/*! @file ilu_scolumn_dfs.c
* \brief Performs a symbolic factorization
*
*
* -- SuperLU routine (version 4.0) --
* Lawrence Berkeley National Laboratory
* June 30, 2009
*
*/
#include "slu_sdefs.h"
/*! \brief
*
*
* Purpose
* =======
* ILU_SCOLUMN_DFS performs a symbolic factorization on column jcol, and
* decide the supernode boundary.
*
* This routine does not use numeric values, but only use the RHS
* row indices to start the dfs.
*
* A supernode representative is the last column of a supernode.
* The nonzeros in U[*,j] are segments that end at supernodal
* representatives. The routine returns a list of such supernodal
* representatives in topological order of the dfs that generates them.
* The location of the first nonzero in each such supernodal segment
* (supernodal entry location) is also returned.
*
* Local parameters
* ================
* nseg: no of segments in current U[*,j]
* jsuper: jsuper=EMPTY if column j does not belong to the same
* supernode as j-1. Otherwise, jsuper=nsuper.
*
* marker2: A-row --> A-row/col (0/1)
* repfnz: SuperA-col --> PA-row
* parent: SuperA-col --> SuperA-col
* xplore: SuperA-col --> index to L-structure
*
* Return value
* ============
* 0 success;
* > 0 number of bytes allocated when run out of space.
*
*/
int
ilu_scolumn_dfs(
const int m, /* in - number of rows in the matrix */
const int jcol, /* in */
int *perm_r, /* in */
int *nseg, /* modified - with new segments appended */
int *lsub_col, /* in - defines the RHS vector to start the
dfs */
int *segrep, /* modified - with new segments appended */
int *repfnz, /* modified */
int *marker, /* modified */
int *parent, /* working array */
int *xplore, /* working array */
GlobalLU_t *Glu /* modified */
)
{
int jcolp1, jcolm1, jsuper, nsuper, nextl;
int k, krep, krow, kmark, kperm;
int *marker2; /* Used for small panel LU */
int fsupc; /* First column of a snode */
int myfnz; /* First nonz column of a U-segment */
int chperm, chmark, chrep, kchild;
int xdfs, maxdfs, kpar, oldrep;
int jptr, jm1ptr;
int ito, ifrom; /* Used to compress row subscripts */
int mem_error;
int *xsup, *supno, *lsub, *xlsub;
int nzlmax;
static int first = 1, maxsuper;
xsup = Glu->xsup;
supno = Glu->supno;
lsub = Glu->lsub;
xlsub = Glu->xlsub;
nzlmax = Glu->nzlmax;
if ( first ) {
maxsuper = sp_ienv(7);
first = 0;
}
jcolp1 = jcol + 1;
jcolm1 = jcol - 1;
nsuper = supno[jcol];
jsuper = nsuper;
nextl = xlsub[jcol];
marker2 = &marker[2*m];
/* For each nonzero in A[*,jcol] do dfs */
for (k = 0; lsub_col[k] != EMPTY; k++) {
krow = lsub_col[k];
lsub_col[k] = EMPTY;
kmark = marker2[krow];
/* krow was visited before, go to the next nonzero */
if ( kmark == jcol ) continue;
/* For each unmarked nbr krow of jcol
* krow is in L: place it in structure of L[*,jcol]
*/
marker2[krow] = jcol;
kperm = perm_r[krow];
if ( kperm == EMPTY ) {
lsub[nextl++] = krow; /* krow is indexed into A */
if ( nextl >= nzlmax ) {
if ((mem_error = sLUMemXpand(jcol, nextl, LSUB, &nzlmax, Glu)))
return (mem_error);
lsub = Glu->lsub;
}
if ( kmark != jcolm1 ) jsuper = EMPTY;/* Row index subset testing */
} else {
/* krow is in U: if its supernode-rep krep
* has been explored, update repfnz[*]
*/
krep = xsup[supno[kperm]+1] - 1;
myfnz = repfnz[krep];
if ( myfnz != EMPTY ) { /* Visited before */
if ( myfnz > kperm ) repfnz[krep] = kperm;
/* continue; */
}
else {
/* Otherwise, perform dfs starting at krep */
oldrep = EMPTY;
parent[krep] = oldrep;
repfnz[krep] = kperm;
xdfs = xlsub[xsup[supno[krep]]];
maxdfs = xlsub[krep + 1];
do {
/*
* For each unmarked kchild of krep
*/
while ( xdfs < maxdfs ) {
kchild = lsub[xdfs];
xdfs++;
chmark = marker2[kchild];
if ( chmark != jcol ) { /* Not reached yet */
marker2[kchild] = jcol;
chperm = perm_r[kchild];
/* Case kchild is in L: place it in L[*,k] */
if ( chperm == EMPTY ) {
lsub[nextl++] = kchild;
if ( nextl >= nzlmax ) {
if ( (mem_error = sLUMemXpand(jcol,nextl,
LSUB,&nzlmax,Glu)) )
return (mem_error);
lsub = Glu->lsub;
}
if ( chmark != jcolm1 ) jsuper = EMPTY;
} else {
/* Case kchild is in U:
* chrep = its supernode-rep. If its rep has
* been explored, update its repfnz[*]
*/
chrep = xsup[supno[chperm]+1] - 1;
myfnz = repfnz[chrep];
if ( myfnz != EMPTY ) { /* Visited before */
if ( myfnz > chperm )
repfnz[chrep] = chperm;
} else {
/* Continue dfs at super-rep of kchild */
xplore[krep] = xdfs;
oldrep = krep;
krep = chrep; /* Go deeper down G(L^t) */
parent[krep] = oldrep;
repfnz[krep] = chperm;
xdfs = xlsub[xsup[supno[krep]]];
maxdfs = xlsub[krep + 1];
} /* else */
} /* else */
} /* if */
} /* while */
/* krow has no more unexplored nbrs;
* place supernode-rep krep in postorder DFS.
* backtrack dfs to its parent
*/
segrep[*nseg] = krep;
++(*nseg);
kpar = parent[krep]; /* Pop from stack, mimic recursion */
if ( kpar == EMPTY ) break; /* dfs done */
krep = kpar;
xdfs = xplore[krep];
maxdfs = xlsub[krep + 1];
} while ( kpar != EMPTY ); /* Until empty stack */
} /* else */
} /* else */
} /* for each nonzero ... */
/* Check to see if j belongs in the same supernode as j-1 */
if ( jcol == 0 ) { /* Do nothing for column 0 */
nsuper = supno[0] = 0;
} else {
fsupc = xsup[nsuper];
jptr = xlsub[jcol]; /* Not compressed yet */
jm1ptr = xlsub[jcolm1];
if ( (nextl-jptr != jptr-jm1ptr-1) ) jsuper = EMPTY;
/* Always start a new supernode for a singular column */
if ( nextl == jptr ) jsuper = EMPTY;
/* Make sure the number of columns in a supernode doesn't
exceed threshold. */
if ( jcol - fsupc >= maxsuper ) jsuper = EMPTY;
/* If jcol starts a new supernode, reclaim storage space in
* lsub from the previous supernode. Note we only store
* the subscript set of the first columns of the supernode.
*/
if ( jsuper == EMPTY ) { /* starts a new supernode */
if ( (fsupc < jcolm1) ) { /* >= 2 columns in nsuper */
#ifdef CHK_COMPRESS
printf(" Compress lsub[] at super %d-%d\n", fsupc, jcolm1);
#endif
ito = xlsub[fsupc+1];
xlsub[jcolm1] = ito;
xlsub[jcol] = ito;
for (ifrom = jptr; ifrom < nextl; ++ifrom, ++ito)
lsub[ito] = lsub[ifrom];
nextl = ito;
}
nsuper++;
supno[jcol] = nsuper;
} /* if a new supernode */
} /* else: jcol > 0 */
/* Tidy up the pointers before exit */
xsup[nsuper+1] = jcolp1;
supno[jcolp1] = nsuper;
xlsub[jcolp1] = nextl;
return 0;
}