scalarMatrices.C

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/*---------------------------------------------------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     |
    \\  /    A nd           | www.openfoam.com
     \\/     M anipulation  |
-------------------------------------------------------------------------------
    Copyright (C) 2011-2016 OpenFOAM Foundation
-------------------------------------------------------------------------------
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/>.
 
\*---------------------------------------------------------------------------*/
 
#include "scalarMatrices.H"
#include "SVD.H"
 
// * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
 
void Foam::LUDecompose
(
    scalarSquareMatrix& matrix,
    labelList& pivotIndices
)
{
    label sign;
    LUDecompose(matrix, pivotIndices, sign);
}
 
 
void Foam::LUDecompose
(
    scalarSquareMatrix& matrix,
    labelList& pivotIndices,
    label& sign
)
{
    label m = matrix.m();
    scalar vv[m];
    sign = 1;
 
    for (label i = 0; i < m; ++i)
    {
        scalar largestCoeff = 0.0;
        scalar temp;
        const scalar* __restrict__ matrixi = matrix[i];
 
        for (label j = 0; j < m; ++j)
        {
            if ((temp = mag(matrixi[j])) > largestCoeff)
            {
                largestCoeff = temp;
            }
        }
 
        if (largestCoeff == 0.0)
        {
            FatalErrorInFunction
                << "Singular matrix" << exit(FatalError);
        }
 
        vv[i] = 1.0/largestCoeff;
    }
 
    for (label j = 0; j < m; ++j)
    {
        scalar* __restrict__ matrixj = matrix[j];
 
        for (label i = 0; i < j; ++i)
        {
            scalar* __restrict__ matrixi = matrix[i];
 
            scalar sum = matrixi[j];
            for (label k = 0; k < i; ++k)
            {
                sum -= matrixi[k]*matrix(k, j);
            }
            matrixi[j] = sum;
        }
 
        label iMax = 0;
 
        scalar largestCoeff = 0.0;
        for (label i = j; i < m; ++i)
        {
            scalar* __restrict__ matrixi = matrix[i];
            scalar sum = matrixi[j];
 
            for (label k = 0; k < j; ++k)
            {
                sum -= matrixi[k]*matrix(k, j);
            }
 
            matrixi[j] = sum;
 
            scalar temp;
            if ((temp = vv[i]*mag(sum)) >= largestCoeff)
            {
                largestCoeff = temp;
                iMax = i;
            }
        }
 
        pivotIndices[j] = iMax;
 
        if (j != iMax)
        {
            scalar* __restrict__ matrixiMax = matrix[iMax];
 
            for (label k = 0; k < m; ++k)
            {
                Swap(matrixj[k], matrixiMax[k]);
            }
 
            sign *= -1;
            vv[iMax] = vv[j];
        }
 
        if (matrixj[j] == 0.0)
        {
            matrixj[j] = SMALL;
        }
 
        if (j != m-1)
        {
            scalar rDiag = 1.0/matrixj[j];
 
            for (label i = j + 1; i < m; ++i)
            {
                matrix(i, j) *= rDiag;
            }
        }
    }
}
 
 
void Foam::LUDecompose(scalarSymmetricSquareMatrix& matrix)
{
    // Store result in upper triangular part of matrix
    label size = matrix.m();
 
    // Set upper triangular parts to zero.
    for (label j = 0; j < size; ++j)
    {
        for (label k = j + 1; k < size; ++k)
        {
            matrix(j, k) = 0.0;
        }
    }
 
    for (label j = 0; j < size; ++j)
    {
        scalar d = 0.0;
 
        for (label k = 0; k < j; ++k)
        {
            scalar s = 0.0;
 
            for (label i = 0; i < k; ++i)
            {
                s += matrix(i, k)*matrix(i, j);
            }
 
            s = (matrix(j, k) - s)/matrix(k, k);
 
            matrix(k, j) = s;
            matrix(j, k) = s;
 
            d += sqr(s);
        }
 
        d = matrix(j, j) - d;
 
        if (d < 0.0)
        {
            FatalErrorInFunction
                << "Matrix is not symmetric positive-definite. Unable to "
                << "decompose."
                << abort(FatalError);
        }
 
        matrix(j, j) = sqrt(d);
    }
}
 
 
// * * * * * * * * * * * * * * * Global Functions  * * * * * * * * * * * * * //
 
void Foam::multiply
(
    scalarRectangularMatrix& ans,         // value changed in return
    const scalarRectangularMatrix& A,
    const scalarRectangularMatrix& B,
    const scalarRectangularMatrix& C
)
{
    if (A.n() != B.m())
    {
        FatalErrorInFunction
            << "A and B must have identical inner dimensions but A.n = "
            << A.n() << " and B.m = " << B.m()
            << abort(FatalError);
    }
 
    if (B.n() != C.m())
    {
        FatalErrorInFunction
            << "B and C must have identical inner dimensions but B.n = "
            << B.n() << " and C.m = " << C.m()
            << abort(FatalError);
    }
 
    ans = scalarRectangularMatrix(A.m(), C.n(), Zero);
 
    for (label i = 0; i < A.m(); ++i)
    {
        for (label g = 0; g < C.n(); ++g)
        {
            for (label l = 0; l < C.m(); ++l)
            {
                scalar ab = 0;
                for (label j = 0; j < A.n(); ++j)
                {
                    ab += A(i, j)*B(j, l);
                }
                ans(i, g) += C(l, g) * ab;
            }
        }
    }
}
 
 
void Foam::multiply
(
    scalarRectangularMatrix& ans,         // value changed in return
    const scalarRectangularMatrix& A,
    const DiagonalMatrix<scalar>& B,
    const scalarRectangularMatrix& C
)
{
    if (A.n() != B.size())
    {
        FatalErrorInFunction
            << "A and B must have identical inner dimensions but A.n = "
            << A.n() << " and B.m = " << B.size()
            << abort(FatalError);
    }
 
    if (B.size() != C.m())
    {
        FatalErrorInFunction
            << "B and C must have identical inner dimensions but B.n = "
            << B.size() << " and C.m = " << C.m()
            << abort(FatalError);
    }
 
    ans = scalarRectangularMatrix(A.m(), C.n(), Zero);
 
    for (label i = 0; i < A.m(); ++i)
    {
        for (label g = 0; g < C.n(); ++g)
        {
            for (label l = 0; l < C.m(); ++l)
            {
                ans(i, g) += C(l, g) * A(i, l)*B[l];
            }
        }
    }
}
 
 
void Foam::multiply
(
    scalarSquareMatrix& ans,         // value changed in return
    const scalarSquareMatrix& A,
    const DiagonalMatrix<scalar>& B,
    const scalarSquareMatrix& C
)
{
    if (A.m() != B.size())
    {
        FatalErrorInFunction
            << "A and B must have identical dimensions but A.m = "
            << A.m() << " and B.m = " << B.size()
            << abort(FatalError);
    }
 
    if (B.size() != C.m())
    {
        FatalErrorInFunction
            << "B and C must have identical dimensions but B.m = "
            << B.size() << " and C.m = " << C.m()
            << abort(FatalError);
    }
 
    const label size = A.m();
 
    ans = scalarSquareMatrix(size, Zero);
 
    for (label i = 0; i < size; ++i)
    {
        for (label g = 0; g < size; ++g)
        {
            for (label l = 0; l < size; ++l)
            {
                ans(i, g) += C(l, g)*A(i, l)*B[l];
            }
        }
    }
}
 
 
//- Pseudo-inverse algorithm for scalar matrices, using Moore-Penrose inverse
Foam::scalarRectangularMatrix Foam::SVDinv
(
    const scalarRectangularMatrix& A,
    scalar minCondition
)
{
    SVD svd(A, minCondition);
    return svd.VSinvUt();
}
 
 
// ************************************************************************* //