Thread Subject: backslash for sparse matrices

Dear all,

I am just trying to figure out, which algorithm is used when invoking \ for a sparse linear system of equations.

for spparms('spumoni',2) I get following output for a A being square and sparse.

sp\: bandwidth = 181+1+181.
sp\: is A diagonal? no.
sp\: is band density (0.01) > bandden (0.50) to try banded solver? no.
sp\: is A triangular? no.
sp\: is A morally triangular? yes.
sp\: permute and solve.

What means morally triangular in that case? Does it mean, A is a permutation of a triangular matrix --> then X is computed with a permuted backsubstitution algorithm.

or does Matlab use CHOLMOD to compute X?

Thanks for your answers,
Wolfgang

"Wolfgang Schwanghart" <schwanghartremove.this@googlemail.com> wrote in
message news:gtmcb9$qtc$1@fred.mathworks.com...
> Dear all,
>
> I am just trying to figure out, which algorithm is used when invoking \
> for a sparse linear system of equations.

Take a look at the Algorithm section of the MLDIVIDE reference page:

http://www.mathworks.com/access/helpdesk/help/techdoc/ref/mldivide.html

--
Steve Lord
slord@mathworks.com

"Wolfgang Schwanghart" <schwanghartremove.this@googlemail.com> wrote in message <gtmcb9$qtc$1@fred.mathworks.com>...
> Dear all,
>
> I am just trying to figure out, which algorithm is used when invoking \ for a sparse linear system of equations.
>
> for spparms('spumoni',2) I get following output for a A being square and sparse.
>
> sp\: bandwidth = 181+1+181.
> sp\: is A diagonal? no.
> sp\: is band density (0.01) > bandden (0.50) to try banded solver? no.
> sp\: is A triangular? no.
> sp\: is A morally triangular? yes.
> sp\: permute and solve.
>
> What means morally triangular in that case? Does it mean, A is a permutation of a triangular matrix --> then X is computed with a permuted backsubstitution algorithm.
>
> or does Matlab use CHOLMOD to compute X?
>
> Thanks for your answers,
> Wolfgang

"Morally triangular" means that A is a permuted triangular matrix. The solver used is one written by The MathWorks (not me). It's not using CHOLMOD in that case.