LLTMatrix.C

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/*---------------------------------------------------------------------------*\
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    Copyright (C) 2016 OpenFOAM Foundation
    Copyright (C) 2019 OpenCFD Ltd.
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License
    This file is part of OpenFOAM.

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#include "LLTMatrix.H"

// * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //

template<class Type>
Foam::LLTMatrix<Type>::LLTMatrix(const SquareMatrix<Type>& mat)
{
    decompose(mat);
}


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

template<class Type>
void Foam::LLTMatrix<Type>::decompose(const SquareMatrix<Type>& mat)
{
    SquareMatrix<Type>& LLT = *this;

    // Initialize the LLT decomposition matrix to M
    LLT = mat;

    const label m = LLT.m();

    for (label i = 0; i < m; ++i)
    {
        for (label j = 0; j < m; ++j)
        {
            if (j > i)
            {
                LLT(i, j) = Zero;
                continue;
            }

            Type sum = LLT(i, j);

            for (label k = 0; k < j; ++k)
            {
                sum -= LLT(i, k)*LLT(j, k);
            }

            if (i > j)
            {
                LLT(i, j) = sum/LLT(j, j);
            }
            else if (sum > 0)
            {
                LLT(i, i) = sqrt(sum);
            }
            else
            {
                FatalErrorInFunction
                    << "Cholesky decomposition failed, "
                       "matrix is not symmetric positive definite"
                    << abort(FatalError);
            }
        }
    }
}


template<class Type>
template<template<typename> class ListContainer>
void Foam::LLTMatrix<Type>::solveImpl
(
    List<Type>& x,
    const ListContainer<Type>& source
) const
{
    // If x and source are different, copy initialize x = source
    if (&x != &source)
    {
        x = source;
    }

    const SquareMatrix<Type>& LLT = *this;
    const label m = LLT.m();

    for (label i = 0; i < m; ++i)
    {
        Type sum = source[i];

        for (label j = 0; j < i; ++j)
        {
            sum = sum - LLT(i, j)*x[j];
        }

        x[i] = sum/LLT(i, i);
    }

    for (label i = m - 1; i >= 0; --i)
    {
        Type sum = x[i];

        for (label j = i + 1; j < m; ++j)
        {
            sum = sum - LLT(j, i)*x[j];
        }

        x[i] = sum/LLT(i, i);
    }
}


template<class Type>
void Foam::LLTMatrix<Type>::solve
(
    List<Type>& x,
    const UList<Type>& source
) const
{
    solveImpl(x, source);
}


template<class Type>
template<class Addr>
void Foam::LLTMatrix<Type>::solve
(
    List<Type>& x,
    const IndirectListBase<Type, Addr>& source
) const
{
    solveImpl(x, source);
}

template<class Type>
Foam::tmp<Foam::Field<Type>> Foam::LLTMatrix<Type>::solve
(
    const UList<Type>& source
) const
{
    auto tresult(tmp<Field<Type>>::New(source.size()));

    solve(tresult.ref(), source);

    return tresult;
}


template<class Type>
template<class Addr>
Foam::tmp<Foam::Field<Type>> Foam::LLTMatrix<Type>::solve
(
    const IndirectListBase<Type, Addr>& source
) const
{
    auto tresult(tmp<Field<Type>>::New(source.size()));

    solve(tresult.ref(), source);

    return tresult;
}


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