# taucs_chget

retrieve the Cholesky factorization at the scilab level

## Calling Sequence

    [Ct,p] = taucs_chget(C_ptr)

## 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). Traditionnaly, 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
    stacksize(3000000)  // the last PlotSparse need memory
    // first load a sparse matrix
    [A] = ReadHBSparse(SCI+"/modules/umfpack/examples/bcsstk24.rsa");
    // compute the factorization
    Cptr = taucs_chfact(A);
    // retrieve the factor at scilab level
    [Ct, p] = taucs_chget(Cptr);
    // plot the initial matrix
    xset("window",0) ; clf()
    PlotSparse(A) ; xtitle("Initial matrix A (bcsstk24.rsa)")
    // plot the permuted matrix
    B = A(p,p);
    xset("window",1) ; clf()
    PlotSparse(B) ; xtitle("Permuted matrix B = A(p,p)")
    // plot the upper triangle Ct
    xset("window",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)

[A] = ReadHBSparse(SCI+"/modules/umfpack/examples/bcsstk24.rsa"); Cptr = taucs_chfact(A); [Ct, p] = taucs_chget(Cptr); PlotSparse(A) ; xtitle("Initial matrix A (bcsstk24.rsa)")

## See Also

- taucs_chfact
- taucs_chsolve
- taucs_chdel
- taucs_chinfo
- taucs_chget
- cond2sp