matrix3DI.H

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/*---------------------------------------------------------------------------*\
  =========                 |
  \\      /  F ield         | cfMesh: A library for mesh generation
   \\    /   O peration     |
    \\  /    A nd           | Author: Franjo Juretic (franjo.juretic@c-fields.com)
     \\/     M anipulation  | Copyright (C) Creative Fields, Ltd.
-------------------------------------------------------------------------------
License
    This file is part of cfMesh.
 
    cfMesh 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.
 
    cfMesh 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 cfMesh.  If not, see <http://www.gnu.org/licenses/>.
 
Class
    matrix3D
 
Description
    Implementation od 3 x 3 matrix
 
\*---------------------------------------------------------------------------*/
 
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
namespace Foam
{
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
inline void matrix3D::calculateDeterminant()
{
    if( calculatedDet_ )
        return;
 
    const FixedList<FixedList<scalar, 3>, 3>& mat = *this;
 
    det_ =
        mat[0][0] * (mat[1][1] * mat[2][2] - mat[1][2] * mat[2][1]) -
        mat[0][1] * (mat[1][0] * mat[2][2] - mat[1][2] * mat[2][0]) +
        mat[0][2] * (mat[1][0] * mat[2][1] - mat[1][1] * mat[2][0]);
 
    calculatedDet_ = true;
}
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
inline matrix3D::matrix3D()
:
    det_(),
    calculatedDet_(false)
{}
 
inline matrix3D::matrix3D(const matrix3D& m)
:
    FixedList<FixedList<scalar, 3>, 3>(m),
    det_(m.det_),
    calculatedDet_(m.calculatedDet_)
{}
 
inline matrix3D::~matrix3D()
{}
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
inline scalar matrix3D::determinant()
{
    calculateDeterminant();
 
    return det_;
}
 
inline matrix3D matrix3D::inverse()
{
    calculateDeterminant();
 
    const FixedList<FixedList<scalar, 3>, 3>& mat = *this;
 
    matrix3D imat;
    imat[0][0] = (mat[1][1] * mat[2][2] - mat[1][2] * mat[2][1]) / det_;
    imat[0][1] = (mat[0][2] * mat[2][1] - mat[0][1] * mat[2][2]) / det_;
    imat[0][2] = (mat[0][1] * mat[1][2] - mat[0][2] * mat[1][1]) / det_;
    imat[1][0] = (mat[1][2] * mat[2][0] - mat[1][0] * mat[2][2]) / det_;
    imat[1][1] = (mat[0][0] * mat[2][2] - mat[0][2] * mat[2][0]) / det_;
    imat[1][2] = (mat[0][2] * mat[1][0] - mat[0][0] * mat[1][2]) / det_;
    imat[2][0] = (mat[1][0] * mat[2][1] - mat[1][1] * mat[2][0]) / det_;
    imat[2][1] = (mat[0][1] * mat[2][0] - mat[0][0] * mat[2][1]) / det_;
    imat[2][2] = (mat[0][0] * mat[1][1] - mat[0][1] * mat[1][0]) / det_;
 
    return imat;
}
 
inline FixedList<scalar, 3> matrix3D::solve
(
    const FixedList<scalar, 3>& source
)
{
    FixedList<scalar, 3> result;
    result[0] = solveFirst(source);
    result[1] = solveSecond(source);
    result[2] = solveThird(source);
 
    return result;
}
 
inline scalar matrix3D::solveFirst(const FixedList<scalar, 3>& source)
{
    calculateDeterminant();
 
    const FixedList<FixedList<scalar, 3>, 3>& mat = *this;
 
    return
    (
        (mat[1][1] * mat[2][2] - mat[1][2] * mat[2][1]) * source[0] +
        (mat[0][2] * mat[2][1] - mat[0][1] * mat[2][2]) * source[1] +
        (mat[0][1] * mat[1][2] - mat[0][2] * mat[1][1]) * source[2]
    ) / det_;
}
 
inline scalar matrix3D::solveSecond(const FixedList<scalar, 3>& source)
{
    calculateDeterminant();
 
    const FixedList<FixedList<scalar, 3>, 3>& mat = *this;
 
    return
    (
        (mat[1][2] * mat[2][0] - mat[1][0] * mat[2][2]) * source[0] +
        (mat[0][0] * mat[2][2] - mat[0][2] * mat[2][0]) * source[1] +
        (mat[0][2] * mat[1][0] - mat[0][0] * mat[1][2]) * source[2]
    ) / det_;
}
 
inline scalar matrix3D::solveThird(const FixedList<scalar, 3>& source)
{
    calculateDeterminant();
 
    const FixedList<FixedList<scalar, 3>, 3>& mat = *this;
 
    return
    (
        (mat[1][0] * mat[2][1] - mat[1][1] * mat[2][0]) * source[0] +
        (mat[0][1] * mat[2][0] - mat[0][0] * mat[2][1]) * source[1] +
        (mat[0][0] * mat[1][1] - mat[0][1] * mat[1][0]) * source[2]
    ) / det_;
}
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
} // End namespace Foam
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //