From bug-octave-request at bevo dot che dot wisc dot edu  Thu Jun  7 13:58:39 2001
Subject: Re: det() hangs on large matrix
From: "John W. Eaton" <jwe at bevo dot che dot wisc dot edu>
To: Christoph Spiel <cspiel at hammersmith-consulting dot com>
Cc: bug-octave at bevo dot che dot wisc dot edu
Date: Thu, 7 Jun 2001 13:57:54 -0500

On  7-Jun-2001, Christoph Spiel <cspiel at hammersmith-consulting dot com> wrote:

| On Tue, Jun 05, 2001 at 11:33:52AM -0500, John W. Eaton wrote:
| > Octave uses DGEDI from Linpack to compute the determinant.  The
| > problem is that in this loop in DGEDI,
| > 
| >    30       IF (DABS(DET(1)) .LT. TEN) GO TO 40
| >                DET(1) = DET(1)/TEN
| >                DET(2) = DET(2) + 1.0D0
| >             GO TO 30
| >    40       CONTINUE
| > 
| > your matrix results in DET(1) == Inf.  So dividing it by TEN does not
| > reduce its value and its absolute value never becomes less than 10,
| > and the loop repeats indefinitely.
| 
| What about using [D|Z]GETRF instead of DGEDI?  [D|Z]GETRF only does an
| LU-factorization, but as det(A) = det(L U) = det(U) = u_1 * ... * u_n,
| we could get a determinant.

I don't think this will solve the problem.  For the particular case
given in the original bug report, Octave's lu function (which is based
on dgetrf) will return a matrix with NaNs for U.

jwe



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