Created attachment 384 [details]
The current way to build the Householder elementary reflectors is not stable for some pathological test cases in the LAPACK tests suite. The attached patch has a makeStableHouseholder() function for this purpose. In addition, it produces positive Householder coefficients as required by the LAPACK test routines and some applications.
Now the main problem is that the way the norm is computed makes it more expensive, and then we should not use by default. But then we should find the the best way to choose it during the various QR decomposition, maybe by adding another template parameter to those classes ?
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