tensor.H

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    Copyright (C) 2011-2014 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
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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.C
    tensor.C

\*---------------------------------------------------------------------------*/

#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

// ************************************************************************* //