Improve QR-algorithm stability #136
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…ute eigenvalues in double shift
Codecov ReportAll modified and coverable lines are covered by tests ✅
Additional details and impacted files@@ Coverage Diff @@
## master #136 +/- ##
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+ Coverage 95.21% 95.47% +0.25%
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Files 10 10
Lines 815 839 +24
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+ Hits 776 801 +25
+ Misses 39 38 -1 ☔ View full report in Codecov by Sentry. |
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haampie
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Previously a perfect single shift was used in the 2x2 case of real eigenvalues, which can be disastrous for ill-conditioned eigenvalues. The new implementation considers 2x2 blocks converged whether complex conjugate or real, and upper triangularizes it in case of real eigenvalues in a much more stable way. The most stable rotation is picked (there's a choice in case of two distinct eigenvalues), plus some formula manipulations and scaling tricks are applied.
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Previously a perfect single shift was used in the 2x2 case of real eigenvalues, which can be disastrous for ill-conditioned eigenvalues.
The new implementation considers 2x2 blocks converged whether complex conjugate or real, and upper triangularizes it in case of real eigenvalues in a much more stable way. The most stable rotation is picked (there's a choice in case of two distinct eigenvalues), plus some formula manipulations and scaling tricks are applied.