Looking at the source it appears to me (verified with a debugger) that symmetry
is accounted for in eig()
I missed it, but I found it now. (I must had a typo in my grep.)
and the hessenberg routines are not called except from
hess(). Since a Hessenberg reduction is intended for nonsymmetric matrices (though it will produce a tridiagonal matrix in the symmetric case with exact arithmetic) it seems like an unnecessary complication to make hess() do something it was not
intended for and currently it shows what the Hessenberg reduction does to a symmetric matrix with non-exact arithmetic.
I does particularly badly for rosser() and that has indeed an educational value. The behavior is different from matlab, but that would not sway me either.
Finally: I use octave to test/develop numerical algorithms and so I need to call specific routines on occasion which is probably not needed for most users. For example, to call a specific eigensolver (QR, divide and conquer, MR^3) I need a wrapper function anyway.
I copied the help list, since this started there and your comment may be interesting to others concerned with accuracy.
Thanks, I consider the matter closed.
-Matyas