SVD.H

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License
    This file is part of OpenFOAM.
 
    OpenFOAM is free software: you can redistribute it and/or modify it
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Class
    Foam::SVD
 
Description
    Singular value decomposition of a rectangular matrix.
 
SourceFiles
    SVD.C
 
\*---------------------------------------------------------------------------*/
 
#ifndef Foam_SVD_H
#define Foam_SVD_H
 
#include "scalarMatrices.H"
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
namespace Foam
{
 
// Forward Declarations
template<class Cmpt> class Tensor;
 
/*---------------------------------------------------------------------------*\
                      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_;
 
 
public:
 
    // Generated Methods
 
        //- No copy construct
        SVD(const SVD&) = delete;
 
        //- No copy assignment
        void operator=(const SVD&) = delete;
 
 
    // Constructors
 
        //- Construct from a rectangular Matrix
        explicit SVD
        (
            const scalarRectangularMatrix& A,
            const scalar minCondition = 0
        );
 
 
    // Access Functions
 
        //- Return U
        const scalarRectangularMatrix& U() const noexcept { return U_; }
 
        //- Return the square matrix V
        const scalarRectangularMatrix& V() const noexcept { return V_; }
 
        //- Return the singular values
        const scalarDiagonalMatrix& S() const noexcept { return S_; }
 
        //- Return the minimum non-zero singular value
        bool converged() const noexcept { return converged_; }
 
        //- Return the number of zero singular values
        label nZeros() const noexcept { return nZeros_; }
 
        //- Return the minimum non-zero singular value
        scalar minNonZeroS() const;
 
 
    // Member Functions
 
        //- Return the matrix product V S^(-1) U^T (the pseudo inverse)
        scalarRectangularMatrix VSinvUt() const;
 
 
    // Static Member Functions
 
        //- Return the pseudo inverse of the given matrix
        static scalarRectangularMatrix pinv
        (
            const scalarRectangularMatrix& A,
            const scalar minCondition = 0
        );
 
        //- Return the pseudo inverse of the given tensor
        static Tensor<scalar> pinv
        (
            const Tensor<scalar>& A,
            const scalar minCondition = 0
        );
};
 
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
} // End namespace Foam
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
#endif
 
// ************************************************************************* //