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 factorisation
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)

See Also

• taucs_chfact cholesky factorisation of a sparse s.p.d. matrix
• taucs_chsolve solve a linear sparse (s.p.d.) system given the Cholesky factors
• 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