Re: Octave hangs forever trying to invert singular matrix

[Vic Norton]

A singular value decomposition,
  [U, S, V] = svd(A, 1);
shows that your matrix has effective rank 478. For sig = diag(S),
  sig(1) = 3.6494
  ...
  sig(478) = 0.020490
  sig(479) = 8.3016e-17
  sig(480) = 3.5993e-17

Even worse, the vector
  onev = ones(480, 1)
essentially lies in the 2-dimensional space corresponding to the two
small singular values. If
  Z = U(:, [479, 480]);
  onev = ones(480, 1);
  onez = U(:, [479, 480]) * (U(:, [479, 480])' * onev);
Then
  norm(onez - onev)/norm(onev) = 9.4929e-15.

I don't see how any numerical routine can give you a reasonable answer.
This is a 0/0 problem.

Regards,

Vic


On Dec 22, 2009, at 1:19 PM, Carlo de Falco wrote:

> 
> On 22 Dec 2009, at 19:17, Carlo de Falco wrote:
> 
>> Hi,
>> 
>> I have a 480x480 sparse matrix of rank 479
>> trying to solve
>> 
>> A\ones(480,1)
>> 
>> makes matlab throw a warning and return garbage
>> 
>>>> A\ones(480,1)
>> Warning: Matrix is close to singular or badly scaled.
>>      Results may be inaccurate. RCOND = 3.815118e-20.
>> 
>> ans =
>> 
>> 1.0e+17 *
>> 
>> -0.2637
>> -0.2637
>> -0.2637
>> -0.2637
>> -0.2637
>> -0.2637
>> -0.2637
>> 
>> on the other hand Octave hangs forever.
>> Is there a way to check before-hand whether the system can be solved  
>> to prevent Octave from going into "Guru meditation mode"?
>> Is this to be considered a bug?
>> 
>> I am using Thomas' 3.2.3 binary on Mac OS X.
>> c.
> 
> If anyone wants to try with the particular matrix that showed the  
> problem for me, it can be found here:
> http://mox.polimi.it/~carlo/calnum/A.mat
> 
> c.
> 
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