SVD.H

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    Copyright (C) 2011-2016 OpenFOAM Foundation
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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
    (at your option) any later version.
 
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    You should have received a copy of the GNU General Public License
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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
 
        //- No copy construct
        SVD(const SVD&) = delete;
 
        //- No copy assignment
        void operator=(const SVD&) = delete;
 
        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 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;
};
 
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
} // End namespace Foam
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
#include "SVDI.H"
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
#endif
 
// ************************************************************************* //