From help-octave-request at bevo dot che dot wisc dot edu  Mon Dec 21 00:26:08 1998
Subject: Help...
From: Livne Oren <livneo at wisdom dot weizmann dot ac dot il>
To: help-octave at bevo dot che dot wisc dot edu
Date: Mon, 21 Dec 1998 08:25:42 +0200 (IST)

Dear Guys,

I am in a great need for eigenvalue package in my Ph.D. studies. I've
used matlab for this package ([V,D]=eig(a)) and it works, but I am
interested in 32 digits precision whereas matlab has 16 only. Hence I
decided to write my own routine. I got some programs (zgeev, qzhes, etc.)
in fortran but they are all unreliable. Octave uses them too and here's an
example that it doesn't work: (I am interested in general complex 4x4 and
8x8 matrices, full eigenvalues & eigenvectors):

a =

 Column 1:

  0.660674095153809 + 0.304533690214157i
  0.218023106455803 + 0.675618231296539i
  0.258169531822205 + 0.914756238460541i
  0.301558434963226 + 0.222921922802925i

 Column 2:

  0.283803135156631 + 0.052084900438786i
  0.474917590618134 + 0.666901826858521i
  0.590481042861938 + 0.390818536281586i
  0.554883301258087 + 0.487036257982254i

 Column 3:

  0.548641562461853 + 0.745089948177338i
  0.714440703392029 + 0.638778746128082i
  0.148456916213036 + 0.686463475227356i
  0.106128662824631 + 0.144878074526787i

 Column 4:

  0.144677996635437 + 0.371638923883438i
  0.906892597675323 + 0.958721995353699i
  0.942158818244934 + 0.547215640544891i
  0.406394332647324 + 0.574961066246033i

octave:66> eig(a)
error: zgeev failed to converge
error: evaluating index expression near line 66, column 1
octave:66> 



Since matlab works for any matrix I suspect the routines I have and which
octave uses are fine but need some driver of balancing the matrix. Can
any of you guys kindly help me? I would be of course interested in source
in C, but even fortran routines are fine. Maybe it just needs a call to
some balancing routine before zgeev, otherwise no convergence for the
eigenvectors. I have this problem already for many months but didn't find
yet ansewr :( I could make a lot of progress in the Ph.D. instead of
calling the slow matlab interface I wrote and/or go to the high precision.

If you find an answer please return to me at livneo at wisdom dot weizmann dot ac dot il
- Thanks! Oren.