How can I create sparse symmetric positive definite linear system?

Dear All :) I'm looking for sparse symmetric positive definite linear system Ax=b. Is it possible to generate it in Matlab? I need matrix A about 50x50 (maximum 100x100 - minimum 20x20) and vector b. It might be floating point numbers... I prefer not compressed format ;)

Thank you in advance.

D.

Answer 1

[Richard Brown]

sprandsym is what you want.

m = 50;
density = 2/m; % for example
rc = 0.1; % Reciprocal condition number
A = sprandsym(m, density, rc, 1);

If you don't want it in compressed column format

A = full(A);

Verify positive definiteness

chol(A);

[D]

Thank you. And is it possible to generate sparse SPD but integer?

[Richard Brown]

Not directly, but you might try scaling and rounding results from sprandsym, or something like that

[sai chand]

How to generate the matrix b.

Can it be a random one independent of the way A is generated?

[sai chand]

I needed to generate a symmetric sparse positive definite matrix. can you help me in that?