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#include "cs.h"
/* compute nnz(V) = S->lnz, S->pinv, S->leftmost, S->m2 from A and S->parent */
static csi cs_vcount (const cs *A, css *S)
{
csi i, k, p, pa, n = A->n, m = A->m, *Ap = A->p, *Ai = A->i, *next, *head,
*tail, *nque, *pinv, *leftmost, *w, *parent = S->parent ;
S->pinv = pinv = cs_malloc (m+n, sizeof (csi)) ; /* allocate pinv, */
S->leftmost = leftmost = cs_malloc (m, sizeof (csi)) ; /* and leftmost */
w = cs_malloc (m+3*n, sizeof (csi)) ; /* get workspace */
if (!pinv || !w || !leftmost)
{
cs_free (w) ; /* pinv and leftmost freed later */
return (0) ; /* out of memory */
}
next = w ; head = w + m ; tail = w + m + n ; nque = w + m + 2*n ;
for (k = 0 ; k < n ; k++) head [k] = -1 ; /* queue k is empty */
for (k = 0 ; k < n ; k++) tail [k] = -1 ;
for (k = 0 ; k < n ; k++) nque [k] = 0 ;
for (i = 0 ; i < m ; i++) leftmost [i] = -1 ;
for (k = n-1 ; k >= 0 ; k--)
{
for (p = Ap [k] ; p < Ap [k+1] ; p++)
{
leftmost [Ai [p]] = k ; /* leftmost[i] = min(find(A(i,:)))*/
}
}
for (i = m-1 ; i >= 0 ; i--) /* scan rows in reverse order */
{
pinv [i] = -1 ; /* row i is not yet ordered */
k = leftmost [i] ;
if (k == -1) continue ; /* row i is empty */
if (nque [k]++ == 0) tail [k] = i ; /* first row in queue k */
next [i] = head [k] ; /* put i at head of queue k */
head [k] = i ;
}
S->lnz = 0 ;
S->m2 = m ;
for (k = 0 ; k < n ; k++) /* find row permutation and nnz(V)*/
{
i = head [k] ; /* remove row i from queue k */
S->lnz++ ; /* count V(k,k) as nonzero */
if (i < 0) i = S->m2++ ; /* add a fictitious row */
pinv [i] = k ; /* associate row i with V(:,k) */
if (--nque [k] <= 0) continue ; /* skip if V(k+1:m,k) is empty */
S->lnz += nque [k] ; /* nque [k] is nnz (V(k+1:m,k)) */
if ((pa = parent [k]) != -1) /* move all rows to parent of k */
{
if (nque [pa] == 0) tail [pa] = tail [k] ;
next [tail [k]] = head [pa] ;
head [pa] = next [i] ;
nque [pa] += nque [k] ;
}
}
for (i = 0 ; i < m ; i++) if (pinv [i] < 0) pinv [i] = k++ ;
cs_free (w) ;
return (1) ;
}
/* symbolic ordering and analysis for QR or LU */
css *cs_sqr (csi order, const cs *A, csi qr)
{
csi n, k, ok = 1, *post ;
css *S ;
if (!CS_CSC (A)) return (NULL) ; /* check inputs */
n = A->n ;
S = cs_calloc (1, sizeof (css)) ; /* allocate result S */
if (!S) return (NULL) ; /* out of memory */
S->q = cs_amd (order, A) ; /* fill-reducing ordering */
if (order && !S->q) return (cs_sfree (S)) ;
if (qr) /* QR symbolic analysis */
{
cs *C = order ? cs_permute (A, NULL, S->q, 0) : ((cs *) A) ;
S->parent = cs_etree (C, 1) ; /* etree of C'*C, where C=A(:,q) */
post = cs_post (S->parent, n) ;
S->cp = cs_counts (C, S->parent, post, 1) ; /* col counts chol(C'*C) */
cs_free (post) ;
ok = C && S->parent && S->cp && cs_vcount (C, S) ;
if (ok) for (S->unz = 0, k = 0 ; k < n ; k++) S->unz += S->cp [k] ;
if (order) cs_spfree (C) ;
}
else
{
S->unz = 4*(A->p [n]) + n ; /* for LU factorization only, */
S->lnz = S->unz ; /* guess nnz(L) and nnz(U) */
}
return (ok ? S : cs_sfree (S)) ; /* return result S */
}
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