symmTensor.H

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    Copyright (C) 2011-2012 OpenFOAM Foundation
    Copyright (C) 2019-2022 OpenCFD Ltd.
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License
    This file is part of OpenFOAM.
 
    OpenFOAM is free software: you can redistribute it and/or modify it
    under the terms of the GNU General Public License as published by
    the Free Software Foundation, either version 3 of the License, or
    (at your option) any later version.
 
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    You should have received a copy of the GNU General Public License
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Typedef
    Foam::symmTensor
 
Description
    SymmTensor of scalars, i.e. SymmTensor<scalar>.
 
    Analytical functions for the computation of real eigenvalues and
    real eigenvectors from a given symmTensor.
 
See also
    Test-SymmTensor.C
 
SourceFiles
    symmTensor.cxx
 
\*---------------------------------------------------------------------------*/
 
#ifndef Foam_symmTensor_H
#define Foam_symmTensor_H
 
#include "SymmTensor.H"
#include "vector.H"
#include "sphericalTensor.H"
#include "tensor.H"
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
namespace Foam
{
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
typedef SymmTensor<scalar> symmTensor;
 
typedef Tensor<scalar> tensor;
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
//- Return real ascending-order eigenvalues of a given symmTensor
//  \param T symmTensor
//
//  \return vector real eigenvalues
vector eigenValues(const symmTensor& T);
 
 
//- Return a real eigenvector corresponding to
//- a given real eigenvalue of a given symmTensor
//  \param T symmTensor
//  \param eVal real eigenvalue
//  \param standardBasis1 symmTensor orthogonal component 1
//  \param standardBasis2 symmTensor orthogonal component 2
//
//  \return vector real eigenvector
vector eigenVector
(
    const symmTensor& T,
    const scalar eVal,
    const vector& standardBasis1,
    const vector& standardBasis2
);
 
 
//- Return real eigenvectors corresponding to
//- given real eigenvalues of a given symmTensor
//  \param T symmTensor
//  \param eVals real eigenvalues
//
//  \return tensor real eigenvectors, each row is an eigenvector
tensor eigenVectors
(
    const symmTensor& T,
    const vector& eVals
);
 
 
//- Return real eigenvectors of a given symmTensor by computing
//- the real eigenvalues of the tensor in the background
//  \param T symmTensor
//
//  \return tensor real eigenvectors, each row is an eigenvector
tensor eigenVectors(const symmTensor& T);
 
 
//- Return inverse of a given symmTensor, and fall back
//- to pseudo-inverse if the symmTensor is singular
//  \param st symmTensor
//
//  \return symmTensor inverse of symmTensor
symmTensor pinv(const symmTensor& st);
 
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
} // End namespace Foam
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
#endif
 
// ************************************************************************* //