145 lines
5.6 KiB
C
145 lines
5.6 KiB
C
#include "cs.h"
|
|
/* breadth-first search for coarse decomposition (C0,C1,R1 or R0,R3,C3) */
|
|
static int cs_bfs (const cs *A, int n, int *wi, int *wj, int *queue,
|
|
const int *imatch, const int *jmatch, int mark)
|
|
{
|
|
int *Ap, *Ai, head = 0, tail = 0, j, i, p, j2 ;
|
|
cs *C ;
|
|
for (j = 0 ; j < n ; j++) /* place all unmatched nodes in queue */
|
|
{
|
|
if (imatch [j] >= 0) continue ; /* skip j if matched */
|
|
wj [j] = 0 ; /* j in set C0 (R0 if transpose) */
|
|
queue [tail++] = j ; /* place unmatched col j in queue */
|
|
}
|
|
if (tail == 0) return (1) ; /* quick return if no unmatched nodes */
|
|
C = (mark == 1) ? ((cs *) A) : cs_transpose (A, 0) ;
|
|
if (!C) return (0) ; /* bfs of C=A' to find R3,C3 from R0 */
|
|
Ap = C->p ; Ai = C->i ;
|
|
while (head < tail) /* while queue is not empty */
|
|
{
|
|
j = queue [head++] ; /* get the head of the queue */
|
|
for (p = Ap [j] ; p < Ap [j+1] ; p++)
|
|
{
|
|
i = Ai [p] ;
|
|
if (wi [i] >= 0) continue ; /* skip if i is marked */
|
|
wi [i] = mark ; /* i in set R1 (C3 if transpose) */
|
|
j2 = jmatch [i] ; /* traverse alternating path to j2 */
|
|
if (wj [j2] >= 0) continue ;/* skip j2 if it is marked */
|
|
wj [j2] = mark ; /* j2 in set C1 (R3 if transpose) */
|
|
queue [tail++] = j2 ; /* add j2 to queue */
|
|
}
|
|
}
|
|
if (mark != 1) cs_spfree (C) ; /* free A' if it was created */
|
|
return (1) ;
|
|
}
|
|
|
|
/* collect matched rows and columns into p and q */
|
|
static void cs_matched (int n, const int *wj, const int *imatch, int *p, int *q,
|
|
int *cc, int *rr, int set, int mark)
|
|
{
|
|
int kc = cc [set], j ;
|
|
int kr = rr [set-1] ;
|
|
for (j = 0 ; j < n ; j++)
|
|
{
|
|
if (wj [j] != mark) continue ; /* skip if j is not in C set */
|
|
p [kr++] = imatch [j] ;
|
|
q [kc++] = j ;
|
|
}
|
|
cc [set+1] = kc ;
|
|
rr [set] = kr ;
|
|
}
|
|
|
|
/* collect unmatched rows into the permutation vector p */
|
|
static void cs_unmatched (int m, const int *wi, int *p, int *rr, int set)
|
|
{
|
|
int i, kr = rr [set] ;
|
|
for (i = 0 ; i < m ; i++) if (wi [i] == 0) p [kr++] = i ;
|
|
rr [set+1] = kr ;
|
|
}
|
|
|
|
/* return 1 if row i is in R2 */
|
|
static int cs_rprune (int i, int j, double aij, void *other)
|
|
{
|
|
int *rr = (int *) other ;
|
|
return (i >= rr [1] && i < rr [2]) ;
|
|
}
|
|
|
|
/* 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)) ;
|
|
}
|