As always, thanks for the reply W.
Yeah I was aiming to compute the smallest eigenvalue.
I guess my tittle was off. I was just trying to aim to the fact that the
stiffness matrix
I wrote to an output file and then I read was singular. Could a problem on
my part but I was still just checking since my changes
were minimal to the step example.
I'll double check what I did later too.
best,
Abbas
On Monday, October 28, 2024 at 10:57:05 PM UTC+1 Wolfgang Bangerth wrote:
>
> On 10/28/24 15:26, Abbas Ballout wrote:
> >
> > I wanted to look at the determinant that results from discritizng the
> > stokes problem so I started out with step22 and added this line right at
> > the end of the assembly:
> > {
> > std::ofstream out("matrix.txt");
> > system_matrix.print(out);
> > out.close();
> > }
> > After writing out the matrix I read the file with a Julia code (I can
> > attach it below if anyone wants to see) and it turns out the determinant
> > is zero. Is that normal? The BCs should have been applied at the point
> > right?
> >
> > Things I have tried:
> > 1) I tried the stokes from step 57 as well. Same thing
> > 2) I plotted the sparsity pattern (attached below) and it's the same
> > one I got from gnuplot with a big zero block in the lower right corner.
> > 3) I did the same thing with a laplace and I got the right determinant.
> >
> > I am doing this because I want to to get the corcivity/LBB constant
> > which is the smallest eigen/SVD value of the system. (mostly for the
> lols)
>
> The determinant of large matrices can not be computed in a reasonable
> way. Take the matrix 0.1*I, for example. If the identity matrix I is of
> size n times n, then the determinant det(0.1*I)=0.1^n, which you cannot
> compute if n>310 because the smallest floating point number that can be
> represented is around 1e-308. Of course n=310 is a pretty small matrix.
>
> There is of course also the issue that computing the determinant is an
> exceptionally expensive operation (at least n^3).
>
> If you're interested in the smallest eigenvalue, compute that rather
> than the determinant.
>
> Best
> W.
>
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