/*
* Nonsymmetric elimination tree
*/
int
sp_coletree(
int *acolst, int *acolend, /* column start and end past 1 */
int *arow, /* row indices of A */
int nr, int nc, /* dimension of A */
int *parent /* parent in elim tree */
)
{
int *root; /* root of subtee of etree */
int *firstcol; /* first nonzero col in each row*/
int rset, cset;
int row, col;
int rroot;
int p;
int *pp;
root = mxCallocInt (nc);
initialize_disjoint_sets (nc, &pp);
/* Compute firstcol[row] = first nonzero column in row */
firstcol = mxCallocInt (nr);
for (row = 0; row < nr; firstcol[row++] = nc);
for (col = 0; col < nc; col++)
for (p = acolst[col]; p < acolend[col]; p++) {
row = arow[p];
firstcol[row] = SUPERLU_MIN(firstcol[row], col);
}
/* Compute etree by Liu's algorithm for symmetric matrices,
except use (firstcol[r],c) in place of an edge (r,c) of A.
Thus each row clique in A'*A is replaced by a star
centered at its first vertex, which has the same fill. */
for (col = 0; col < nc; col++) {
cset = make_set (col, pp);
root[cset] = col;
parent[col] = nc; /* Matlab */
for (p = acolst[col]; p < acolend[col]; p++) {
row = firstcol[arow[p]];
if (row >= col) continue;
rset = find (row, pp);
rroot = root[rset];
if (rroot != col) {
parent[rroot] = col;
cset = link (cset, rset, pp);
root[cset] = col;
}
}
}
SUPERLU_FREE (root);
SUPERLU_FREE (firstcol);
finalize_disjoint_sets (pp);
return 0;
}
/*! \brief Symmetric elimination tree
*
* <pre>
* p = spsymetree (A);
*
* Find the elimination tree for symmetric matrix A.
* This uses Liu's algorithm, and runs in time O(nz*log n).
*
* Input:
* Square sparse matrix A. No check is made for symmetry;
* elements below and on the diagonal are ignored.
* Numeric values are ignored, so any explicit zeros are
* treated as nonzero.
* Output:
* Integer array of parents representing the etree, with n
* meaning a root of the elimination forest.
* Note:
* This routine uses only the upper triangle, while sparse
* Cholesky (as in spchol.c) uses only the lower. Matlab's
* dense Cholesky uses only the upper. This routine could
* be modified to use the lower triangle either by transposing
* the matrix or by traversing it by rows with auxiliary
* pointer and link arrays.
*
* John R. Gilbert, Xerox, 10 Dec 1990
* Based on code by JRG dated 1987, 1988, and 1990.
* Modified by X.S. Li, November 1999.
* </pre>
*/
int
sp_symetree_dist(
int_t *acolst, int_t *acolend, /* column starts and ends past 1 */
int_t *arow, /* row indices of A */
int_t n, /* dimension of A */
int_t *parent /* parent in elim tree */
)
{
int_t *root; /* root of subtee of etree */
int_t rset, cset;
int_t row, col;
int_t rroot;
int_t p;
int_t *pp;
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(0, "Enter sp_symetree()");
#endif
root = mxCallocInt (n);
initialize_disjoint_sets (n, &pp);
for (col = 0; col < n; col++) {
cset = make_set (col, pp);
root[cset] = col;
parent[col] = n; /* Matlab */
for (p = acolst[col]; p < acolend[col]; p++) {
row = arow[p];
if (row >= col) continue;
rset = find (row, pp);
rroot = root[rset];
if (rroot != col) {
parent[rroot] = col;
cset = link (cset, rset, pp);
root[cset] = col;
}
}
}
SUPERLU_FREE (root);
finalize_disjoint_sets (pp);
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(0, "Exit sp_symetree()");
#endif
return 0;
} /* SP_SYMETREE_DIST */
/*
* Symmetric elimination tree
*/
int
sp_symetree(
int *acolst, int *acolend, /* column starts and ends past 1 */
int *arow, /* row indices of A */
int n, /* dimension of A */
int *parent /* parent in elim tree */
)
{
int *root; /* root of subtree of etree */
int rset, cset;
int row, col;
int rroot;
int p;
root = mxCallocInt (n);
initialize_disjoint_sets (n);
for (col = 0; col < n; col++) {
cset = make_set (col);
root[cset] = col;
parent[col] = n; /* Matlab */
for (p = acolst[col]; p < acolend[col]; p++) {
row = arow[p];
if (row >= col) continue;
rset = find (row);
rroot = root[rset];
if (rroot != col) {
parent[rroot] = col;
cset = link (cset, rset);
root[cset] = col;
}
}
}
SUPERLU_FREE (root);
finalize_disjoint_sets ();
return 0;
} /* SP_SYMETREE */