taucs_chget

Arguments

C_ptr

a pointer to the Cholesky factorization (C,p : A(p,p)=CC')

Ct

a scilab sparse matrix (you get the upper triangle i.e. Ct is equal to C')

p

column vector storing the permutation

Description

This function may be used if you want to plot the sparse pattern of the Cholesky factorization (or if you code something which use the factors). Traditionally, the factorization is written :

P A P' = C C'

with P' the permutation matrix associated to the permutation p. As we get the upper triangle Ct (= C'), in scilab syntax we can write :

A(p,p) = Ct' * Ct

Examples

// Example #1 : a small linear test system
A = sparse( [ 2 -1  0  0  0;
             -1  2 -1  0  0;
              0 -1  2 -1  0;
              0  0 -1  2 -1;
              0  0  0 -1  2] );
Cp = taucs_chfact(A);
[Ct, p] = taucs_chget(Cp);
full(A(p,p) - Ct'*Ct)  // this must be near the null matrix
taucs_chdel(Cp)

// Example #2 a real example
// first load a sparse matrix
[A] = ReadHBSparse(SCI+"/modules/umfpack/demos/bcsstk24.rsa");
// compute the factorization
Cptr = taucs_chfact(A);
// retrieve the factor at scilab level
[Ct, p] = taucs_chget(Cptr);
// plot the initial matrix
scf(0);
clf
PlotSparse(A) ; xtitle("Initial matrix A (bcsstk24.rsa)")
// plot the permuted matrix
B = A(p,p);
scf(1);
clf
PlotSparse(B) ; xtitle("Permuted matrix B = A(p,p)")
// plot the upper triangle Ct
scf(2);
clf
PlotSparse(Ct) ; xtitle("The pattern of Ct (A(p,p) = C*Ct)")
// retrieve cnz
[OK, n, cnz] = taucs_chinfo(Cptr)
// cnz is superior to the realnumber of non zeros elements of C :
cnz_exact = nnz(Ct)
// do not forget to clear memory
taucs_chdel(Cptr)

See also

• taucs_chfact — cholesky factorization of a sparse s.p.d. matrix
• taucs_chsolve — solves a linear s.p.d. system A*X = B from Cholesky factors of the sparse A
• taucs_chdel — utility function used with taucs_chfact
• taucs_chinfo — get information on Cholesky factors
• taucs_chget — retrieve the Cholesky factorization at the scilab level
• cond2sp — computes an approximation of the 2-norm condition number of a s.p.d. sparse matrix