// Magic Software, Inc.
// http://www.magic-software.com
// Copyright (c) 2000, All Rights Reserved
//
// Source code from Magic Software is supplied under the terms of a license
// agreement and may not be copied or disclosed except in accordance with the
// terms of that agreement. The various license agreements may be found at
// the Magic Software web site. This file is subject to the license
//
// FREE SOURCE CODE
// http://www.magic-software.com/License/free.pdf
#include "MgcEigen.h"
#include "mathtypes.h"
//#include "debug.h"
#include "math.h"
//#include "MgcRTLib.h"
//---------------------------------------------------------------------------
MgcEigen::MgcEigen (int iSize)
{
// ASSERT( iSize >= 2 );
m_iSize = iSize;
m_aafMat = new real*[m_iSize];
for (int i = 0; i < m_iSize; i++)
m_aafMat[i] = new real[m_iSize];
m_afDiag = new real[m_iSize];
m_afSubd = new real[m_iSize];
}
//---------------------------------------------------------------------------
MgcEigen::~MgcEigen ()
{
delete[] m_afSubd;
delete[] m_afDiag;
for (int i = 0; i < m_iSize; i++)
delete[] m_aafMat[i];
delete[] m_aafMat;
}
//---------------------------------------------------------------------------
void MgcEigen::Tridiagonal2 (real** m_aafMat, real* m_afDiag,
real* m_afSubd)
{
// matrix is already tridiagonal
m_afDiag[0] = m_aafMat[0][0];
m_afDiag[1] = m_aafMat[1][1];
m_afSubd[0] = m_aafMat[0][1];
m_afSubd[1] = 0.0;
m_aafMat[0][0] = 1.0;
m_aafMat[0][1] = 0.0;
m_aafMat[1][0] = 0.0;
m_aafMat[1][1] = 1.0;
}
//---------------------------------------------------------------------------
void MgcEigen::Tridiagonal3 (real** m_aafMat, real* m_afDiag,
real* m_afSubd)
{
real fM00 = m_aafMat[0][0];
real fM01 = m_aafMat[0][1];
real fM02 = m_aafMat[0][2];
real fM11 = m_aafMat[1][1];
real fM12 = m_aafMat[1][2];
real fM22 = m_aafMat[2][2];
m_afDiag[0] = fM00;
m_afSubd[2] = 0.0;
if ( fM02 != 0.0 )
{
real fLength = (real)sqrt(fM01*fM01+fM02*fM02);
real fInvLength = 1.0f/fLength;
fM01 *= fInvLength;
fM02 *= fInvLength;
real fQ = 2.0f*fM01*fM12+fM02*(fM22-fM11);
m_afDiag[1] = fM11+fM02*fQ;
m_afDiag[2] = fM22-fM02*fQ;
m_afSubd[0] = fLength;
m_afSubd[1] = fM12-fM01*fQ;
m_aafMat[0][0] = 1.0; m_aafMat[0][1] = 0.0; m_aafMat[0][2] = 0.0;
m_aafMat[1][0] = 0.0; m_aafMat[1][1] = fM01; m_aafMat[1][2] = fM02;
m_aafMat[2][0] = 0.0; m_aafMat[2][1] = fM02; m_aafMat[2][2] = -fM01;
}
else
{
m_afDiag[1] = fM11;
m_afDiag[2] = fM22;
m_afSubd[0] = fM01;
m_afSubd[1] = fM12;
m_aafMat[0][0] = 1.0; m_aafMat[0][1] = 0.0; m_aafMat[0][2] = 0.0;
m_aafMat[1][0] = 0.0; m_aafMat[1][1] = 1.0; m_aafMat[1][2] = 0.0;
m_aafMat[2][0] = 0.0; m_aafMat[2][1] = 0.0; m_aafMat[2][2] = 1.0;
}
}
//---------------------------------------------------------------------------
void MgcEigen::Tridiagonal4 (real** m_aafMat, real* m_afDiag,
real* m_afSubd)
{
// save matrix M
real fM00 = m_aafMat[0][0];
real fM01 = m_aafMat[0][1];
real fM02 = m_aafMat[0][2];
real fM03 = m_aafMat[0][3];
real fM11 = m_aafMat[1][1];
real fM12 = m_aafMat[1][2];
real fM13 = m_aafMat[1][3];
real fM22 = m_aafMat[2][2];
real fM23 = m_aafMat[2][3];
real fM33 = m_aafMat[3][3];
m_afDiag[0] = fM00;
m_afSubd[3] = 0.0;
m_aafMat[0][0] = 1.0;
m_aafMat[0][1] = 0.0;
m_aafMat[0][2] = 0.0;
m_aafMat[0][3] = 0.0;
m_aafMat[1][0] = 0.0;
m_aafMat[2][0] = 0.0;
m_aafMat[3][0] = 0.0;
float fLength, fInvLength;
if ( fM02 != 0.0 || fM03 != 0.0 )
{
real fQ11, fQ12, fQ13;
real fQ21, fQ22, fQ23;
real fQ31, fQ32, fQ33;
// build column Q1
fLength = (real)sqrt(fM01*fM01+fM02*fM02+fM03*fM03);
fInvLength = 1.0f/fLength;
fQ11 = fM01*fInvLength;
fQ21 = fM02*fInvLength;
fQ31 = fM03*fInvLength;
m_afSubd[0] = fLength;
// compute S*Q1
real fV0 = fM11*fQ11+fM12*fQ21+fM13*fQ31;
real fV1 = fM12*fQ11+fM22*fQ21+fM23*fQ31;
real fV2 = fM13*fQ11+fM23*fQ21+fM33*fQ31;
m_afDiag[1] = fQ11*fV0+fQ21*fV1+fQ31*fV2;
// build column Q3 = Q1x(S*Q1)
fQ13 = fQ21*fV2-fQ31*fV1;
fQ23 = fQ31*fV0-fQ11*fV2;
fQ33 = fQ11*fV1-fQ21*fV0;
fLength = (real)sqrt(fQ13*fQ13+fQ23*fQ23+fQ33*fQ33);
if ( fLength > 0.0 )
{
fInvLength = 1.0f/fLength;
fQ13 *= fInvLength;
fQ23 *= fInvLength;
fQ33 *= fInvLength;
// build column Q2 = Q3xQ1
fQ12 = fQ23*fQ31-fQ33*fQ21;
fQ22 = fQ33*fQ11-fQ13*fQ31;
fQ32 = fQ13*fQ21-fQ23*fQ11;
fV0 = fQ12*fM11+fQ22*fM12+fQ32*fM13;
fV1 = fQ12*fM12+fQ22*fM22+fQ32*fM23;
fV2 = fQ12*fM13+fQ22*fM23+fQ32*fM33;
m_afSubd[1] = fQ11*fV0+fQ21*fV1+fQ31*fV2;
m_afDiag[2] = fQ12*fV0+fQ22*fV1+fQ32*fV2;
m_afSubd[2] = fQ13*fV0+fQ23*fV1+fQ33*fV2;
fV0 = fQ13*fM11+fQ23*fM12+fQ33*fM13;
fV1 = fQ13*fM12+fQ23*fM22+fQ33*fM23;
fV2 = fQ13*fM13+fQ23*fM23+fQ33*fM33;
m_afDiag[3] = fQ13*fV0+fQ23*fV1+fQ33*fV2;
}
else
{
// S*Q1 parallel to Q1, choose any valid Q2 and Q3
m_afSubd[1] = 0;
fLength = fQ21*fQ21+fQ31*fQ31;
if ( fLength > 0.0 )
{
fInvLength = 1.0f/fLength;
real fTmp = fQ11-1.0f;
fQ12 = -fQ21;
fQ22 = 1.0f+fTmp*fQ21*fQ21*fInvLength;
fQ32 = fTmp*fQ21*fQ31*fInvLength;
fQ13 = -fQ31;
fQ23 = fQ32;
fQ33 = 1.0f+fTmp*fQ31*fQ31*fInvLength;
fV0 = fQ12*fM11+fQ22*fM12+fQ32*fM13;
fV1 = fQ12*fM12+fQ22*fM22+fQ32*fM23;
fV2 = fQ12*fM13+fQ22*fM23+fQ32*fM33;
m_afDiag[2] = fQ12*fV0+fQ22*fV1+fQ32*fV2;
m_afSubd[2] = fQ13*fV0+fQ23*fV1+fQ33*fV2;
fV0 = fQ13*fM11+fQ23*fM12+fQ33*fM13;
fV1 = fQ13*fM12+fQ23*fM22+fQ33*fM23;
fV2 = fQ13*fM13+fQ23*fM23+fQ33*fM33;
m_afDiag[3] = fQ13*fV0+fQ23*fV1+fQ33*fV2;
}
else
{
// Q1 = (+-1,0,0)
fQ12 = 0.0; fQ22 = 1.0; fQ32 = 0.0;
fQ13 = 0.0; fQ23 = 0.0; fQ33 = 1.0;
m_afDiag[2] = fM22;
m_afDiag[3] = fM33;
m_afSubd[2] = fM23;
}
}
m_aafMat[1][1] = fQ11; m_aafMat[1][2] = fQ12; m_aafMat[1][3] = fQ13;
m_aafMat[2][1] = fQ21; m_aafMat[2][2] = fQ22; m_aafMat[2][3] = fQ23;
m_aafMat[3][1] = fQ31; m_aafMat[3][2] = fQ32; m_aafMat[3][3] = fQ33;
}
else
{
m_afDiag[1] = fM11;
m_afSubd[0] = fM01;
m_aafMat[1][1] = 1.0;
m_aafMat[2][1] = 0.0;
m_aafMat[3][1] = 0.0;
if ( fM13 != 0.0 )
{
fLength = (real)sqrt(fM12*fM12+fM13*fM13);
fInvLength = 1.0f/fLength;
fM12 *= fInvLength;
fM13 *= fInvLength;
real fQ = 2.0f*fM12*fM23+fM13*(fM33-fM22);
m_afDiag[2] = fM22+fM13*fQ;
m_afDiag[3] = fM33-fM13*fQ;
m_afSubd[1] = fLength;
m_afSubd[2] = fM23-fM12*fQ;
m_aafMat[1][2] = 0.0;
m_aafMat[1][3] = 0.0;
m_aafMat[2][2] = fM12;
m_aafMat[2][3] = fM13;
m_aafMat[3][2] = fM13;
m_aafMat[3][3] = -fM12;
}
else
{
m_afDiag[2] = fM22;
m_afDiag[3] = fM33;
m_afSubd[1] = fM12;
m_afSubd[2] = fM23;
m_aafMat[1][2] = 0.0;
m_aafMat[1][3] = 0.0;
m_aafMat[2][2] = 1.0;
m_aafMat[2][3] = 0.0;
m_aafMat[3][2] = 0.0;
m_aafMat[3][3] = 1.0;
}
}
}
//---------------------------------------------------------------------------
void MgcEigen::TridiagonalN (int iSize, real** m_aafMat,
real* m_afDiag, real* m_afSubd)
{
int i0, i1, i2, i3;
for (i0 = iSize-1, i3 = iSize-2; i0 >= 1; i0--, i3--)
{
real fH = 0.0, fScale = 0.0;
if ( i3 > 0 )
{
for (i2 = 0; i2 <= i3; i2++)
fScale += (real)fabs(m_aafMat[i0][i2]);
if ( fScale == 0 )
{
m_afSubd[i0] = m_aafMat[i0][i3];
}
else
{
float fInvScale = 1.0f/fScale;
for (i2 = 0; i2 <= i3; i2++)
{
m_aafMat[i0][i2] *= fInvScale;
fH += m_aafMat[i0][i2]*m_aafMat[i0][i2];
}
real fF = m_aafMat[i0][i3];
real fG = (real)sqrt(fH);
if ( fF > 0.0 )
fG = -fG;
m_afSubd[i0] = fScale*fG;
fH -= fF*fG;
m_aafMat[i0][i3] = fF-fG;
fF = 0.0;
float fInvH = 1.0f/fH;
for (i1 = 0; i1 <= i3; i1++)
{
m_aafMat[i1][i0] = m_aafMat[i0][i1]*fInvH;
fG = 0.0;
for (i2 = 0; i2 <= i1; i2++)
fG += m_aafMat[i1][i2]*m_aafMat[i0][i2];
for (i2 = i1+1; i2 <= i3; i2++)
fG += m_aafMat[i2][i1]*m_aafMat[i0][i2];
m_afSubd[i1] = fG*fInvH;
fF += m_afSubd[i1]*m_aafMat[i0][i1];
}
real fHalfFdivH = 0.5f*fF*fInvH;
for (i1 = 0; i1 <= i3; i1++)
{
fF = m_aafMat[i0][i1];
fG = m_afSubd[i1] - fHalfFdivH*fF;
m_afSubd[i1] = fG;
for (i2 = 0; i2 <= i1; i2++)
{
m_aafMat[i1][i2] -= fF*m_afSubd[i2] +
fG*m_aafMat[i0][i2];
}
}
}
}
else
{
m_afSubd[i0] = m_aafMat[i0][i3];
}
m_afDiag[i0] = fH;
}
m_afDiag[0] = m_afSubd[0] = 0;
for (i0 = 0, i3 = -1; i0 <= iSize-1; i0++, i3++)
{
if ( m_afDiag[i0] )
{
for (i1 = 0; i1 <= i3; i1++)
{
real fSum = 0;
for (i2 = 0; i2 <= i3; i2++)
fSum += m_aafMat[i0][i2]*m_aafMat[i2][i1];
for (i2 = 0; i2 <= i3; i2++)
m_aafMat[i2][i1] -= fSum*m_aafMat[i2][i0];
}
}
m_afDiag[i0] = m_aafMat[i0][i0];
m_aafMat[i0][i0] = 1;
for (i1 = 0; i1 <= i3; i1++)
m_aafMat[i1][i0] = m_aafMat[i0][i1] = 0;
}
// re-ordering if MgcEigen::QLAlgorithm is used subsequently
for (i0 = 1, i3 = 0; i0 < iSize; i0++, i3++)
m_afSubd[i3] = m_afSubd[i0];
m_afSubd[iSize-1] = 0;
}
//---------------------------------------------------------------------------
bool MgcEigen::QLAlgorithm (int iSize, real* m_afDiag, real* m_afSubd,
real** m_aafMat)
{
const int iMaxIter = 32;
for (int i0 = 0; i0 < iSize; i0++)
{
int i1;
for (i1 = 0; i1 < iMaxIter; i1++)
{
int i2;
for (i2 = i0; i2 <= iSize-2; i2++)
{
real fTmp = (real) (fabs(m_afDiag[i2])+fabs(m_afDiag[i2+1]));
if ( fabs(m_afSubd[i2]) + fTmp == fTmp )
break;
}
if ( i2 == i0 )
break;
real fG = (m_afDiag[i0+1]-m_afDiag[i0])/(2.0f*m_afSubd[i0]);
real fR = (real)sqrt(fG*fG+1.0);
if ( fG < 0.0 )
fG = m_afDiag[i2]-m_afDiag[i0]+m_afSubd[i0]/(fG-fR);
else
fG = m_afDiag[i2]-m_afDiag[i0]+m_afSubd[i0]/(fG+fR);
real fSin = 1.0, fCos = 1.0, fP = 0.0;
for (int i3 = i2-1; i3 >= i0; i3--)
{
real fF = fSin*m_afSubd[i3];
real fB = fCos*m_afSubd[i3];
if ( fabs(fF) >= fabs(fG) )
{
fCos = fG/fF;
fR = (real)sqrt(fCos*fCos+1.0);
m_afSubd[i3+1] = fF*fR;
fSin = 1.0f/fR;
fCos *= fSin;
}
else
{
fSin = fF/fG;
fR = (real)sqrt(fSin*fSin+1.0);
m_afSubd[i3+1] = fG*fR;
fCos = 1.0f/fR;
fSin *= fCos;
}
fG = m_afDiag[i3+1]-fP;
fR = (m_afDiag[i3]-fG)*fSin+2.0f*fB*fCos;
fP = fSin*fR;
m_afDiag[i3+1] = fG+fP;
fG = fCos*fR-fB;
for (int i4 = 0; i4 < iSize; i4++)
{
fF = m_aafMat[i4][i3+1];
m_aafMat[i4][i3+1] = fSin*m_aafMat[i4][i3]+fCos*fF;
m_aafMat[i4][i3] = fCos*m_aafMat[i4][i3]-fSin*fF;
}
}
m_afDiag[i0] -= fP;
m_afSubd[i0] = fG;
m_afSubd[i2] = 0.0;
}
if ( i1 == iMaxIter )
return false;
}
return true;
}
//---------------------------------------------------------------------------
void MgcEigen::DecreasingSort (int iSize, real* afEigval,
real** aafEigvec)
{
// sort eigenvalues in decreasing order, e[0] >= ... >= e[iSize-1]
for (int i0 = 0, i1; i0 <= iSize-2; i0++)
{
// locate maximum eigenvalue
i1 = i0;
real fMax = afEigval[i1];
int i2;
for (i2 = i0+1; i2 < iSize; i2++)
{
if ( afEigval[i2] > fMax )
{
i1 = i2;
fMax = afEigval[i1];
}
}
if ( i1 != i0 )
{
// swap eigenvalues
afEigval[i1] = afEigval[i0];
afEigval[i0] = fMax;
// swap eigenvectors
for (i2 = 0; i2 < iSize; i2++)
{
real fTmp = aafEigvec[i2][i0];
aafEigvec[i2][i0] = aafEigvec[i2][i1];
aafEigvec[i2][i1] = fTmp;
}
}
}
}
//---------------------------------------------------------------------------
void MgcEigen::IncreasingSort (int iSize, real* afEigval,
real** aafEigvec)
{
// sort eigenvalues in increasing order, e[0] <= ... <= e[iSize-1]
for (int i0 = 0, i1; i0 <= iSize-2; i0++)
{
// locate minimum eigenvalue
i1 = i0;
real fMin = afEigval[i1];
int i2;
for (i2 = i0+1; i2 < iSize; i2++)
{
if ( afEigval[i2] < fMin )
{
i1 = i2;
fMin = afEigval[i1];
}
}
if ( i1 != i0 )
{
// swap eigenvalues
afEigval[i1] = afEigval[i0];
afEigval[i0] = fMin;
// swap eigenvectors
for (i2 = 0; i2 < iSize; i2++)
{
real fTmp = aafEigvec[i2][i0];
aafEigvec[i2][i0] = aafEigvec[i2][i1];
aafEigvec[i2][i1] = fTmp;
}
}
}
}
//---------------------------------------------------------------------------
void MgcEigen::SetMatrix (real** aafMat)
{
for (int iRow = 0; iRow < m_iSize; iRow++)
{
for (int iCol = 0; iCol < m_iSize; iCol++)
m_aafMat[iRow][iCol] = aafMat[iRow][iCol];
}
}
//---------------------------------------------------------------------------
void MgcEigen::EigenStuff2 ()
{
Tridiagonal2(m_aafMat,m_afDiag,m_afSubd);
QLAlgorithm(m_iSize,m_afDiag,m_afSubd,m_aafMat);
}
//---------------------------------------------------------------------------
void MgcEigen::EigenStuff3 ()
{
Tridiagonal3(m_aafMat,m_afDiag,m_afSubd);
QLAlgorithm(m_iSize,m_afDiag,m_afSubd,m_aafMat);
}
//---------------------------------------------------------------------------
void MgcEigen::EigenStuff4 ()
{
Tridiagonal4(m_aafMat,m_afDiag,m_afSubd);
QLAlgorithm(m_iSize,m_afDiag,m_afSubd,m_aafMat);
}
//---------------------------------------------------------------------------
void MgcEigen::EigenStuffN ()
{
TridiagonalN(m_iSize,m_aafMat,m_afDiag,m_afSubd);
QLAlgorithm(m_iSize,m_afDiag,m_afSubd,m_aafMat);
}
//---------------------------------------------------------------------------
void MgcEigen::EigenStuff ()
{
switch ( m_iSize )
{
case 2:
Tridiagonal2(m_aafMat,m_afDiag,m_afSubd);
break;
case 3:
Tridiagonal3(m_aafMat,m_afDiag,m_afSubd);
break;
case 4:
Tridiagonal4(m_aafMat,m_afDiag,m_afSubd);
break;
default:
TridiagonalN(m_iSize,m_aafMat,m_afDiag,m_afSubd);
break;
}
QLAlgorithm(m_iSize,m_afDiag,m_afSubd,m_aafMat);
}
//---------------------------------------------------------------------------
void MgcEigen::DecrSortEigenStuff2 ()
{
Tridiagonal2(m_aafMat,m_afDiag,m_afSubd);
QLAlgorithm(m_iSize,m_afDiag,m_afSubd,m_aafMat);
DecreasingSort(m_iSize,m_afDiag,m_aafMat);
}
//---------------------------------------------------------------------------
void MgcEigen::DecrSortEigenStuff3 ()
{
Tridiagonal3(m_aafMat,m_afDiag,m_afSubd);
QLAlgorithm(m_iSize,m_afDiag,m_afSubd,m_aafMat);
DecreasingSort(m_iSize,m_afDiag,m_aafMat);
}
//---------------------------------------------------------------------------
void MgcEigen::DecrSortEigenStuff4 ()
{
Tridiagonal4(m_aafMat,m_afDiag,m_afSubd);
QLAlgorithm(m_iSize,m_afDiag,m_afSubd,m_aafMat);
DecreasingSort(m_iSize,m_afDiag,m_aafMat);
}
//---------------------------------------------------------------------------
void MgcEigen::DecrSortEigenStuffN ()
{
TridiagonalN(m_iSize,m_aafMat,m_afDiag,m_afSubd);
QLAlgorithm(m_iSize,m_afDiag,m_afSubd,m_aafMat);
DecreasingSort(m_iSize,m_afDiag,m_aafMat);
}
//---------------------------------------------------------------------------
void MgcEigen::DecrSortEigenStuff ()
{
switch ( m_iSize )
{
case 2:
Tridiagonal2(m_aafMat,m_afDiag,m_afSubd);
break;
case 3:
Tridiagonal3(m_aafMat,m_afDiag,m_afSubd);
break;
case 4:
Tridiagonal4(m_aafMat,m_afDiag,m_afSubd);
break;
default:
TridiagonalN(m_iSize,m_aafMat,m_afDiag,m_afSubd);
break;
}
QLAlgorithm(m_iSize,m_afDiag,m_afSubd,m_aafMat);
DecreasingSort(m_iSize,m_afDiag,m_aafMat);
}
//---------------------------------------------------------------------------
void MgcEigen::IncrSortEigenStuff2 ()
{
Tridiagonal2(m_aafMat,m_afDiag,m_afSubd);
QLAlgorithm(m_iSize,m_afDiag,m_afSubd,m_aafMat);
IncreasingSort(m_iSize,m_afDiag,m_aafMat);
}
//---------------------------------------------------------------------------
void MgcEigen::IncrSortEigenStuff3 ()
{
Tridiagonal3(m_aafMat,m_afDiag,m_afSubd);
QLAlgorithm(m_iSize,m_afDiag,m_afSubd,m_aafMat);
IncreasingSort(m_iSize,m_afDiag,m_aafMat);
}
//---------------------------------------------------------------------------
void MgcEigen::IncrSortEigenStuff4 ()
{
Tridiagonal4(m_aafMat,m_afDiag,m_afSubd);
QLAlgorithm(m_iSize,m_afDiag,m_afSubd,m_aafMat);
IncreasingSort(m_iSize,m_afDiag,m_aafMat);
}
//---------------------------------------------------------------------------
void MgcEigen::IncrSortEigenStuffN ()
{
TridiagonalN(m_iSize,m_aafMat,m_afDiag,m_afSubd);
QLAlgorithm(m_iSize,m_afDiag,m_afSubd,m_aafMat);
IncreasingSort(m_iSize,m_afDiag,m_aafMat);
}
//---------------------------------------------------------------------------
void MgcEigen::IncrSortEigenStuff ()
{
switch ( m_iSize )
{
case 2:
Tridiagonal2(m_aafMat,m_afDiag,m_afSubd);
break;
case 3:
Tridiagonal3(m_aafMat,m_afDiag,m_afSubd);
break;
case 4:
Tridiagonal4(m_aafMat,m_afDiag,m_afSubd);
break;
default:
TridiagonalN(m_iSize,m_aafMat,m_afDiag,m_afSubd);
break;
}
QLAlgorithm(m_iSize,m_afDiag,m_afSubd,m_aafMat);
IncreasingSort(m_iSize,m_afDiag,m_aafMat);
}
//---------------------------------------------------------------------------
#ifdef EIGEN_TEST
int main ()
{
MgcEigen kES(3);
kES.Matrix(0,0) = 2.0; kES.Matrix(0,1) = 1.0; kES.Matrix(0,2) = 1.0;
kES.Matrix(1,0) = 1.0; kES.Matrix(1,1) = 2.0; kES.Matrix(1,2) = 1.0;
kES.Matrix(2,0) = 1.0; kES.Matrix(2,1) = 1.0; kES.Matrix(2,2) = 2.0;
kES.IncrSortEigenStuff3();
cout.setf(ios::fixed);
cout << "eigenvalues = " << endl;
int iRow;
for (iRow = 0; iRow < 3; iRow++)
cout << kES.GetEigenvalue(iRow) << ' ';
cout << endl;
cout << "eigenvectors = " << endl;
for (iRow = 0; iRow < 3; iRow++)
{
for (int iCol = 0; iCol < 3; iCol++)
cout << kES.GetEigenvector(iRow,iCol) << ' ';
cout << endl;
}
// eigenvalues =
// 1.000000 1.000000 4.000000
// eigenvectors =
// 0.411953 0.704955 0.577350
// 0.404533 -0.709239 0.577350
// -0.816485 0.004284 0.577350
return 0;
}
#endif