SVD.H

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/*---------------------------------------------------------------------------*\
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  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     |
    \\  /    A nd           | Copyright (C) 2011-2015 OpenFOAM Foundation
     \\/     M anipulation  |
-------------------------------------------------------------------------------
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::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_;
 
        //- The matrix product V S^(-1) U^T
        scalarRectangularMatrix VSinvUt_;
 
        //- The number of zero singular values
        label nZeros_;
 
 
    // Private Member Functions
 
        //- Disallow default bitwise copy construct
        SVD(const SVD&);
 
        //- Disallow default bitwise assignment
        void operator=(const SVD&);
 
        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);
 
 
    // 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 VSinvUt (the pseudo inverse)
        inline const scalarRectangularMatrix& VSinvUt() const;
 
        //- Return the number of zero singular values
        inline label nZeros() const;
 
        //- Return the minimum non-zero singular value
        inline scalar minNonZeroS() const;
};
 
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
} // End namespace Foam
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
#include "SVDI.H"
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
#endif
 
// ************************************************************************* //