This results in the stable_norm_5 unit test to fail on several systems (mostly clang, but I experienced it on g++4.9-cygwin, as well)
The problem is that sometimes abs for complex is implemented similar to this:
__complex_abs(const complex<_Tp>& __z)
_Tp __x = __z.real();
_Tp __y = __z.imag();
const _Tp __s = std::max(abs(__x), abs(__y));
if (__s == _Tp()) // well ...
__x /= __s;
__y /= __s;
return __s * sqrt(__x * __x + __y * __y);
This causes a division of Inf/Inf which results in NaN instead of Inf (which is a bug not caused by us). Nevertheless, even for working abs implementations, we could (actually for all *Norm implementations) increase stability and improve performance by computing the norm of a real-valued vector of twice the size (at least for Euclidean norm).
Related to that: Some of our decompositions (e.g. eigenvalue/svd) normalize the input matrix by dividing by .cwiseAbs().maxCoeff(). IMO it would make sense here to take use the max of (real().cwiseAbs(), imag().cwiseAbs()) here as well (no, need to compute any complex abs)
Agree with both proposals.