SVD.H

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License
    This file is part of OpenFOAM.

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    the Free Software Foundation, either version 3 of the License, or
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Class
    Foam::SVD

Description
    Singular value decomposition of a rectangular matrix.

SourceFiles
    SVDI.H
    SVD.C

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

#ifndef SVD_H
#define SVD_H

#include "scalarMatrices.H"

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

namespace Foam
{

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

/*---------------------------------------------------------------------------*\
                             Class SVD Declaration
\*---------------------------------------------------------------------------*/

class SVD
{
    // Private Data

        //- Rectangular matrix with the same dimensions as the input
        scalarRectangularMatrix U_;

        //- Square matrix V
        scalarRectangularMatrix V_;

        //- The singular values
        DiagonalMatrix<scalar> S_;

        //- Convergence flag
        bool converged_;

        //- The number of zero singular values
        label nZeros_;


    // Private Member Functions

        template<class T>
        inline const T sign(const T& a, const T& b);


public:

    // Constructors

        //- Construct from a rectangular Matrix
        SVD(const scalarRectangularMatrix& A, const scalar minCondition = 0);

        //- Disallow default bitwise copy construction
        SVD(const SVD&) = delete;


    // Access functions

        //- Return U
        inline const scalarRectangularMatrix& U() const;

        //- Return the square matrix V
        inline const scalarRectangularMatrix& V() const;

        //- Return the singular values
        inline const scalarDiagonalMatrix& S() const;

        //- Return the minimum non-zero singular value
        inline bool converged() const;

        //- Return the number of zero singular values
        inline label nZeros() const;

        //- Return the minimum non-zero singular value
        inline scalar minNonZeroS() const;

        //- Return the matrix product V S^(-1) U^T (the pseudo inverse)
        scalarRectangularMatrix VSinvUt() const;


    // Member Operators

        //- Disallow default bitwise assignment
        void operator=(const SVD&) = delete;
};


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

} // End namespace Foam

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

#include "SVDI.H"

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

#endif

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