1 #include "cs.h"
2 /* compute nnz(V) = S->lnz, S->pinv, S->leftmost, S->m2 from A and S->parent */
cs_vcount(const cs * A,css * S)3 static CS_INT cs_vcount (const cs *A, css *S)
4 {
5 CS_INT i, k, p, pa, n = A->n, m = A->m, *Ap = A->p, *Ai = A->i, *next, *head,
6 *tail, *nque, *pinv, *leftmost, *w, *parent = S->parent ;
7 S->pinv = pinv = cs_malloc (m+n, sizeof (CS_INT)) ; /* allocate pinv, */
8 S->leftmost = leftmost = cs_malloc (m, sizeof (CS_INT)) ; /* and leftmost */
9 w = cs_malloc (m+3*n, sizeof (CS_INT)) ; /* get workspace */
10 if (!pinv || !w || !leftmost)
11 {
12 cs_free (w) ; /* pinv and leftmost freed later */
13 return (0) ; /* out of memory */
14 }
15 next = w ; head = w + m ; tail = w + m + n ; nque = w + m + 2*n ;
16 for (k = 0 ; k < n ; k++) head [k] = -1 ; /* queue k is empty */
17 for (k = 0 ; k < n ; k++) tail [k] = -1 ;
18 for (k = 0 ; k < n ; k++) nque [k] = 0 ;
19 for (i = 0 ; i < m ; i++) leftmost [i] = -1 ;
20 for (k = n-1 ; k >= 0 ; k--)
21 {
22 for (p = Ap [k] ; p < Ap [k+1] ; p++)
23 {
24 leftmost [Ai [p]] = k ; /* leftmost[i] = min(find(A(i,:)))*/
25 }
26 }
27 for (i = m-1 ; i >= 0 ; i--) /* scan rows in reverse order */
28 {
29 pinv [i] = -1 ; /* row i is not yet ordered */
30 k = leftmost [i] ;
31 if (k == -1) continue ; /* row i is empty */
32 if (nque [k]++ == 0) tail [k] = i ; /* first row in queue k */
33 next [i] = head [k] ; /* put i at head of queue k */
34 head [k] = i ;
35 }
36 S->lnz = 0 ;
37 S->m2 = m ;
38 for (k = 0 ; k < n ; k++) /* find row permutation and nnz(V)*/
39 {
40 i = head [k] ; /* remove row i from queue k */
41 S->lnz++ ; /* count V(k,k) as nonzero */
42 if (i < 0) i = S->m2++ ; /* add a fictitious row */
43 pinv [i] = k ; /* associate row i with V(:,k) */
44 if (--nque [k] <= 0) continue ; /* skip if V(k+1:m,k) is empty */
45 S->lnz += nque [k] ; /* nque [k] is nnz (V(k+1:m,k)) */
46 if ((pa = parent [k]) != -1) /* move all rows to parent of k */
47 {
48 if (nque [pa] == 0) tail [pa] = tail [k] ;
49 next [tail [k]] = head [pa] ;
50 head [pa] = next [i] ;
51 nque [pa] += nque [k] ;
52 }
53 }
54 for (i = 0 ; i < m ; i++) if (pinv [i] < 0) pinv [i] = k++ ;
55 cs_free (w) ;
56 return (1) ;
57 }
58
59 /* symbolic ordering and analysis for QR or LU */
cs_sqr(CS_INT order,const cs * A,CS_INT qr)60 css *cs_sqr (CS_INT order, const cs *A, CS_INT qr)
61 {
62 CS_INT n, k, ok = 1, *post ;
63 css *S ;
64 if (!CS_CSC (A)) return (NULL) ; /* check inputs */
65 n = A->n ;
66 S = cs_calloc (1, sizeof (css)) ; /* allocate result S */
67 if (!S) return (NULL) ; /* out of memory */
68 S->q = cs_amd (order, A) ; /* fill-reducing ordering */
69 if (order && !S->q) return (cs_sfree (S)) ;
70 if (qr) /* QR symbolic analysis */
71 {
72 cs *C = order ? cs_permute (A, NULL, S->q, 0) : ((cs *) A) ;
73 S->parent = cs_etree (C, 1) ; /* etree of C'*C, where C=A(:,q) */
74 post = cs_post (S->parent, n) ;
75 S->cp = cs_counts (C, S->parent, post, 1) ; /* col counts chol(C'*C) */
76 cs_free (post) ;
77 ok = C && S->parent && S->cp && cs_vcount (C, S) ;
78 if (ok) for (S->unz = 0, k = 0 ; k < n ; k++) S->unz += S->cp [k] ;
79 if (order) cs_spfree (C) ;
80 }
81 else
82 {
83 S->unz = 4*(A->p [n]) + n ; /* for LU factorization only, */
84 S->lnz = S->unz ; /* guess nnz(L) and nnz(U) */
85 }
86 return (ok ? S : cs_sfree (S)) ; /* return result S */
87 }
88