1 #include "cs.h"
2 /* column counts of LL'=A or LL'=A'A, given parent & post ordering */
3 #define HEAD(k,j) (ata ? head [k] : j)
4 #define NEXT(J) (ata ? next [J] : -1)
init_ata(cs * AT,const CS_INT * post,CS_INT * w,CS_INT ** head,CS_INT ** next)5 static void init_ata (cs *AT, const CS_INT *post, CS_INT *w, CS_INT **head, CS_INT **next)
6 {
7 CS_INT i, k, p, m = AT->n, n = AT->m, *ATp = AT->p, *ATi = AT->i ;
8 *head = w+4*n, *next = w+5*n+1 ;
9 for (k = 0 ; k < n ; k++) w [post [k]] = k ; /* invert post */
10 for (i = 0 ; i < m ; i++)
11 {
12 for (k = n, p = ATp[i] ; p < ATp[i+1] ; p++) k = CS_MIN (k, w [ATi[p]]);
13 (*next) [i] = (*head) [k] ; /* place row i in linked list k */
14 (*head) [k] = i ;
15 }
16 }
cs_counts(const cs * A,const CS_INT * parent,const CS_INT * post,CS_INT ata)17 CS_INT *cs_counts (const cs *A, const CS_INT *parent, const CS_INT *post, CS_INT ata)
18 {
19 CS_INT i, j, k, n, m, J, s, p, q, jleaf, *ATp, *ATi, *maxfirst, *prevleaf,
20 *ancestor, *head = NULL, *next = NULL, *colcount, *w, *first, *delta ;
21 cs *AT ;
22 if (!CS_CSC (A) || !parent || !post) return (NULL) ; /* check inputs */
23 m = A->m ; n = A->n ;
24 s = 4*n + (ata ? (n+m+1) : 0) ;
25 delta = colcount = cs_malloc (n, sizeof (CS_INT)) ; /* allocate result */
26 w = cs_malloc (s, sizeof (CS_INT)) ; /* get workspace */
27 AT = cs_transpose (A, 0) ; /* AT = A' */
28 if (!AT || !colcount || !w) return (cs_idone (colcount, AT, w, 0)) ;
29 ancestor = w ; maxfirst = w+n ; prevleaf = w+2*n ; first = w+3*n ;
30 for (k = 0 ; k < s ; k++) w [k] = -1 ; /* clear workspace w [0..s-1] */
31 for (k = 0 ; k < n ; k++) /* find first [j] */
32 {
33 j = post [k] ;
34 delta [j] = (first [j] == -1) ? 1 : 0 ; /* delta[j]=1 if j is a leaf */
35 for ( ; j != -1 && first [j] == -1 ; j = parent [j]) first [j] = k ;
36 }
37 ATp = AT->p ; ATi = AT->i ;
38 if (ata) init_ata (AT, post, w, &head, &next) ;
39 for (i = 0 ; i < n ; i++) ancestor [i] = i ; /* each node in its own set */
40 for (k = 0 ; k < n ; k++)
41 {
42 j = post [k] ; /* j is the kth node in postordered etree */
43 if (parent [j] != -1) delta [parent [j]]-- ; /* j is not a root */
44 for (J = HEAD (k,j) ; J != -1 ; J = NEXT (J)) /* J=j for LL'=A case */
45 {
46 for (p = ATp [J] ; p < ATp [J+1] ; p++)
47 {
48 i = ATi [p] ;
49 q = cs_leaf (i, j, first, maxfirst, prevleaf, ancestor, &jleaf);
50 if (jleaf >= 1) delta [j]++ ; /* A(i,j) is in skeleton */
51 if (jleaf == 2) delta [q]-- ; /* account for overlap in q */
52 }
53 }
54 if (parent [j] != -1) ancestor [j] = parent [j] ;
55 }
56 for (j = 0 ; j < n ; j++) /* sum up delta's of each child */
57 {
58 if (parent [j] != -1) colcount [parent [j]] += colcount [j] ;
59 }
60 return (cs_idone (colcount, AT, w, 1)) ; /* success: free workspace */
61 }
62