symmTensor2D.H

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License
    This file is part of OpenFOAM.
 
    OpenFOAM is free software: you can redistribute it and/or modify it
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Typedef
    Foam::symmTensor2D
 
Description
    SymmTensor2D of scalars, i.e. SymmTensor2D<scalar>.
 
    Analytical functions for the computation of real eigenvalues
    and real eigenvectors from a given symmTensor2D.
 
    Reference:
    \verbatim
        2-by-2 eigenvalue algorithm (tag:K):
            Kronenburg, M. J. (2015).
            A method for fast diagonalization of
            a 2x2 or 3x3 real symmetric matrix.
            arXiv:1306.6291.
    \endverbatim
 
See also
    Test-SymmTensor2D.C
 
SourceFiles
    symmTensor2D.C
 
\*---------------------------------------------------------------------------*/
 
#ifndef symmTensor2D_H
#define symmTensor2D_H
 
#include "SymmTensor2D.H"
#include "vector2D.H"
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
namespace Foam
{
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
typedef SymmTensor2D<scalar> symmTensor2D;
 
typedef Tensor2D<scalar> tensor2D;
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
//- Return real arbitrary-order eigenvalues of a given symmTensor2D
//  \param T symmTensor2D
//
//  \return vector2D real eigenvalues
vector2D eigenValues(const symmTensor2D& T);
 
 
//- Return a real eigenvector corresponding to
//- a given real eigenvalue of a given symmTensor2D
//  \param T symmTensor2D
//  \param eVal real eigenvalue
//  \param standardBasis symmTensor2D orthogonal component, e.g. vector2D(1, 0)
//
//  \return vector2D real eigenvector
vector2D eigenVector
(
    const symmTensor2D& T,
    const scalar eVal,
    const vector2D& standardBasis
);
 
 
//- Return real eigenvectors corresponding to
//- given real eigenvalues of a given symmTensor2D
//  \param T symmTensor2D
//  \param eVals real eigenvalues
//
//  \return tensor2D real eigenvectors, each row is an eigenvector
tensor2D eigenVectors(const symmTensor2D& T, const vector2D& eVals);
 
 
//- Return real eigenvectors of a given symmTensor2D by computing
//- the real eigenvalues of the symmTensor2D in the background
//  \param T symmTensor2D
//
//  \return tensor2D real eigenvectors, each row is an eigenvector
tensor2D eigenVectors(const symmTensor2D& T);
 
 
} // End namespace Foam
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
#endif
 
// ************************************************************************* //