*tgex2: loosen swap acceptance threshold to fix false rejections#1299
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*tgex2: loosen swap acceptance threshold to fix false rejections#1299jschueller wants to merge 1 commit into
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The weak stability test in *TGEX2 rejects a block swap when the off-diagonal block norm BQRA21 exceeds THRESHA = TWENTY*EPS*SA. For certain matrices (reported by MathWorks from MATLAB's ORDQZ), this threshold is too tight -- BQRA21 can be ~5x larger than TWENTY*EPS*SA due to round-off in the preceding QZ steps, even though the swap is mathematically valid (verified via Sylvester equation-based proof). Increase the safety factor from TWENTY (20) to HUNDRED (100), which fixes all known failing cases (3x3 and 4x4 pencils) while remaining well below the BRQA21 bound that guards against truly invalid swaps. Closes Reference-LAPACK#1201
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The weak stability test in TGEX2 rejects a block swap when the off-diagonal block norm BQRA21 exceeds THRESHA = TWENTYEPSSA. For certain matrices (reported by MathWorks from MATLAB's ORDQZ), this threshold is too tight -- BQRA21 can be ~5x larger than TWENTYEPS*SA due to round-off in the preceding QZ steps, even though the swap is mathematically valid (verified via Sylvester equation-based proof).
Increase the safety factor from TWENTY (20) to HUNDRED (100), which fixes all known failing cases (3x3 and 4x4 pencils) while remaining well below the BRQA21 bound that guards against truly invalid swaps.
Closes #1201