/* symbolic ordering and analysis for QR or LU */
css *cs_sqr (CS_INT order, const cs *A, CS_INT qr)
{
CS_INT 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 */
}
css *cs_schol(int order, const cs *A) {
int n, *c, *post, *P;
cs *C;
css *S;
if (!CS_CSC (A))
return (NULL); /* check inputs */
n = A->n;
S = (css *) cs_calloc(1, sizeof(css)); /* allocate result S */
if (!S)
return (NULL); /* out of memory */
P = cs_amd(order, A); /* P = amd(A+A'), or natural */
S->pinv = cs_pinv(P, n); /* find inverse permutation */
cs_free(P);
if (order && !S->pinv)
return (cs_sfree(S));
C = cs_symperm(A, S->pinv, 0); /* C = spones(triu(A(P,P))) */
S->parent = cs_etree(C, 0); /* find etree of C */
post = cs_post(S->parent, n); /* postorder the etree */
c = cs_counts(C, S->parent, post, 0); /* find column counts of chol(C) */
cs_free(post);
cs_spfree(C);
S->cp = (int *) cs_malloc(n + 1, sizeof(int)); /* allocate result S->cp */
S->unz = S->lnz = cs_cumsum(S->cp, c, n); /* find column pointers for L */
cs_free(c);
return ((S->lnz >= 0) ? S : cs_sfree(S));
}