Bug: det() gives false zero

[Charlie Dyson]

I've been using octave to try to find zeros of the determinants of
various matrices depending upon some parameter, but have found that
when the entries in such matrices have wildly different magnitudes
det() may claim that the matrix is singular when it is not. Using
Octave 3.0.1 running on XP.

Unfortunately I'll be going on holiday in a few hours so probably
won't be able to get back to you for a week or so.

Here's some code that reproduces the problem, along with a workaround
I've been using to cope with it.

Incidentally, I couldn't see any email address at
http://www.gnu.org/software/octave/bugs.html, though I was able to
find one in the pdf manual.

Many thanks,

Charlie Dyson

-- CUT --
D = [ -1.001254707117086 0.00125470711708553 1 0 0 0
 0.00125470711708553 -1.001254707117086 0 1 0 0
 0 0 -1.050021149616144 -280214911531872 1 0
 0 0 -5.590061183230268e-021 -0.9499793732213449 0 1
 1 0 0 0 0 0
 0 0 0 0 0 1 ];

disp("Compute determinant with det function:")
disp( det(D) );
disp("Should not have been zero!");
disp( "" );

disp("Now try LU decomposition");
[l,u,p] = lu( D );
disp("Should all be non-zero:");
disp( det(l) );
disp( det(u) );
disp( det(p) );
disp("Again we have a false zero");
disp("");

disp("Now compute det of L, U by product of diagonal");
detL = 1;
for n = 1:rows(D)
	detL = detL*l(n,n);
endfor
detU = 1;
for n = 1:rows(D)
	detU = detU*u(n,n);
endfor
disp("Det of l,u,p given by:");
disp( detL );
disp( detU );
disp( det(p) );

disp("Correct value of determinant is:");
disp( detL*detU*det(p) )