diff options
author | Gael Guennebaud <g.gael@free.fr> | 2016-07-06 13:45:30 +0200 |
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committer | Gael Guennebaud <g.gael@free.fr> | 2016-07-06 13:45:30 +0200 |
commit | 5b3a6f51d353bb3b35f6d15f2455774b73d088e0 (patch) | |
tree | 945cb44f2a69c3bb16e6fc465c4d7e035ab3c059 /Eigen/src/Eigenvalues/RealSchur.h | |
parent | d2b5a19e0f2871b553b21c21dfc834eebab8d348 (diff) |
Improve numerical robustness of RealSchur: add scaling and compare sub-diag entries to largest diagonal entry instead of the 2 neighbors.
Diffstat (limited to 'Eigen/src/Eigenvalues/RealSchur.h')
-rw-r--r-- | Eigen/src/Eigenvalues/RealSchur.h | 29 |
1 files changed, 21 insertions, 8 deletions
diff --git a/Eigen/src/Eigenvalues/RealSchur.h b/Eigen/src/Eigenvalues/RealSchur.h index f4ded69b6..1f333f64b 100644 --- a/Eigen/src/Eigenvalues/RealSchur.h +++ b/Eigen/src/Eigenvalues/RealSchur.h @@ -236,7 +236,7 @@ template<typename _MatrixType> class RealSchur typedef Matrix<Scalar,3,1> Vector3s; Scalar computeNormOfT(); - Index findSmallSubdiagEntry(Index iu); + Index findSmallSubdiagEntry(Index iu, const Scalar& maxDiagEntry); void splitOffTwoRows(Index iu, bool computeU, const Scalar& exshift); void computeShift(Index iu, Index iter, Scalar& exshift, Vector3s& shiftInfo); void initFrancisQRStep(Index il, Index iu, const Vector3s& shiftInfo, Index& im, Vector3s& firstHouseholderVector); @@ -253,19 +253,25 @@ RealSchur<MatrixType>& RealSchur<MatrixType>::compute(const EigenBase<InputType> if (maxIters == -1) maxIters = m_maxIterationsPerRow * matrix.rows(); + Scalar scale = matrix.derived().cwiseAbs().maxCoeff(); + // Step 1. Reduce to Hessenberg form - m_hess.compute(matrix.derived()); + m_hess.compute(matrix.derived()/scale); // Step 2. Reduce to real Schur form computeFromHessenberg(m_hess.matrixH(), m_hess.matrixQ(), computeU); + + m_matT *= scale; return *this; } template<typename MatrixType> template<typename HessMatrixType, typename OrthMatrixType> RealSchur<MatrixType>& RealSchur<MatrixType>::computeFromHessenberg(const HessMatrixType& matrixH, const OrthMatrixType& matrixQ, bool computeU) -{ - m_matT = matrixH; +{ + using std::abs; + + m_matT = matrixH; if(computeU) m_matU = matrixQ; @@ -287,14 +293,18 @@ RealSchur<MatrixType>& RealSchur<MatrixType>::computeFromHessenberg(const HessMa if(norm!=0) { + Scalar maxDiagEntry = m_matT.cwiseAbs().diagonal().maxCoeff(); + while (iu >= 0) { - Index il = findSmallSubdiagEntry(iu); + Index il = findSmallSubdiagEntry(iu,maxDiagEntry); // Check for convergence if (il == iu) // One root found { m_matT.coeffRef(iu,iu) = m_matT.coeff(iu,iu) + exshift; + // keep track of the largest diagonal coefficient + maxDiagEntry = numext::maxi(maxDiagEntry,abs(m_matT.coeffRef(iu,iu))); if (iu > 0) m_matT.coeffRef(iu, iu-1) = Scalar(0); iu--; @@ -303,6 +313,8 @@ RealSchur<MatrixType>& RealSchur<MatrixType>::computeFromHessenberg(const HessMa else if (il == iu-1) // Two roots found { splitOffTwoRows(iu, computeU, exshift); + // keep track of the largest diagonal coefficient + maxDiagEntry = numext::maxi(maxDiagEntry,numext::maxi(abs(m_matT.coeff(iu,iu)), abs(m_matT.coeff(iu-1,iu-1)))); iu -= 2; iter = 0; } @@ -317,6 +329,8 @@ RealSchur<MatrixType>& RealSchur<MatrixType>::computeFromHessenberg(const HessMa Index im; initFrancisQRStep(il, iu, shiftInfo, im, firstHouseholderVector); performFrancisQRStep(il, im, iu, computeU, firstHouseholderVector, workspace); + // keep track of the largest diagonal coefficient + maxDiagEntry = numext::maxi(maxDiagEntry,m_matT.cwiseAbs().diagonal().segment(im,iu-im).maxCoeff()); } } } @@ -346,14 +360,13 @@ inline typename MatrixType::Scalar RealSchur<MatrixType>::computeNormOfT() /** \internal Look for single small sub-diagonal element and returns its index */ template<typename MatrixType> -inline Index RealSchur<MatrixType>::findSmallSubdiagEntry(Index iu) +inline Index RealSchur<MatrixType>::findSmallSubdiagEntry(Index iu, const Scalar& maxDiagEntry) { using std::abs; Index res = iu; while (res > 0) { - Scalar s = abs(m_matT.coeff(res-1,res-1)) + abs(m_matT.coeff(res,res)); - if (abs(m_matT.coeff(res,res-1)) <= NumTraits<Scalar>::epsilon() * s) + if (abs(m_matT.coeff(res,res-1)) <= NumTraits<Scalar>::epsilon() * maxDiagEntry) break; res--; } |