/* 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) ;
}
/* allocate a cs_dmperm or cs_scc result */
csd *cs_dalloc (int m, int n)
{
csd *D ;
D = cs_calloc (1, sizeof (csd)) ;
if (!D) return (NULL) ;
D->p = cs_malloc (m, sizeof (int)) ;
D->r = cs_malloc (m+6, sizeof (int)) ;
D->q = cs_malloc (n, sizeof (int)) ;
D->s = cs_malloc (n+6, sizeof (int)) ;
return ((!D->p || !D->r || !D->q || !D->s) ? cs_dfree (D) : D) ;
}
/* 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) ;
}
}
/* free workspace and return a csd result */
csd *cs_ddone (csd *D, cs *C, void *w, int ok)
{
cs_spfree (C) ; /* free temporary matrix */
cs_free (w) ; /* free workspace */
return (ok ? D : cs_dfree (D)) ; /* return result if OK, else free it */
}
/* Given A, compute coarse and then fine dmperm */
csd *cs_dmperm (const cs *A, int seed)
{
int m, n, i, j, k, cnz, nc, *jmatch, *imatch, *wi, *wj, *pinv, *Cp, *Ci,
*ps, *rs, nb1, nb2, *p, *q, *cc, *rr, *r, *s, ok ;
cs *C ;
csd *D, *scc ;
/* --- Maximum matching ------------------------------------------------- */
if (!CS_CSC (A)) return (NULL) ; /* check inputs */
m = A->m ; n = A->n ;
D = cs_dalloc (m, n) ; /* allocate result */
if (!D) return (NULL) ;
p = D->p ; q = D->q ; r = D->r ; s = D->s ; cc = D->cc ; rr = D->rr ;
jmatch = cs_maxtrans (A, seed) ; /* max transversal */
imatch = jmatch + m ; /* imatch = inverse of jmatch */
if (!jmatch) return (cs_ddone (D, NULL, jmatch, 0)) ;
/* --- Coarse decomposition --------------------------------------------- */
wi = r ; wj = s ; /* use r and s as workspace */
for (j = 0 ; j < n ; j++) wj [j] = -1 ; /* unmark all cols for bfs */
for (i = 0 ; i < m ; i++) wi [i] = -1 ; /* unmark all rows for bfs */
cs_bfs (A, n, wi, wj, q, imatch, jmatch, 1) ; /* find C1, R1 from C0*/
ok = cs_bfs (A, m, wj, wi, p, jmatch, imatch, 3) ; /* find R3, C3 from R0*/
if (!ok) return (cs_ddone (D, NULL, jmatch, 0)) ;
cs_unmatched (n, wj, q, cc, 0) ; /* unmatched set C0 */
cs_matched (n, wj, imatch, p, q, cc, rr, 1, 1) ; /* set R1 and C1 */
cs_matched (n, wj, imatch, p, q, cc, rr, 2, -1) ; /* set R2 and C2 */
cs_matched (n, wj, imatch, p, q, cc, rr, 3, 3) ; /* set R3 and C3 */
cs_unmatched (m, wi, p, rr, 3) ; /* unmatched set R0 */
cs_free (jmatch) ;
/* --- Fine decomposition ----------------------------------------------- */
pinv = cs_pinv (p, m) ; /* pinv=p' */
if (!pinv) return (cs_ddone (D, NULL, NULL, 0)) ;
C = cs_permute (A, pinv, q, 0) ;/* C=A(p,q) (it will hold A(R2,C2)) */
cs_free (pinv) ;
if (!C) return (cs_ddone (D, NULL, NULL, 0)) ;
Cp = C->p ;
nc = cc [3] - cc [2] ; /* delete cols C0, C1, and C3 from C */
if (cc [2] > 0) for (j = cc [2] ; j <= cc [3] ; j++) Cp [j-cc[2]] = Cp [j] ;
C->n = nc ;
if (rr [2] - rr [1] < m) /* delete rows R0, R1, and R3 from C */
{
cs_fkeep (C, cs_rprune, rr) ;
cnz = Cp [nc] ;
Ci = C->i ;
if (rr [1] > 0) for (k = 0 ; k < cnz ; k++) Ci [k] -= rr [1] ;
}
C->m = nc ;
scc = cs_scc (C) ; /* find strongly connected components of C*/
if (!scc) return (cs_ddone (D, C, NULL, 0)) ;
/* --- Combine coarse and fine decompositions --------------------------- */
ps = scc->p ; /* C(ps,ps) is the permuted matrix */
rs = scc->r ; /* kth block is rs[k]..rs[k+1]-1 */
nb1 = scc->nb ; /* # of blocks of A(R2,C2) */
for (k = 0 ; k < nc ; k++) wj [k] = q [ps [k] + cc [2]] ;
for (k = 0 ; k < nc ; k++) q [k + cc [2]] = wj [k] ;
for (k = 0 ; k < nc ; k++) wi [k] = p [ps [k] + rr [1]] ;
for (k = 0 ; k < nc ; k++) p [k + rr [1]] = wi [k] ;
nb2 = 0 ; /* create the fine block partitions */
r [0] = s [0] = 0 ;
if (cc [2] > 0) nb2++ ; /* leading coarse block A (R1, [C0 C1]) */
for (k = 0 ; k < nb1 ; k++) /* coarse block A (R2,C2) */
{
r [nb2] = rs [k] + rr [1] ; /* A (R2,C2) splits into nb1 fine blocks */
s [nb2] = rs [k] + cc [2] ;
nb2++ ;
}
if (rr [2] < m)
{
r [nb2] = rr [2] ; /* trailing coarse block A ([R3 R0], C3) */
s [nb2] = cc [3] ;
nb2++ ;
}
r [nb2] = m ;
s [nb2] = n ;
D->nb = nb2 ;
cs_dfree (scc) ;
return (cs_ddone (D, C, NULL, 1)) ;
}