symmTensor.H

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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.C

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

#ifndef symmTensor_H
#define 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

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