How can I use "symbfact" to speed up several consecutive Cholesky factorizations?

Hi all,

I just came across the "symbfact" command. It seems powerful, but I'm wondering exactly how take advantage of it. I need to do several hundred consecutive Cholesky factorizations of matrices that have the same sparsity structure (different entries). Symbfact tells me the sparsity structure of the resulting Cholesky factors, but how can I take advantage of that?

>> % For nxn Q, n~20000

>> L = chol(Q);

>> S = symbfact(L);

>> % How can I use S to efficiently calculate subsequent L's?

Thanks!

Answer 1

[Richard Brown]

You can't (unless something has changed recently). When I had to do this, I ended up working with the C code in CSparse directly.

[Ted]

That seems strange! It seems like the main purpose of "symbfact" is my application. Is it good for anything then?

When you worked with CSparse, did you end up using the template sparsity structure of L to customize the recursively defined formulas for L's entries? Formulas here: http://rosettacode.org/wiki/Cholesky_decomposition

That's the only other strategy I can think of, but it's very tedious and challenging. What did you do?

[Richard Brown]

I split the function cs_cholsol into two -- in the distributed version it performs symbolic and numerical factorisation, and then the triangular solves all in the one function.

I took out the symbolic step, and added the css object as an input parameter so that you can just compute it once.

[Ted]

Thank you for sharing! Did your strategy yield significant speed-up?

[Richard Brown]

It did -- for my problem the symbolic part was taking more than half the time

[Alec Jacobson]

Has anything changed on this front? Is it still impossible to use the symbolic factorization from symbfact for repeated solves?