tensor.H

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/*---------------------------------------------------------------------------*\
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-------------------------------------------------------------------------------
    Copyright (C) 2011-2014 OpenFOAM Foundation
    Copyright (C) 2019-2022 OpenCFD Ltd.
-------------------------------------------------------------------------------
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.
 
    OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
    FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
    for more details.
 
    You should have received a copy of the GNU General Public License
    along with OpenFOAM.  If not, see <http://www.gnu.org/licenses/>.
 
Class
    Foam::tensor
 
Description
    Tensor of scalars, i.e. Tensor<scalar>.
 
    Analytical functions for the computation of complex eigenvalues and
    complex eigenvectors from a given tensor.
 
See also
    Test-Tensor.C
 
SourceFiles
    floatTensors.cxx
    tensor.cxx
 
\*---------------------------------------------------------------------------*/
 
#ifndef Foam_tensor_H
#define Foam_tensor_H
 
#include "Tensor.H"
#include "vector.H"
#include "sphericalTensor.H"
#include "symmTensor.H"
#include "complex.H"
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
namespace Foam
{
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

typedef Tensor<float> floatTensor;

typedef Tensor<double> doubleTensor;
 
// With float or double precision (depending on compilation)
typedef Tensor<scalar> tensor;
 
 
// * * * * * * * * * * * * * * * Global Functions  * * * * * * * * * * * * * //
 
//- Return complex eigenvalues of a given tensor
//  \param T tensor
//
//  \return Vector<complex> eigenvalues
Vector<complex> eigenValues(const tensor& T);
 
 
//- Return a complex eigenvector corresponding to
//- a given complex eigenvalue of a given tensor
//  \param T tensor
//  \param eVal complex eigenvalue
//  \param standardBasis1 tensor orthogonal component 1
//  \param standardBasis2 tensor orthogonal component 2
//
//  \return Vector<complex> eigenvector
Vector<complex> eigenVector
(
    const tensor& T,
    const complex& eVal,
    const Vector<complex>& standardBasis1,
    const Vector<complex>& standardBasis2
);
 
 
//- Return complex eigenvectors corresponding to
//- given complex eigenvalues of a given tensor
//  \param T tensor
//  \param eVals complex eigenvalues
//
//  \return Tensor<complex> eigenvectors, each row is an eigenvector
Tensor<complex> eigenVectors
(
    const tensor& T,
    const Vector<complex>& eVals
);
 
 
//- Return complex eigenvectors of a given tensor by computing
//- the complex eigenvalues of the tensor in the background
//  \param T tensor
//
//  \return Tensor<complex> complex eigenvectors, each row is an eigenvector
Tensor<complex> eigenVectors(const tensor& T);
 
 
//- Return inverse of a given tensor, and fall back
//- into pseudo-inverse if the tensor is singular
//  \param t tensor
//
//  \return tensor inverse of tensor
tensor pinv(const tensor& t);
 
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
} // End namespace Foam
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
#endif
 
// ************************************************************************* //