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/*---------------------------------------------------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     | Website:  https://openfoam.org
    \\  /    A nd           | Copyright (C) 2011-2026 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/>.
\*---------------------------------------------------------------------------*/

#include "scalarMatrices.H"
#include "SVD.H"

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

namespace Foam
{

defineCompoundTypeName(RectangularMatrix<scalar>, scalarRectangularMatrix);
addCompoundToRunTimeSelectionTable
(
    RectangularMatrix<scalar>,
    scalarRectangularMatrix
);

defineCompoundTypeName(SquareMatrix<scalar>, scalarSquareMatrix);
addCompoundToRunTimeSelectionTable(SquareMatrix<scalar>, scalarSquareMatrix);

defineCompoundTypeName
(
    SymmetricSquareMatrix<scalar>,
    scalarSymmetricSquareMatrix
);
addCompoundToRunTimeSelectionTable
(
    SymmetricSquareMatrix<scalar>,
    scalarSymmetricSquareMatrix
);

defineCompoundTypeName(DiagonalMatrix<scalar>, scalarDiagonalMatrix);
addCompoundToRunTimeSelectionTable
(
    DiagonalMatrix<scalar>,
    scalarDiagonalMatrix
);

}

// * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //

void Foam::LUDecompose
(
    scalarSquareMatrix& A,
    labelList& pivotIndices
)
{
    label sign;
    LUDecompose(A, pivotIndices, sign);
}


void Foam::LUDecompose
(
    scalarSquareMatrix& A,
    labelList& pivotIndices,
    label& sign
)
{
    const label m = A.m();
    scalarList vv(m);
    sign = 1;

    for (label i=0; i<m; i++)
    {
        scalar largestCoeff = 0;
        scalar temp;
        const scalar* __restrict__ Ai = A[i];

        for (label j=0; j<m; j++)
        {
            if ((temp = mag(Ai[j])) > largestCoeff)
            {
                largestCoeff = temp;
            }
        }

        if (largestCoeff == 0)
        {
            FatalErrorInFunction
                << "Singular A" << exit(FatalError);
        }

        vv[i] = 1.0/largestCoeff;
    }

    for (label j=0; j<m; j++)
    {
        scalar* __restrict__ Aj = A[j];

        for (label i=0; i<j; i++)
        {
            scalar* __restrict__ Ai = A[i];

            scalar sum = Ai[j];
            for (label k=0; k<i; k++)
            {
                sum -= Ai[k]*A(k, j);
            }
            Ai[j] = sum;
        }

        label iMax = 0;

        scalar largestCoeff = 0;
        for (label i=j; i<m; i++)
        {
            scalar* __restrict__ Ai = A[i];
            scalar sum = Ai[j];

            for (label k=0; k<j; k++)
            {
                sum -= Ai[k]*A(k, j);
            }

            Ai[j] = sum;

            scalar temp;
            if ((temp = vv[i]*mag(sum)) >= largestCoeff)
            {
                largestCoeff = temp;
                iMax = i;
            }
        }

        pivotIndices[j] = iMax;

        if (j != iMax)
        {
            scalar* __restrict__ AiMax = A[iMax];

            for (label k=0; k<m; k++)
            {
                Swap(Aj[k], AiMax[k]);
            }

            sign *= -1;
            vv[iMax] = vv[j];
        }

        if (Aj[j] == 0)
        {
            Aj[j] = small;
        }

        if (j != m-1)
        {
            const scalar rDiag = 1.0/Aj[j];

            for (label i=j+1; i<m; i++)
            {
                A(i, j) *= rDiag;
            }
        }
    }
}


void Foam::LUDecompose(scalarSquareMatrix& A, const scalar rowTol)
{
    const label m = A.m();

    for (label i=0; i<m; i++)
    {
        for (label k=0; k<i; k++)
        {
            // Compute the row multiplier for the lower triangular matrix L
            A(i, k) /= A(k, k);

            // If the row multiplier is 0 skip the inner j loop
            if (mag(A(i, k)) < rowTol)
            {
                A(i, k) = 0;
                continue;
            }

            // Update the remaining elements of the row
            for (label j=k+1; j<m; j++)
            {
                A(i, j) -= A(i, k)*A(k, j);
            }
        }
    }
}


void Foam::LUDecompose(scalarSymmetricSquareMatrix& A)
{
    // Store result in upper triangular part of matrix
    const label m = A.m();

    // Set upper triangular parts to zero.
    for (label j=0; j<m; j++)
    {
        for (label k=j + 1; k<m; k++)
        {
            A(j, k) = 0;
        }
    }

    for (label j=0; j<m; j++)
    {
        scalar d = 0;

        for (label k=0; k<j; k++)
        {
            scalar s = 0;

            for (label i=0; i<k; i++)
            {
                s += A(i, k)*A(i, j);
            }

            s = (A(j, k) - s)/A(k, k);

            A(k, j) = s;
            A(j, k) = s;

            d += sqr(s);
        }

        d = A(j, j) - d;

        if (d < 0)
        {
            FatalErrorInFunction
                << "Matrix is not symmetric positive-definite. Unable to "
                << "decompose."
                << abort(FatalError);
        }

        A(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(), scalar(0));

    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(), scalar(0));

    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];
            }
        }
    }
}


Foam::scalarRectangularMatrix Foam::SVDinv
(
    const scalarRectangularMatrix& A,
    scalar minCondition
)
{
    SVD svd(A, minCondition);
    return svd.VSinvUt();
}


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

	/---------------------------------------------------------------------------\
	========= \|
	\\ / F ield \| OpenFOAM: The Open Source CFD Toolbox
	\\ / O peration \| Website: https://openfoam.org
	\\ / A nd \| Copyright (C) 2011-2026 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/>.

	\---------------------------------------------------------------------------/

	#include "scalarMatrices.H"
	#include "SVD.H"

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

	namespace Foam
	{

	defineCompoundTypeName(RectangularMatrix<scalar>, scalarRectangularMatrix);
	addCompoundToRunTimeSelectionTable
	(
	RectangularMatrix<scalar>,
	scalarRectangularMatrix
	);

	defineCompoundTypeName(SquareMatrix<scalar>, scalarSquareMatrix);
	addCompoundToRunTimeSelectionTable(SquareMatrix<scalar>, scalarSquareMatrix);

	defineCompoundTypeName
	(
	SymmetricSquareMatrix<scalar>,
	scalarSymmetricSquareMatrix
	);
	addCompoundToRunTimeSelectionTable
	(
	SymmetricSquareMatrix<scalar>,
	scalarSymmetricSquareMatrix
	);

	defineCompoundTypeName(DiagonalMatrix<scalar>, scalarDiagonalMatrix);
	addCompoundToRunTimeSelectionTable
	(
	DiagonalMatrix<scalar>,
	scalarDiagonalMatrix
	);

	}

	// * * * * * * * * * * * * * * * Member Functions * * * * * * * * * * * * * //

	void Foam::LUDecompose
	(
	scalarSquareMatrix& A,
	labelList& pivotIndices
	)
	{
	label sign;
	LUDecompose(A, pivotIndices, sign);
	}


	void Foam::LUDecompose
	(
	scalarSquareMatrix& A,
	labelList& pivotIndices,
	label& sign
	)
	{
	const label m = A.m();
	scalarList vv(m);
	sign = 1;

	for (label i=0; i<m; i++)
	{
	scalar largestCoeff = 0;
	scalar temp;
	const scalar* __restrict__ Ai = A[i];

	for (label j=0; j<m; j++)
	{
	if ((temp = mag(Ai[j])) > largestCoeff)
	{
	largestCoeff = temp;
	}
	}

	if (largestCoeff == 0)
	{
	FatalErrorInFunction
	<< "Singular A" << exit(FatalError);
	}

	vv[i] = 1.0/largestCoeff;
	}

	for (label j=0; j<m; j++)
	{
	scalar* __restrict__ Aj = A[j];

	for (label i=0; i<j; i++)
	{
	scalar* __restrict__ Ai = A[i];

	scalar sum = Ai[j];
	for (label k=0; k<i; k++)
	{
	sum -= Ai[k]*A(k, j);
	}
	Ai[j] = sum;
	}

	label iMax = 0;

	scalar largestCoeff = 0;
	for (label i=j; i<m; i++)
	{
	scalar* __restrict__ Ai = A[i];
	scalar sum = Ai[j];

	for (label k=0; k<j; k++)
	{
	sum -= Ai[k]*A(k, j);
	}

	Ai[j] = sum;

	scalar temp;
	if ((temp = vv[i]*mag(sum)) >= largestCoeff)
	{
	largestCoeff = temp;
	iMax = i;
	}
	}

	pivotIndices[j] = iMax;

	if (j != iMax)
	{
	scalar* __restrict__ AiMax = A[iMax];

	for (label k=0; k<m; k++)
	{
	Swap(Aj[k], AiMax[k]);
	}

	sign *= -1;
	vv[iMax] = vv[j];
	}

	if (Aj[j] == 0)
	{
	Aj[j] = small;
	}

	if (j != m-1)
	{
	const scalar rDiag = 1.0/Aj[j];

	for (label i=j+1; i<m; i++)
	{
	A(i, j) *= rDiag;
	}
	}
	}
	}


	void Foam::LUDecompose(scalarSquareMatrix& A, const scalar rowTol)
	{
	const label m = A.m();

	for (label i=0; i<m; i++)
	{
	for (label k=0; k<i; k++)
	{
	// Compute the row multiplier for the lower triangular matrix L
	A(i, k) /= A(k, k);

	// If the row multiplier is 0 skip the inner j loop
	if (mag(A(i, k)) < rowTol)
	{
	A(i, k) = 0;
	continue;
	}

	// Update the remaining elements of the row
	for (label j=k+1; j<m; j++)
	{
	A(i, j) -= A(i, k)*A(k, j);
	}
	}
	}
	}


	void Foam::LUDecompose(scalarSymmetricSquareMatrix& A)
	{
	// Store result in upper triangular part of matrix
	const label m = A.m();

	// Set upper triangular parts to zero.
	for (label j=0; j<m; j++)
	{
	for (label k=j + 1; k<m; k++)
	{
	A(j, k) = 0;
	}
	}

	for (label j=0; j<m; j++)
	{
	scalar d = 0;

	for (label k=0; k<j; k++)
	{
	scalar s = 0;

	for (label i=0; i<k; i++)
	{
	s += A(i, k)*A(i, j);
	}

	s = (A(j, k) - s)/A(k, k);

	A(k, j) = s;
	A(j, k) = s;

	d += sqr(s);
	}

	d = A(j, j) - d;

	if (d < 0)
	{
	FatalErrorInFunction
	<< "Matrix is not symmetric positive-definite. Unable to "
	<< "decompose."
	<< abort(FatalError);
	}

	A(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(), scalar(0));

	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(), scalar(0));

	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];
	}
	}
	}
	}


	Foam::scalarRectangularMatrix Foam::SVDinv
	(
	const scalarRectangularMatrix& A,
	scalar minCondition
	)
	{
	SVD svd(A, minCondition);
	return svd.VSinvUt();
	}


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