int mod2sparse_decomp
( mod2sparse *A, /* Input matrix, M by N */
int K, /* Size of sub-matrix to find LU decomposition of */
mod2sparse *L, /* Matrix in which L is stored, M by K */
mod2sparse *U, /* Matrix in which U is stored, K by N */
int *rows, /* Array where row indexes are stored, M long */
int *cols, /* Array where column indexes are stored, N long */
mod2sparse_strategy strategy, /* Strategy to follow in picking rows/columns */
int abandon_number, /* Number of columns to abandon at some point */
int abandon_when /* When to abandon these columns */
)
{
int *rinv=NULL, *cinv=NULL, *acnt=NULL, *rcnt=NULL;
mod2sparse *B=NULL;
int M, N;
mod2entry *e=NULL, *f=NULL, *fn=NULL, *e2=NULL;
int i=0, j=0, k=0, cc=0, cc2=0, cc3=0, cr2=0, pr=0;
int found, nnf;
M = mod2sparse_rows(A);
N = mod2sparse_cols(A);
if (mod2sparse_cols(L)!=K || mod2sparse_rows(L)!=M
|| mod2sparse_cols(U)!=N || mod2sparse_rows(U)!=K)
{ fprintf (stderr,
"mod2sparse_decomp: Matrices have incompatible dimensions\n");
exit(1);
}
if (abandon_number>N-K)
{ fprintf(stderr,"Trying to abandon more columns than allowed\n");
exit(1);
}
rinv = (int*)chk_alloc (M, sizeof *rinv);
cinv = (int*)chk_alloc (N, sizeof *cinv);
if (abandon_number>0)
{
acnt = (int*)chk_alloc (M+1, sizeof *acnt);
}
if (strategy==Mod2sparse_minprod)
{
rcnt = (int*)chk_alloc (M, sizeof *rcnt);
}
mod2sparse_clear(L);
mod2sparse_clear(U);
/* Copy A to B. B will be modified, then discarded. */
B = mod2sparse_allocate(M,N);
mod2sparse_copy(A,B);
/* Count 1s in rows of B, if using minprod strategy. */
if (strategy==Mod2sparse_minprod)
{ for (i = 0; i<M; i++)
{ rcnt[i] = mod2sparse_count_row(B,i);
}
}
/* Set up initial row and column choices. */
for (i = 0; i<M; i++) rows[i] = rinv[i] = i;
for (j = 0; j<N; j++) cols[j] = cinv[j] = j;
/* Find L and U one column at a time. */
nnf = 0;
for (i = 0; i<K; i++)
{
/* Choose the next row and column of B. */
switch (strategy)
{
case Mod2sparse_first:
{
found = 0;
for (k = i; k<N; k++)
{ e = mod2sparse_first_in_col(B,cols[k]);
while (!mod2sparse_at_end(e))
{ if (rinv[mod2sparse_row(e)]>=i)
{ found = 1;
goto out_first;
}
e = mod2sparse_next_in_col(e);
}
}
out_first:
break;
}
case Mod2sparse_mincol:
{
found = 0;
for (j = i; j<N; j++)
{ cc2 = mod2sparse_count_col(B,cols[j]);
if (!found || cc2<cc)
{ e2 = mod2sparse_first_in_col(B,cols[j]);
while (!mod2sparse_at_end(e2))
{ if (rinv[mod2sparse_row(e2)]>=i)
{ found = 1;
cc = cc2;
e = e2;
k = j;
break;
}
e2 = mod2sparse_next_in_col(e2);
}
}
}
break;
}
case Mod2sparse_minprod:
{
found = 0;
for (j = i; j<N; j++)
{ cc2 = mod2sparse_count_col(B,cols[j]);
e2 = mod2sparse_first_in_col(B,cols[j]);
while (!mod2sparse_at_end(e2))
{ if (rinv[mod2sparse_row(e2)]>=i)
{ cr2 = rcnt[mod2sparse_row(e2)];
if (!found || cc2==1 || (cc2-1)*(cr2-1)<pr)
{ found = 1;
pr = cc2==1 ? 0 : (cc2-1)*(cr2-1);
e = e2;
k = j;
}
}
e2 = mod2sparse_next_in_col(e2);
}
}
break;
}
default:
{ fprintf(stderr,"mod2sparse_decomp: Unknown stategy\n");
exit(1);
}
}
if (!found)
{ nnf += 1;
}
/* Update 'rows' and 'cols'. Looks at 'k' and 'e' found above. */
if (found)
{
if (cinv[mod2sparse_col(e)]!=k) abort();
cols[k] = cols[i];
cols[i] = mod2sparse_col(e);
cinv[cols[k]] = k;
cinv[cols[i]] = i;
k = rinv[mod2sparse_row(e)];
if (k<i) abort();
rows[k] = rows[i];
rows[i] = mod2sparse_row(e);
rinv[rows[k]] = k;
rinv[rows[i]] = i;
}
/* Update L, U, and B. */
f = mod2sparse_first_in_col(B,cols[i]);
while (!mod2sparse_at_end(f))
{
fn = mod2sparse_next_in_col(f);
k = mod2sparse_row(f);
if (rinv[k]>i)
{ mod2sparse_add_row(B,k,B,mod2sparse_row(e));
if (strategy==Mod2sparse_minprod)
{ rcnt[k] = mod2sparse_count_row(B,k);
}
mod2sparse_insert(L,k,i);
}
else if (rinv[k]<i)
{ mod2sparse_insert(U,rinv[k],cols[i]);
}
else
{ mod2sparse_insert(L,k,i);
mod2sparse_insert(U,i,cols[i]);
}
f = fn;
}
/* Get rid of all entries in the current column of B, just to save space. */
for (;;)
{ f = mod2sparse_first_in_col(B,cols[i]);
if (mod2sparse_at_end(f)) break;
mod2sparse_delete(B,f);
}
/* Abandon columns of B with lots of entries if it's time for that. */
if (abandon_number>0 && i==abandon_when)
{
for (k = 0; k<M+1; k++)
{ acnt[k] = 0;
}
for (j = 0; j<N; j++)
{ k = mod2sparse_count_col(B,j);
acnt[k] += 1;
}
cc = abandon_number;
k = M;
while (acnt[k]<cc)
{ cc -= acnt[k];
k -= 1;
if (k<0) abort();
}
cc2 = 0;
for (j = 0; j<N; j++)
{ cc3 = mod2sparse_count_col(B,j);
if (cc3>k || cc3==k && cc>0)
{ if (cc3==k) cc -= 1;
for (;;)
{ f = mod2sparse_first_in_col(B,j);
if (mod2sparse_at_end(f)) break;
mod2sparse_delete(B,f);
}
cc2 += 1;
}
}
if (cc2!=abandon_number) abort();
if (strategy==Mod2sparse_minprod)
{ for (j = 0; j<M; j++)
{ rcnt[j] = mod2sparse_count_row(B,j);
}
}
}
}
/* Get rid of all entries in the rows of L past row K, after reordering. */
for (i = K; i<M; i++)
{ for (;;)
{ f = mod2sparse_first_in_row(L,rows[i]);
if (mod2sparse_at_end(f)) break;
mod2sparse_delete(L,f);
}
}
mod2sparse_free(B);
free(rinv);
free(cinv);
if (strategy==Mod2sparse_minprod) free(rcnt);
if (abandon_number>0) free(acnt);
return nnf;
}
int main
( int argc,
char **argv
)
{
char *alist_file, *pchk_file;
FILE *af, *pf;
int mxrw, mxcw;
int *rw, *cw;
int i, j, k;
mod2entry *e;
int trans;
int nozeros;
int last;
trans = 0;
nozeros = 0;
for (;;)
{
if (argc>1 && strcmp(argv[1],"-t")==0)
{ trans = 1;
argc -= 1;
argv += 1;
}
else if (argc>1 && strcmp(argv[1],"-z")==0)
{ nozeros = 1;
argc -= 1;
argv += 1;
}
else
{ break;
}
}
if (argc!=3)
{ usage();
}
pchk_file = argv[1];
alist_file = argv[2];
read_pchk(pchk_file);
if (trans)
{ mod2sparse *HT;
HT = H;
H = mod2sparse_allocate(N,M);
mod2sparse_transpose(HT,H);
M = mod2sparse_rows(H);
N = mod2sparse_cols(H);
}
af = open_file_std(alist_file,"wb");
if (af==NULL)
{ fprintf(stderr,"Can't create alist file: %s\n",alist_file);
exit(1);
}
fprintf(af,"%d %d\n",M,N);
rw = (int *) chk_alloc (M, sizeof *rw);
mxrw = 0;
for (i = 0; i<M; i++)
{ rw[i] = mod2sparse_count_row(H,i);
if (rw[i]>mxrw)
{ mxrw = rw[i];
}
}
cw = (int *) chk_alloc (N, sizeof *cw);
mxcw = 0;
for (j = 0; j<N; j++)
{ cw[j] = mod2sparse_count_col(H,j);
if (cw[j]>mxcw)
{ mxcw = cw[j];
}
}
fprintf(af,"%d %d\n",mxrw,mxcw);
for (i = 0; i<M; i++)
{ fprintf(af,"%d%c",rw[i],i==M-1?'\n':' ');
}
for (j = 0; j<N; j++)
{ fprintf(af,"%d%c",cw[j],j==N-1?'\n':' ');
}
for (i = 0; i<M; i++)
{ e = mod2sparse_first_in_row(H,i);
last = 0;
for (k = 0; !last; k++)
{ last = nozeros ? k==rw[i]-1 : k==mxrw-1;
fprintf (af, "%d%c", mod2sparse_at_end(e)?0:mod2sparse_col(e)+1,
last?'\n':' ');
if (!mod2sparse_at_end(e))
{ e = mod2sparse_next_in_row(e);
}
}
}
for (j = 0; j<N; j++)
{ e = mod2sparse_first_in_col(H,j);
last = 0;
for (k = 0; !last; k++)
{ last = nozeros ? k==cw[j]-1 : k==mxcw-1;
fprintf (af, "%d%c", mod2sparse_at_end(e)?0:mod2sparse_row(e)+1,
last?'\n':' ');
if (!mod2sparse_at_end(e))
{ e = mod2sparse_next_in_col(e);
}
}
}
if (ferror(af) || fclose(af)!=0)
{ fprintf(stderr,"Error writing to alist file %s\n",alist_file);
exit(1);
}
return 0;
}