690 lines
21 KiB
C++
690 lines
21 KiB
C++
// Magic Software, Inc.
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// http://www.magic-software.com
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// Copyright (c) 2000, All Rights Reserved
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//
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// Source code from Magic Software is supplied under the terms of a license
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// agreement and may not be copied or disclosed except in accordance with the
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// terms of that agreement. The various license agreements may be found at
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// the Magic Software web site. This file is subject to the license
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//
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// FREE SOURCE CODE
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// http://www.magic-software.com/License/free.pdf
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#include "MgcEigen.h"
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#include "mathtypes.h"
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//#include "debug.h"
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#include "math.h"
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//#include "MgcRTLib.h"
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//---------------------------------------------------------------------------
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MgcEigen::MgcEigen (int iSize)
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{
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// ASSERT( iSize >= 2 );
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m_iSize = iSize;
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m_aafMat = new real*[m_iSize];
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for (int i = 0; i < m_iSize; i++)
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m_aafMat[i] = new real[m_iSize];
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m_afDiag = new real[m_iSize];
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m_afSubd = new real[m_iSize];
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}
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//---------------------------------------------------------------------------
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MgcEigen::~MgcEigen ()
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{
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delete[] m_afSubd;
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delete[] m_afDiag;
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for (int i = 0; i < m_iSize; i++)
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delete[] m_aafMat[i];
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delete[] m_aafMat;
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}
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//---------------------------------------------------------------------------
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void MgcEigen::Tridiagonal2 (real** m_aafMat, real* m_afDiag,
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real* m_afSubd)
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{
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// matrix is already tridiagonal
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m_afDiag[0] = m_aafMat[0][0];
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m_afDiag[1] = m_aafMat[1][1];
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m_afSubd[0] = m_aafMat[0][1];
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m_afSubd[1] = 0.0;
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m_aafMat[0][0] = 1.0;
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m_aafMat[0][1] = 0.0;
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m_aafMat[1][0] = 0.0;
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m_aafMat[1][1] = 1.0;
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}
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//---------------------------------------------------------------------------
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void MgcEigen::Tridiagonal3 (real** m_aafMat, real* m_afDiag,
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real* m_afSubd)
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{
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real fM00 = m_aafMat[0][0];
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real fM01 = m_aafMat[0][1];
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real fM02 = m_aafMat[0][2];
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real fM11 = m_aafMat[1][1];
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real fM12 = m_aafMat[1][2];
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real fM22 = m_aafMat[2][2];
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m_afDiag[0] = fM00;
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m_afSubd[2] = 0.0;
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if ( fM02 != 0.0 )
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{
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real fLength = (real)sqrt(fM01*fM01+fM02*fM02);
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real fInvLength = 1.0/fLength;
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fM01 *= fInvLength;
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fM02 *= fInvLength;
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real fQ = 2.0*fM01*fM12+fM02*(fM22-fM11);
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m_afDiag[1] = fM11+fM02*fQ;
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m_afDiag[2] = fM22-fM02*fQ;
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m_afSubd[0] = fLength;
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m_afSubd[1] = fM12-fM01*fQ;
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m_aafMat[0][0] = 1.0; m_aafMat[0][1] = 0.0; m_aafMat[0][2] = 0.0;
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m_aafMat[1][0] = 0.0; m_aafMat[1][1] = fM01; m_aafMat[1][2] = fM02;
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m_aafMat[2][0] = 0.0; m_aafMat[2][1] = fM02; m_aafMat[2][2] = -fM01;
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}
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else
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{
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m_afDiag[1] = fM11;
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m_afDiag[2] = fM22;
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m_afSubd[0] = fM01;
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m_afSubd[1] = fM12;
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m_aafMat[0][0] = 1.0; m_aafMat[0][1] = 0.0; m_aafMat[0][2] = 0.0;
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m_aafMat[1][0] = 0.0; m_aafMat[1][1] = 1.0; m_aafMat[1][2] = 0.0;
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m_aafMat[2][0] = 0.0; m_aafMat[2][1] = 0.0; m_aafMat[2][2] = 1.0;
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}
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}
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//---------------------------------------------------------------------------
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void MgcEigen::Tridiagonal4 (real** m_aafMat, real* m_afDiag,
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real* m_afSubd)
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{
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// save matrix M
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real fM00 = m_aafMat[0][0];
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real fM01 = m_aafMat[0][1];
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real fM02 = m_aafMat[0][2];
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real fM03 = m_aafMat[0][3];
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real fM11 = m_aafMat[1][1];
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real fM12 = m_aafMat[1][2];
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real fM13 = m_aafMat[1][3];
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real fM22 = m_aafMat[2][2];
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real fM23 = m_aafMat[2][3];
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real fM33 = m_aafMat[3][3];
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m_afDiag[0] = fM00;
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m_afSubd[3] = 0.0;
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m_aafMat[0][0] = 1.0;
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m_aafMat[0][1] = 0.0;
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m_aafMat[0][2] = 0.0;
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m_aafMat[0][3] = 0.0;
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m_aafMat[1][0] = 0.0;
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m_aafMat[2][0] = 0.0;
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m_aafMat[3][0] = 0.0;
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float fLength, fInvLength;
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if ( fM02 != 0.0 || fM03 != 0.0 )
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{
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real fQ11, fQ12, fQ13;
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real fQ21, fQ22, fQ23;
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real fQ31, fQ32, fQ33;
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// build column Q1
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fLength = (real)sqrt(fM01*fM01+fM02*fM02+fM03*fM03);
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fInvLength = 1.0/fLength;
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fQ11 = fM01*fInvLength;
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fQ21 = fM02*fInvLength;
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fQ31 = fM03*fInvLength;
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m_afSubd[0] = fLength;
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// compute S*Q1
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real fV0 = fM11*fQ11+fM12*fQ21+fM13*fQ31;
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real fV1 = fM12*fQ11+fM22*fQ21+fM23*fQ31;
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real fV2 = fM13*fQ11+fM23*fQ21+fM33*fQ31;
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m_afDiag[1] = fQ11*fV0+fQ21*fV1+fQ31*fV2;
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// build column Q3 = Q1x(S*Q1)
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fQ13 = fQ21*fV2-fQ31*fV1;
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fQ23 = fQ31*fV0-fQ11*fV2;
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fQ33 = fQ11*fV1-fQ21*fV0;
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fLength = (real)sqrt(fQ13*fQ13+fQ23*fQ23+fQ33*fQ33);
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if ( fLength > 0.0 )
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{
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fInvLength = 1.0/fLength;
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fQ13 *= fInvLength;
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fQ23 *= fInvLength;
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fQ33 *= fInvLength;
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// build column Q2 = Q3xQ1
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fQ12 = fQ23*fQ31-fQ33*fQ21;
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fQ22 = fQ33*fQ11-fQ13*fQ31;
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fQ32 = fQ13*fQ21-fQ23*fQ11;
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fV0 = fQ12*fM11+fQ22*fM12+fQ32*fM13;
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fV1 = fQ12*fM12+fQ22*fM22+fQ32*fM23;
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fV2 = fQ12*fM13+fQ22*fM23+fQ32*fM33;
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m_afSubd[1] = fQ11*fV0+fQ21*fV1+fQ31*fV2;
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m_afDiag[2] = fQ12*fV0+fQ22*fV1+fQ32*fV2;
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m_afSubd[2] = fQ13*fV0+fQ23*fV1+fQ33*fV2;
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fV0 = fQ13*fM11+fQ23*fM12+fQ33*fM13;
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fV1 = fQ13*fM12+fQ23*fM22+fQ33*fM23;
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fV2 = fQ13*fM13+fQ23*fM23+fQ33*fM33;
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m_afDiag[3] = fQ13*fV0+fQ23*fV1+fQ33*fV2;
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}
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else
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{
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// S*Q1 parallel to Q1, choose any valid Q2 and Q3
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m_afSubd[1] = 0;
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fLength = fQ21*fQ21+fQ31*fQ31;
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if ( fLength > 0.0 )
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{
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fInvLength = 1.0/fLength;
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real fTmp = fQ11-1.0;
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fQ12 = -fQ21;
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fQ22 = 1.0+fTmp*fQ21*fQ21*fInvLength;
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fQ32 = fTmp*fQ21*fQ31*fInvLength;
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fQ13 = -fQ31;
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fQ23 = fQ32;
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fQ33 = 1.0+fTmp*fQ31*fQ31*fInvLength;
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fV0 = fQ12*fM11+fQ22*fM12+fQ32*fM13;
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fV1 = fQ12*fM12+fQ22*fM22+fQ32*fM23;
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fV2 = fQ12*fM13+fQ22*fM23+fQ32*fM33;
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m_afDiag[2] = fQ12*fV0+fQ22*fV1+fQ32*fV2;
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m_afSubd[2] = fQ13*fV0+fQ23*fV1+fQ33*fV2;
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fV0 = fQ13*fM11+fQ23*fM12+fQ33*fM13;
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fV1 = fQ13*fM12+fQ23*fM22+fQ33*fM23;
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fV2 = fQ13*fM13+fQ23*fM23+fQ33*fM33;
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m_afDiag[3] = fQ13*fV0+fQ23*fV1+fQ33*fV2;
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}
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else
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{
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// Q1 = (+-1,0,0)
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fQ12 = 0.0; fQ22 = 1.0; fQ32 = 0.0;
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fQ13 = 0.0; fQ23 = 0.0; fQ33 = 1.0;
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m_afDiag[2] = fM22;
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m_afDiag[3] = fM33;
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m_afSubd[2] = fM23;
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}
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}
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m_aafMat[1][1] = fQ11; m_aafMat[1][2] = fQ12; m_aafMat[1][3] = fQ13;
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m_aafMat[2][1] = fQ21; m_aafMat[2][2] = fQ22; m_aafMat[2][3] = fQ23;
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m_aafMat[3][1] = fQ31; m_aafMat[3][2] = fQ32; m_aafMat[3][3] = fQ33;
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}
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else
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{
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m_afDiag[1] = fM11;
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m_afSubd[0] = fM01;
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m_aafMat[1][1] = 1.0;
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m_aafMat[2][1] = 0.0;
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m_aafMat[3][1] = 0.0;
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if ( fM13 != 0.0 )
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{
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fLength = (real)sqrt(fM12*fM12+fM13*fM13);
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fInvLength = 1.0/fLength;
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fM12 *= fInvLength;
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fM13 *= fInvLength;
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real fQ = 2.0*fM12*fM23+fM13*(fM33-fM22);
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m_afDiag[2] = fM22+fM13*fQ;
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m_afDiag[3] = fM33-fM13*fQ;
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m_afSubd[1] = fLength;
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m_afSubd[2] = fM23-fM12*fQ;
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m_aafMat[1][2] = 0.0;
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m_aafMat[1][3] = 0.0;
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m_aafMat[2][2] = fM12;
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m_aafMat[2][3] = fM13;
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m_aafMat[3][2] = fM13;
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m_aafMat[3][3] = -fM12;
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}
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else
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{
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m_afDiag[2] = fM22;
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m_afDiag[3] = fM33;
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m_afSubd[1] = fM12;
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m_afSubd[2] = fM23;
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m_aafMat[1][2] = 0.0;
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m_aafMat[1][3] = 0.0;
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m_aafMat[2][2] = 1.0;
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m_aafMat[2][3] = 0.0;
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m_aafMat[3][2] = 0.0;
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m_aafMat[3][3] = 1.0;
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}
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}
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}
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//---------------------------------------------------------------------------
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void MgcEigen::TridiagonalN (int iSize, real** m_aafMat,
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real* m_afDiag, real* m_afSubd)
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{
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int i0, i1, i2, i3;
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for (i0 = iSize-1, i3 = iSize-2; i0 >= 1; i0--, i3--)
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{
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real fH = 0.0, fScale = 0.0;
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if ( i3 > 0 )
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{
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for (i2 = 0; i2 <= i3; i2++)
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fScale += abs(m_aafMat[i0][i2]);
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if ( fScale == 0 )
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{
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m_afSubd[i0] = m_aafMat[i0][i3];
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}
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else
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{
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float fInvScale = 1.0/fScale;
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for (i2 = 0; i2 <= i3; i2++)
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{
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m_aafMat[i0][i2] *= fInvScale;
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fH += m_aafMat[i0][i2]*m_aafMat[i0][i2];
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}
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real fF = m_aafMat[i0][i3];
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real fG = (real)sqrt(fH);
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if ( fF > 0.0 )
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fG = -fG;
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m_afSubd[i0] = fScale*fG;
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fH -= fF*fG;
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m_aafMat[i0][i3] = fF-fG;
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fF = 0.0;
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float fInvH = 1.0/fH;
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for (i1 = 0; i1 <= i3; i1++)
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{
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m_aafMat[i1][i0] = m_aafMat[i0][i1]*fInvH;
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fG = 0.0;
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for (i2 = 0; i2 <= i1; i2++)
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fG += m_aafMat[i1][i2]*m_aafMat[i0][i2];
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for (i2 = i1+1; i2 <= i3; i2++)
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fG += m_aafMat[i2][i1]*m_aafMat[i0][i2];
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m_afSubd[i1] = fG*fInvH;
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fF += m_afSubd[i1]*m_aafMat[i0][i1];
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}
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real fHalfFdivH = 0.5*fF*fInvH;
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for (i1 = 0; i1 <= i3; i1++)
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{
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fF = m_aafMat[i0][i1];
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fG = m_afSubd[i1] - fHalfFdivH*fF;
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m_afSubd[i1] = fG;
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for (i2 = 0; i2 <= i1; i2++)
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{
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m_aafMat[i1][i2] -= fF*m_afSubd[i2] +
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fG*m_aafMat[i0][i2];
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}
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}
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}
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}
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else
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{
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m_afSubd[i0] = m_aafMat[i0][i3];
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}
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m_afDiag[i0] = fH;
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}
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m_afDiag[0] = m_afSubd[0] = 0;
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for (i0 = 0, i3 = -1; i0 <= iSize-1; i0++, i3++)
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{
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if ( m_afDiag[i0] )
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{
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for (i1 = 0; i1 <= i3; i1++)
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{
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real fSum = 0;
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for (i2 = 0; i2 <= i3; i2++)
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fSum += m_aafMat[i0][i2]*m_aafMat[i2][i1];
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for (i2 = 0; i2 <= i3; i2++)
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m_aafMat[i2][i1] -= fSum*m_aafMat[i2][i0];
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}
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}
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m_afDiag[i0] = m_aafMat[i0][i0];
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m_aafMat[i0][i0] = 1;
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for (i1 = 0; i1 <= i3; i1++)
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m_aafMat[i1][i0] = m_aafMat[i0][i1] = 0;
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}
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// re-ordering if MgcEigen::QLAlgorithm is used subsequently
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for (i0 = 1, i3 = 0; i0 < iSize; i0++, i3++)
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m_afSubd[i3] = m_afSubd[i0];
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m_afSubd[iSize-1] = 0;
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}
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//---------------------------------------------------------------------------
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bool MgcEigen::QLAlgorithm (int iSize, real* m_afDiag, real* m_afSubd,
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real** m_aafMat)
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{
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const int iMaxIter = 32;
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for (int i0 = 0; i0 < iSize; i0++)
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{
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int i1;
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for (i1 = 0; i1 < iMaxIter; i1++)
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{
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int i2;
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for (i2 = i0; i2 <= iSize-2; i2++)
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{
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real fTmp =
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abs(m_afDiag[i2])+abs(m_afDiag[i2+1]);
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if ( abs(m_afSubd[i2]) + fTmp == fTmp )
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break;
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}
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if ( i2 == i0 )
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break;
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real fG = (m_afDiag[i0+1]-m_afDiag[i0])/(2.0*m_afSubd[i0]);
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real fR = (real)sqrt(fG*fG+1.0);
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if ( fG < 0.0 )
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fG = m_afDiag[i2]-m_afDiag[i0]+m_afSubd[i0]/(fG-fR);
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else
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fG = m_afDiag[i2]-m_afDiag[i0]+m_afSubd[i0]/(fG+fR);
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real fSin = 1.0, fCos = 1.0, fP = 0.0;
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for (int i3 = i2-1; i3 >= i0; i3--)
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{
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real fF = fSin*m_afSubd[i3];
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real fB = fCos*m_afSubd[i3];
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if ( abs(fF) >= abs(fG) )
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{
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fCos = fG/fF;
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fR = (real)sqrt(fCos*fCos+1.0);
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m_afSubd[i3+1] = fF*fR;
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fSin = 1.0/fR;
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fCos *= fSin;
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}
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else
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{
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fSin = fF/fG;
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fR = (real)sqrt(fSin*fSin+1.0);
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m_afSubd[i3+1] = fG*fR;
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fCos = 1.0/fR;
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fSin *= fCos;
|
|
}
|
|
fG = m_afDiag[i3+1]-fP;
|
|
fR = (m_afDiag[i3]-fG)*fSin+2.0*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
|