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// Geometric Tools, LLC
// Copyright (c) 1998-2014
// Distributed under the Boost Software License, Version 1.0.
// http://www.boost.org/LICENSE_1_0.txt
// http://www.geometrictools.com/License/Boost/LICENSE_1_0.txt
//
// File Version: 5.0.4 (2014/07/09)
#include "Wm5MathematicsPCH.h"
#include "Wm5EigenDecomposition.h"
namespace Wm5
{
//----------------------------------------------------------------------------
template <typename Real>
EigenDecomposition<Real>::EigenDecomposition (int size)
:
mMatrix(size, size),
mSolver(size, MAX_ITERATIONS),
mEigenvalues(size)
{
assertion(size >= 2, "Invalid size in Eigendecomposition constructor\n");
}
//----------------------------------------------------------------------------
template <typename Real>
EigenDecomposition<Real>::EigenDecomposition (const Matrix2<Real>& mat)
:
mMatrix(2, 2, &mat[0][0]),
mSolver(2, MAX_ITERATIONS),
mEigenvalues(2)
{
}
//----------------------------------------------------------------------------
template <typename Real>
EigenDecomposition<Real>::EigenDecomposition (const Matrix3<Real>& mat)
:
mMatrix(3, 3, &mat[0][0]),
mSolver(3, MAX_ITERATIONS),
mEigenvalues(3)
{
}
//----------------------------------------------------------------------------
template <typename Real>
EigenDecomposition<Real>::EigenDecomposition (const GMatrix<Real>& mat)
:
mMatrix(mat),
mSolver(mat.GetNumRows(), MAX_ITERATIONS),
mEigenvalues(mat.GetNumRows())
{
assertion(mat.GetNumRows() >= 2
&& mat.GetNumRows() == mat.GetNumColumns(),
"Square matrix required in EigenDecomposition constructor\n");
}
//----------------------------------------------------------------------------
template <typename Real>
EigenDecomposition<Real>::~EigenDecomposition ()
{
}
//----------------------------------------------------------------------------
template <typename Real>
Real& EigenDecomposition<Real>::operator() (int row, int column)
{
return mMatrix[row][column];
}
//----------------------------------------------------------------------------
template <typename Real>
EigenDecomposition<Real>& EigenDecomposition<Real>::operator= (
const Matrix2<Real>& mat)
{
mMatrix.SetMatrix(2, 2, &mat[0][0]);
mSolver = SymmetricEigensolverGTE<Real>(2, MAX_ITERATIONS);
mEigenvalues.resize(2);
return *this;
}
//----------------------------------------------------------------------------
template <typename Real>
EigenDecomposition<Real>& EigenDecomposition<Real>::operator= (
const Matrix3<Real>& mat)
{
mMatrix.SetMatrix(3, 3, &mat[0][0]);
mSolver = SymmetricEigensolverGTE<Real>(3, MAX_ITERATIONS);
mEigenvalues.resize(3);
return *this;
}
//----------------------------------------------------------------------------
template <typename Real>
EigenDecomposition<Real>& EigenDecomposition<Real>::operator= (
const GMatrix<Real>& mat)
{
mMatrix = mat;
mSolver = SymmetricEigensolverGTE<Real>(mat.GetNumRows(), MAX_ITERATIONS);
mEigenvalues.resize(mat.GetNumRows());
return *this;
}
//----------------------------------------------------------------------------
template <typename Real>
void EigenDecomposition<Real>::Solve (bool increasingSort)
{
mSolver.Solve(mMatrix.GetElements(), (increasingSort ? +1 : -1));
mSolver.GetEigenvalues(&mEigenvalues[0]);
mSolver.GetEigenvectors(mMatrix.GetElements());
if (!mSolver.IsRotation())
{
// The return matrix of eigenvectors is a reflection. Negate the
// first column to make it a rotation.
for (int r = 0; r < mMatrix.GetNumRows(); ++r)
{
mMatrix[r][0] = -mMatrix[r][0];
}
}
}
//----------------------------------------------------------------------------
template <typename Real>
Real EigenDecomposition<Real>::GetEigenvalue (int i) const
{
assertion(0 <= i && i < mMatrix.GetNumRows(),
"Invalid index in GetEigenvalue\n");
return mEigenvalues[i];
}
//----------------------------------------------------------------------------
template <typename Real>
const Real* EigenDecomposition<Real>::GetEigenvalues () const
{
return &mEigenvalues[0];
}
//----------------------------------------------------------------------------
template <typename Real>
Vector2<Real> EigenDecomposition<Real>::GetEigenvector2 (int i) const
{
int size = mMatrix.GetNumRows();
if (size == 2)
{
Vector2<Real> eigenvector;
for (int row = 0; row < size; ++row)
{
eigenvector[row] = mMatrix[row][i];
}
return eigenvector;
}
assertion(false, "Mismatched dimension in GetEigenvector2\n");
return Vector2<Real>::ZERO;
}
//----------------------------------------------------------------------------
template <typename Real>
Matrix2<Real> EigenDecomposition<Real>::GetEigenvectors2 () const
{
assertion(mMatrix.GetNumRows() == 2,
"Mismatched dimension in GetEigenvectors2\n");
Matrix2<Real> eigenvectors;
for (int row = 0; row < 2; ++row)
{
for (int column = 0; column < 2; ++column)
{
eigenvectors[row][column] = mMatrix[row][column];
}
}
return eigenvectors;
}
//----------------------------------------------------------------------------
template <typename Real>
Vector3<Real> EigenDecomposition<Real>::GetEigenvector3 (int i) const
{
int size = mMatrix.GetNumRows();
if (size == 3)
{
Vector3<Real> eigenvector;
for (int row = 0; row < size; ++row)
{
eigenvector[row] = mMatrix[row][i];
}
return eigenvector;
}
assertion(false, "Mismatched dimension in GetEigenvector3\n");
return Vector3<Real>::ZERO;
}
//----------------------------------------------------------------------------
template <typename Real>
Matrix3<Real> EigenDecomposition<Real>::GetEigenvectors3 () const
{
assertion(mMatrix.GetNumRows() == 3,
"Mismatched dimension in GetEigenvectors2\n");
Matrix3<Real> eigenvectors;
for (int row = 0; row < 3; ++row)
{
for (int column = 0; column < 3; ++column)
{
eigenvectors[row][column] = mMatrix[row][column];
}
}
return eigenvectors;
}
//----------------------------------------------------------------------------
template <typename Real>
GVector<Real> EigenDecomposition<Real>::GetEigenvector (int i) const
{
return mMatrix.GetColumn(i);
}
//----------------------------------------------------------------------------
template <typename Real>
const GMatrix<Real>& EigenDecomposition<Real>::GetEigenvectors () const
{
return mMatrix;
}
//----------------------------------------------------------------------------
//----------------------------------------------------------------------------
// Explicit instantiation.
//----------------------------------------------------------------------------
template WM5_MATHEMATICS_ITEM
class EigenDecomposition<float>;
template WM5_MATHEMATICS_ITEM
class EigenDecomposition<double>;
}
//----------------------------------------------------------------------------
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