bool LinearSystem<Real>::SolveSymmetricCG (const GMatrix<Real>& rkA, const Real* afB, Real* afX) { // based on the algorithm in "Matrix Computations" by Golum and Van Loan assert( rkA.GetRows() == rkA.GetColumns() ); int iSize = rkA.GetRows(); Real* afR = new Real[iSize]; Real* afP = new Real[iSize]; Real* afW = new Real[iSize]; // first iteration memset(afX,0,iSize*sizeof(Real)); memcpy(afR,afB,iSize*sizeof(Real)); Real fRho0 = Dot(iSize,afR,afR); memcpy(afP,afR,iSize*sizeof(Real)); Multiply(rkA,afP,afW); Real fAlpha = fRho0/Dot(iSize,afP,afW); UpdateX(iSize,afX,fAlpha,afP); UpdateR(iSize,afR,fAlpha,afW); Real fRho1 = Dot(iSize,afR,afR); // remaining iterations const int iMax = 1024; int i; for (i = 1; i < iMax; i++) { Real fRoot0 = Math<Real>::Sqrt(fRho1); Real fNorm = Dot(iSize,afB,afB); Real fRoot1 = Math<Real>::Sqrt(fNorm); if ( fRoot0 <= ms_fTolerance*fRoot1 ) break; Real fBeta = fRho1/fRho0; UpdateP(iSize,afP,fBeta,afR); Multiply(rkA,afP,afW); fAlpha = fRho1/Dot(iSize,afP,afW); UpdateX(iSize,afX,fAlpha,afP); UpdateR(iSize,afR,fAlpha,afW); fRho0 = fRho1; fRho1 = Dot(iSize,afR,afR); } delete[] afW; delete[] afP; delete[] afR; return i < iMax; }
Eigen<Real>::Eigen (const GMatrix<Real>& rkM) : m_kMat(rkM) { m_iSize = rkM.GetRows(); assert(m_iSize >= 2 && (rkM.GetColumns() == m_iSize)); m_afDiag = WM4_NEW Real[m_iSize]; m_afSubd = WM4_NEW Real[m_iSize]; m_bIsRotation = false; }
void LinearSystem<Real>::Multiply (const GMatrix<Real>& rkA, const Real* afX, Real* afProd) { int iSize = rkA.GetRows(); memset(afProd,0,iSize*sizeof(Real)); for (int iRow = 0; iRow < iSize; iRow++) { for (int iCol = 0; iCol < iSize; iCol++) afProd[iRow] += rkA[iRow][iCol]*afX[iCol]; } }
Eigen<Real>::Eigen (const GMatrix<Real>& rkM) : m_kMat(rkM) { m_iSize = rkM.GetRows(); assert( m_iSize >= 2 && (rkM.GetColumns() == m_iSize) ); m_afDiag = new Real[m_iSize]; m_afSubd = new Real[m_iSize]; // set according to the parity of the number of Householder reflections m_bIsRotation = ((m_iSize % 2) == 0); }
EigenDecomposition<Real>::EigenDecomposition (const GMatrix<Real>& mat) : mMatrix(mat) { mSize = mat.GetRows(); assertion(mSize >= 2 && (mat.GetColumns() == mSize), "Square matrix required in EigenDecomposition constructor\n"); mDiagonal = new1<Real>(mSize); mSubdiagonal = new1<Real>(mSize); mIsRotation = false; }
bool LinearSystem<Real>::Inverse (const GMatrix<Real>& rkA, GMatrix<Real>& rkInvA) { // computations are performed in-place assert(rkA.GetRows() == rkA.GetColumns()); int iSize = rkInvA.GetRows(); rkInvA = rkA; int* aiColIndex = WM4_NEW int[iSize]; int* aiRowIndex = WM4_NEW int[iSize]; bool* abPivoted = WM4_NEW bool[iSize]; memset(abPivoted,0,iSize*sizeof(bool)); int i1, i2, iRow = 0, iCol = 0; Real fSave; // elimination by full pivoting for (int i0 = 0; i0 < iSize; i0++) { // search matrix (excluding pivoted rows) for maximum absolute entry Real fMax = 0.0f; for (i1 = 0; i1 < iSize; i1++) { if (!abPivoted[i1]) { for (i2 = 0; i2 < iSize; i2++) { if (!abPivoted[i2]) { Real fAbs = Math<Real>::FAbs(rkInvA[i1][i2]); if (fAbs > fMax) { fMax = fAbs; iRow = i1; iCol = i2; } } } } } if (fMax == (Real)0.0) { // matrix is not invertible WM4_DELETE[] aiColIndex; WM4_DELETE[] aiRowIndex; WM4_DELETE[] abPivoted; return false; } abPivoted[iCol] = true; // swap rows so that A[iCol][iCol] contains the pivot entry if (iRow != iCol) { rkInvA.SwapRows(iRow,iCol); } // keep track of the permutations of the rows aiRowIndex[i0] = iRow; aiColIndex[i0] = iCol; // scale the row so that the pivot entry is 1 Real fInv = ((Real)1.0)/rkInvA[iCol][iCol]; rkInvA[iCol][iCol] = (Real)1.0; for (i2 = 0; i2 < iSize; i2++) { rkInvA[iCol][i2] *= fInv; } // zero out the pivot column locations in the other rows for (i1 = 0; i1 < iSize; i1++) { if (i1 != iCol) { fSave = rkInvA[i1][iCol]; rkInvA[i1][iCol] = (Real)0.0; for (i2 = 0; i2 < iSize; i2++) { rkInvA[i1][i2] -= rkInvA[iCol][i2]*fSave; } } } }
bool LinearSystem<Real>::SymmetricInverse (const GMatrix<Real>& rkA, GMatrix<Real>& rkInvA) { // Same algorithm as SolveSymmetric, but applied simultaneously to // columns of identity matrix. int iSize = rkA.GetRows(); GMatrix<Real> kTmp = rkA; Real* afV = new Real[iSize]; assert( afV ); int i0, i1; for (i0 = 0; i0 < iSize; i0++) { for (i1 = 0; i1 < iSize; i1++) rkInvA[i0][i1] = ( i0 != i1 ? (Real)0.0 : (Real)1.0 ); } for (i1 = 0; i1 < iSize; i1++) { for (i0 = 0; i0 < i1; i0++) afV[i0] = kTmp[i1][i0]*kTmp[i0][i0]; afV[i1] = kTmp[i1][i1]; for (i0 = 0; i0 < i1; i0++) afV[i1] -= kTmp[i1][i0]*afV[i0]; kTmp[i1][i1] = afV[i1]; for (i0 = i1+1; i0 < iSize; i0++) { for (int i2 = 0; i2 < i1; i2++) kTmp[i0][i1] -= kTmp[i0][i2]*afV[i2]; kTmp[i0][i1] /= afV[i1]; } } delete[] afV; for (int iCol = 0; iCol < iSize; iCol++) { // forward substitution for (i0 = 0; i0 < iSize; i0++) { for (i1 = 0; i1 < i0; i1++) rkInvA[i0][iCol] -= kTmp[i0][i1]*rkInvA[i1][iCol]; } // diagonal division for (i0 = 0; i0 < iSize; i0++) { if ( Math<Real>::FAbs(kTmp[i0][i0]) <= Math<Real>::EPSILON ) return false; rkInvA[i0][iCol] /= kTmp[i0][i0]; } // back substitution for (i0 = iSize-2; i0 >= 0; i0--) { for (i1 = i0+1; i1 < iSize; i1++) rkInvA[i0][iCol] -= kTmp[i1][i0]*rkInvA[i1][iCol]; } } return true; }
bool LinearSystem<Real>::Inverse (const GMatrix<Real>& rkA, GMatrix<Real>& rkInvA) { // computations are performed in-place assert( rkA.GetRows() == rkA.GetColumns() ); int iSize = rkInvA.GetRows(); rkInvA = rkA; if (aiColIndex == NULL) aiColIndex = new int[iSize]; //assert( aiColIndex ); if (aiRowIndex == NULL) aiRowIndex = new int[iSize]; //assert( aiRowIndex ); if (abPivoted == NULL) abPivoted = new bool[iSize]; //assert( abPivoted ); memset(abPivoted,0,iSize*sizeof(bool)); int i1, i2, iRow = 0, iCol = 0; Real fSave; // elimination by full pivoting for (int i0 = 0; i0 < iSize; i0++) { // search matrix (excluding pivoted rows) for maximum absolute entry Real fMax = 0.0f; for (i1 = 0; i1 < iSize; i1++) { if ( !abPivoted[i1] ) { for (i2 = 0; i2 < iSize; i2++) { if ( !abPivoted[i2] ) { Real fAbs = fabs(rkInvA[i1][i2]); if ( fAbs > fMax ) { fMax = fAbs; iRow = i1; iCol = i2; } } } } } if ( fMax == (Real)0.0 ) { // matrix is not invertible delete[] aiColIndex; delete[] aiRowIndex; delete[] abPivoted; return false; } abPivoted[iCol] = true; // swap rows so that A[iCol][iCol] contains the pivot entry if ( iRow != iCol ) rkInvA.SwapRows(iRow,iCol); // keep track of the permutations of the rows aiRowIndex[i0] = iRow; aiColIndex[i0] = iCol; // scale the row so that the pivot entry is 1 Real fInv = ((Real)1.0)/rkInvA[iCol][iCol]; rkInvA[iCol][iCol] = (Real)1.0; for (i2 = 0; i2 < iSize; i2++) rkInvA[iCol][i2] *= fInv; // zero out the pivot column locations in the other rows for (i1 = 0; i1 < iSize; i1++) { if ( i1 != iCol ) { fSave = rkInvA[i1][iCol]; rkInvA[i1][iCol] = (Real)0.0; for (i2 = 0; i2 < iSize; i2++) rkInvA[i1][i2] -= rkInvA[iCol][i2]*fSave; } } } // reorder rows so that A[][] stores the inverse of the original matrix for (i1 = iSize-1; i1 >= 0; i1--) { if ( aiRowIndex[i1] != aiColIndex[i1] ) { for (i2 = 0; i2 < iSize; i2++) { fSave = rkInvA[i2][aiRowIndex[i1]]; rkInvA[i2][aiRowIndex[i1]] = rkInvA[i2][aiColIndex[i1]]; rkInvA[i2][aiColIndex[i1]] = fSave; } } } //delete[] aiColIndex; //delete[] aiRowIndex; //delete[] abPivoted; return true; }