Error in SGESVDX in Lapack3.6.1 (also in 3.6.0)

[elivanova]

There looks like a bug in SGESVDX in Lapack3.6.1 (also in 3.6.0):

At the beginning, SGESVDX check the NORM of A and then calls SLASCL to modify the values of the elements if they are extreme (line 506-514). At the end calls SLASCL to adjust back the values of elements of S if A has been modified (line 817-814). The problem is that, in many cases, S is not changed even A is modified. That means that the modification in A does not get transfered into S. There should be no adjustment need for S. And this unnecessary adjustment causes overflow or underflow in many cases. An exampleis:

JOBU='V', JOBVT='V', RANGE='V', N=1, and A and S have some big numbers. A gets modifiled but S does not change (look at the call to SBDSVDX). Calling to SLASCL at the end causes overflow.

Workaround: check if S is changed before calling to SLASCL at the end. This may not be real fix.

[julielangou]

Same than #38