/* solve a linear system using Cholesky, LU, and QR, with various orderings */
int demo2 (problem *Prob)
{
cs *A, *C ;
double *b, *x, *resid, t, tol ;
int k, m, n, ok, order, nb, ns, *r, *s, *rr, sprank ;
csd *D ;
if (!Prob) return (0) ;
A = Prob->A ; C = Prob->C ; b = Prob->b ; x = Prob->x ; resid = Prob->resid;
m = A->m ; n = A->n ;
tol = Prob->sym ? 0.001 : 1 ; /* partial pivoting tolerance */
D = cs_dmperm (C, 1) ; /* randomized dmperm analysis */
if (!D) return (0) ;
nb = D->nb ; r = D->r ; s = D->s ; rr = D->rr ;
sprank = rr [3] ;
for (ns = 0, k = 0 ; k < nb ; k++)
{
ns += ((r [k+1] == r [k]+1) && (s [k+1] == s [k]+1)) ;
}
printf ("blocks: %g singletons: %g structural rank: %g\n",
(double) nb, (double) ns, (double) sprank) ;
cs_dfree (D) ;
for (order = 0 ; order <= 3 ; order += 3) /* natural and amd(A'*A) */
{
if (!order && m > 1000) continue ;
printf ("QR ") ;
print_order (order) ;
rhs (x, b, m) ; /* compute right-hand side */
t = tic () ;
ok = cs_qrsol (order, C, x) ; /* min norm(Ax-b) with QR */
printf ("time: %8.2f ", toc (t)) ;
print_resid (ok, C, x, b, resid) ; /* print residual */
}
if (m != n || sprank < n) return (1) ; /* return if rect. or singular*/
for (order = 0 ; order <= 3 ; order++) /* try all orderings */
{
if (!order && m > 1000) continue ;
printf ("LU ") ;
print_order (order) ;
rhs (x, b, m) ; /* compute right-hand side */
t = tic () ;
ok = cs_lusol (order, C, x, tol) ; /* solve Ax=b with LU */
printf ("time: %8.2f ", toc (t)) ;
print_resid (ok, C, x, b, resid) ; /* print residual */
}
if (!Prob->sym) return (1) ;
for (order = 0 ; order <= 1 ; order++) /* natural and amd(A+A') */
{
if (!order && m > 1000) continue ;
printf ("Chol ") ;
print_order (order) ;
rhs (x, b, m) ; /* compute right-hand side */
t = tic () ;
ok = cs_cholsol (order, C, x) ; /* solve Ax=b with Cholesky */
printf ("time: %8.2f ", toc (t)) ;
print_resid (ok, C, x, b, resid) ; /* print residual */
}
return (1) ;
}
/* cs_dmperm: maximum matching or Dulmage-Mendelsohn permutation. */
void mexFunction
(
int nargout,
mxArray *pargout [ ],
int nargin,
const mxArray *pargin [ ]
)
{
double seed ;
cs *A, Amatrix ;
csd *D ;
csi m, n, *jmatch, iseed ;
if (nargin < 1 || nargin > 2 || nargout > 6)
{
mexErrMsgTxt ("Usage: [p,q,r,s,cc,rr] = cs_dmperm (A,seed)") ;
}
seed = (nargin > 1) ? mxGetScalar (pargin [1]) : 0 ; /* get seed */
iseed = (seed > 0 && seed < 1) ? (seed * RAND_MAX) : seed ;
A = cs_mex_get_sparse (&Amatrix, 0, 0, pargin [0]) ; /* get A */
n = A->n ;
m = A->m ;
if (nargout <= 1)
{
jmatch = cs_maxtrans (A, iseed) ; /* max. matching */
pargout [0] = cs_mex_put_int (jmatch+m, n, 1, 0) ; /* return imatch */
cs_free (jmatch) ;
}
else
{
D = cs_dmperm (A, iseed) ; /* Dulmage-Mendelsohn decomposition */
pargout [0] = cs_mex_put_int (D->p, m, 1, 0) ;
pargout [1] = cs_mex_put_int (D->q, n, 1, 0) ;
pargout [2] = cs_mex_put_int (D->r, D->nb+1, 1, 0) ;
pargout [3] = cs_mex_put_int (D->s, D->nb+1, 1, 0) ;
pargout [4] = cs_mex_put_int (D->cc, 5, 1, 0) ;
pargout [5] = cs_mex_put_int (D->rr, 5, 1, 0) ;
cs_dfree (D) ;
}
}
