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bug #1557: fix RealSchur and EigenSolver for matrices with only zeros on the diagonal.

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(grafted from 2de8da70fd0b35849845dc76b2741bb0689f0643
)
This commit is contained in:
Gael Guennebaud 2018-12-12 17:30:08 +01:00
parent 25a1160849
commit 549c32cb42
1 changed files with 11 additions and 4 deletions
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15
Eigen/src/Eigenvalues/RealSchur.h
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@ -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& considerAsZero);
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);
@ -302,12 +302,16 @@ RealSchur<MatrixType>& RealSchur<MatrixType>::computeFromHessenberg(const HessMa
Index totalIter = 0; // iteration count for whole matrix
Scalar exshift(0); // sum of exceptional shifts
Scalar norm = computeNormOfT();
// sub-diagonal entries smaller than considerAsZero will be treated as zero.
// We use eps^2 to enable more precision in small eigenvalues.
Scalar considerAsZero = numext::maxi( norm * numext::abs2(NumTraits<Scalar>::epsilon()),
(std::numeric_limits<Scalar>::min)() );
if(norm!=Scalar(0))
{
while (iu >= 0)
{
Index il = findSmallSubdiagEntry(iu);
Index il = findSmallSubdiagEntry(iu,considerAsZero);
// Check for convergence
if (il == iu) // One root found
@ -364,14 +368,17 @@ 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& considerAsZero)
{
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)
s = numext::maxi(s * NumTraits<Scalar>::epsilon(), considerAsZero);
if (abs(m_matT.coeff(res,res-1)) <= s)
break;
res--;
}