array< eigen_pair_type > | eig_pair |
Eigenpairs. | |
Private Member Functions | |
OneDExponentialCovarianceFunction (const OneDExponentialCovarianceFunction &) | |
Prohibit copying. | |
OneDExponentialCovarianceFunction & | operator= (const OneDExponentialCovarianceFunction &) |
Prohibit copying. | |
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:
Definition at line 119 of file Stokhos_KL_OneDExponentialCovarianceFunction.hpp.
typedef ExponentialOneDEigenFunction<value_type> Stokhos::KL::OneDExponentialCovarianceFunction< value_type >::eigen_function_type |
Definition at line 122 of file Stokhos_KL_OneDExponentialCovarianceFunction.hpp.
typedef OneDEigenPair<eigen_function_type> Stokhos::KL::OneDExponentialCovarianceFunction< value_type >::eigen_pair_type |
Definition at line 123 of file Stokhos_KL_OneDExponentialCovarianceFunction.hpp.
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protected |
Definition at line 157 of file Stokhos_KL_OneDExponentialCovarianceFunction.hpp.
Stokhos::KL::OneDExponentialCovarianceFunction< value_type >::OneDExponentialCovarianceFunction | ( | int | M, |
const value_type & | a, | ||
const value_type & | b, | ||
const value_type & | L, | ||
const int | dim_name, | ||
Teuchos::ParameterList & | solverParams | ||
) |
Constructor.
Definition at line 45 of file Stokhos_KL_OneDExponentialCovarianceFunctionImp.hpp.
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inline |
Destructor.
Definition at line 134 of file Stokhos_KL_OneDExponentialCovarianceFunction.hpp.
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private |
Prohibit copying.
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inline |
Evaluate covariance.
Definition at line 137 of file Stokhos_KL_OneDExponentialCovarianceFunction.hpp.
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inline |
Get eigenpairs.
Definition at line 143 of file Stokhos_KL_OneDExponentialCovarianceFunction.hpp.
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private |
Prohibit copying.
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protected |
A basic root finder based on Newton's method.
Definition at line 99 of file Stokhos_KL_OneDExponentialCovarianceFunctionImp.hpp.
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protected |
A basic root finder based on bisection.
Definition at line 123 of file Stokhos_KL_OneDExponentialCovarianceFunctionImp.hpp.
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protected |
Correlation length.
Definition at line 160 of file Stokhos_KL_OneDExponentialCovarianceFunction.hpp.
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protected |
Eigenpairs.
Definition at line 163 of file Stokhos_KL_OneDExponentialCovarianceFunction.hpp.