/*! \brief
* <pre>
* Purpose
* =======
* ilu_cdrop_row() - Drop some small rows from the previous
* supernode (L-part only).
* </pre>
*/
int ilu_cdrop_row(
superlu_options_t *options, /* options */
int first, /* index of the first column in the supernode */
int last, /* index of the last column in the supernode */
double drop_tol, /* dropping parameter */
int quota, /* maximum nonzero entries allowed */
int *nnzLj, /* in/out number of nonzeros in L(:, 1:last) */
double *fill_tol, /* in/out - on exit, fill_tol=-num_zero_pivots,
* does not change if options->ILU_MILU != SMILU1 */
GlobalLU_t *Glu, /* modified */
float swork[], /* working space
* the length of swork[] should be no less than
* the number of rows in the supernode */
float swork2[], /* working space with the same size as swork[],
* used only by the second dropping rule */
int lastc /* if lastc == 0, there is nothing after the
* working supernode [first:last];
* if lastc == 1, there is one more column after
* the working supernode. */ )
{
register int i, j, k, m1;
register int nzlc; /* number of nonzeros in column last+1 */
register int xlusup_first, xlsub_first;
int m, n; /* m x n is the size of the supernode */
int r = 0; /* number of dropped rows */
register float *temp;
register complex *lusup = (complex *) Glu->lusup;
register int *lsub = Glu->lsub;
register int *xlsub = Glu->xlsub;
register int *xlusup = Glu->xlusup;
register float d_max = 0.0, d_min = 1.0;
int drop_rule = options->ILU_DropRule;
milu_t milu = options->ILU_MILU;
norm_t nrm = options->ILU_Norm;
complex zero = {0.0, 0.0};
complex one = {1.0, 0.0};
complex none = {-1.0, 0.0};
int i_1 = 1;
int inc_diag; /* inc_diag = m + 1 */
int nzp = 0; /* number of zero pivots */
float alpha = pow((double)(Glu->n), -1.0 / options->ILU_MILU_Dim);
xlusup_first = xlusup[first];
xlsub_first = xlsub[first];
m = xlusup[first + 1] - xlusup_first;
n = last - first + 1;
m1 = m - 1;
inc_diag = m + 1;
nzlc = lastc ? (xlusup[last + 2] - xlusup[last + 1]) : 0;
temp = swork - n;
/* Quick return if nothing to do. */
if (m == 0 || m == n || drop_rule == NODROP)
{
*nnzLj += m * n;
return 0;
}
/* basic dropping: ILU(tau) */
for (i = n; i <= m1; )
{
/* the average abs value of ith row */
switch (nrm)
{
case ONE_NORM:
temp[i] = scasum_(&n, &lusup[xlusup_first + i], &m) / (double)n;
break;
case TWO_NORM:
temp[i] = scnrm2_(&n, &lusup[xlusup_first + i], &m)
/ sqrt((double)n);
break;
case INF_NORM:
default:
k = icamax_(&n, &lusup[xlusup_first + i], &m) - 1;
temp[i] = c_abs1(&lusup[xlusup_first + i + m * k]);
break;
}
/* drop small entries due to drop_tol */
if (drop_rule & DROP_BASIC && temp[i] < drop_tol)
{
r++;
/* drop the current row and move the last undropped row here */
if (r > 1) /* add to last row */
{
/* accumulate the sum (for MILU) */
switch (milu)
{
case SMILU_1:
case SMILU_2:
caxpy_(&n, &one, &lusup[xlusup_first + i], &m,
&lusup[xlusup_first + m - 1], &m);
break;
case SMILU_3:
for (j = 0; j < n; j++)
lusup[xlusup_first + (m - 1) + j * m].r +=
c_abs1(&lusup[xlusup_first + i + j * m]);
break;
case SILU:
default:
break;
}
ccopy_(&n, &lusup[xlusup_first + m1], &m,
&lusup[xlusup_first + i], &m);
} /* if (r > 1) */
else /* move to last row */
{
cswap_(&n, &lusup[xlusup_first + m1], &m,
&lusup[xlusup_first + i], &m);
if (milu == SMILU_3)
for (j = 0; j < n; j++) {
lusup[xlusup_first + m1 + j * m].r =
c_abs1(&lusup[xlusup_first + m1 + j * m]);
lusup[xlusup_first + m1 + j * m].i = 0.0;
}
}
lsub[xlsub_first + i] = lsub[xlsub_first + m1];
m1--;
continue;
} /* if dropping */
else
{
if (temp[i] > d_max) d_max = temp[i];
if (temp[i] < d_min) d_min = temp[i];
}
i++;
} /* for */
/* Secondary dropping: drop more rows according to the quota. */
quota = ceil((double)quota / (double)n);
if (drop_rule & DROP_SECONDARY && m - r > quota)
{
register double tol = d_max;
/* Calculate the second dropping tolerance */
if (quota > n)
{
if (drop_rule & DROP_INTERP) /* by interpolation */
{
d_max = 1.0 / d_max; d_min = 1.0 / d_min;
tol = 1.0 / (d_max + (d_min - d_max) * quota / (m - n - r));
}
else /* by quick select */
{
int len = m1 - n + 1;
scopy_(&len, swork, &i_1, swork2, &i_1);
tol = sqselect(len, swork2, quota - n);
#if 0
register int *itemp = iwork - n;
A = temp;
for (i = n; i <= m1; i++) itemp[i] = i;
qsort(iwork, m1 - n + 1, sizeof(int), _compare_);
tol = temp[itemp[quota]];
#endif
}
}
for (i = n; i <= m1; )
{
if (temp[i] <= tol)
{
register int j;
r++;
/* drop the current row and move the last undropped row here */
if (r > 1) /* add to last row */
{
/* accumulate the sum (for MILU) */
switch (milu)
{
case SMILU_1:
case SMILU_2:
caxpy_(&n, &one, &lusup[xlusup_first + i], &m,
&lusup[xlusup_first + m - 1], &m);
break;
case SMILU_3:
for (j = 0; j < n; j++)
lusup[xlusup_first + (m - 1) + j * m].r +=
c_abs1(&lusup[xlusup_first + i + j * m]);
break;
case SILU:
default:
break;
}
ccopy_(&n, &lusup[xlusup_first + m1], &m,
&lusup[xlusup_first + i], &m);
} /* if (r > 1) */
else /* move to last row */
{
cswap_(&n, &lusup[xlusup_first + m1], &m,
&lusup[xlusup_first + i], &m);
if (milu == SMILU_3)
for (j = 0; j < n; j++) {
lusup[xlusup_first + m1 + j * m].r =
c_abs1(&lusup[xlusup_first + m1 + j * m]);
lusup[xlusup_first + m1 + j * m].i = 0.0;
}
}
lsub[xlsub_first + i] = lsub[xlsub_first + m1];
m1--;
temp[i] = temp[m1];
continue;
}
i++;
} /* for */
} /* if secondary dropping */
for (i = n; i < m; i++) temp[i] = 0.0;
if (r == 0)
{
*nnzLj += m * n;
return 0;
}
/* add dropped entries to the diagnal */
if (milu != SILU)
{
register int j;
complex t;
float omega;
for (j = 0; j < n; j++)
{
t = lusup[xlusup_first + (m - 1) + j * m];
if (t.r == 0.0 && t.i == 0.0) continue;
omega = SUPERLU_MIN(2.0 * (1.0 - alpha) / c_abs1(&t), 1.0);
cs_mult(&t, &t, omega);
switch (milu)
{
case SMILU_1:
if ( !(c_eq(&t, &none)) ) {
c_add(&t, &t, &one);
cc_mult(&lusup[xlusup_first + j * inc_diag],
&lusup[xlusup_first + j * inc_diag],
&t);
}
else
{
cs_mult(
&lusup[xlusup_first + j * inc_diag],
&lusup[xlusup_first + j * inc_diag],
*fill_tol);
#ifdef DEBUG
printf("[1] ZERO PIVOT: FILL col %d.\n", first + j);
fflush(stdout);
#endif
nzp++;
}
break;
case SMILU_2:
cs_mult(&lusup[xlusup_first + j * inc_diag],
&lusup[xlusup_first + j * inc_diag],
1.0 + c_abs1(&t));
break;
case SMILU_3:
c_add(&t, &t, &one);
cc_mult(&lusup[xlusup_first + j * inc_diag],
&lusup[xlusup_first + j * inc_diag],
&t);
break;
case SILU:
default:
break;
}
}
if (nzp > 0) *fill_tol = -nzp;
}
/* Remove dropped entries from the memory and fix the pointers. */
m1 = m - r;
for (j = 1; j < n; j++)
{
register int tmp1, tmp2;
tmp1 = xlusup_first + j * m1;
tmp2 = xlusup_first + j * m;
for (i = 0; i < m1; i++)
lusup[i + tmp1] = lusup[i + tmp2];
}
for (i = 0; i < nzlc; i++)
lusup[xlusup_first + i + n * m1] = lusup[xlusup_first + i + n * m];
for (i = 0; i < nzlc; i++)
lsub[xlsub[last + 1] - r + i] = lsub[xlsub[last + 1] + i];
for (i = first + 1; i <= last + 1; i++)
{
xlusup[i] -= r * (i - first);
xlsub[i] -= r;
}
if (lastc)
{
xlusup[last + 2] -= r * n;
xlsub[last + 2] -= r;
}
*nnzLj += (m - r) * n;
return r;
}
int
ilu_ccopy_to_ucol(
int jcol, /* in */
int nseg, /* in */
int *segrep, /* in */
int *repfnz, /* in */
int *perm_r, /* in */
complex *dense, /* modified - reset to zero on return */
int drop_rule,/* in */
milu_t milu, /* in */
double drop_tol, /* in */
int quota, /* maximum nonzero entries allowed */
complex *sum, /* out - the sum of dropped entries */
int *nnzUj, /* in - out */
GlobalLU_t *Glu, /* modified */
float *work /* working space with minimum size n,
* used by the second dropping rule */
)
{
/*
* Gather from SPA dense[*] to global ucol[*].
*/
int ksub, krep, ksupno;
int i, k, kfnz, segsze;
int fsupc, isub, irow;
int jsupno, nextu;
int new_next, mem_error;
int *xsup, *supno;
int *lsub, *xlsub;
complex *ucol;
int *usub, *xusub;
int nzumax;
int m; /* number of entries in the nonzero U-segments */
register float d_max = 0.0, d_min = 1.0 / dlamch_("Safe minimum");
register double tmp;
complex zero = {0.0, 0.0};
int i_1 = 1;
xsup = Glu->xsup;
supno = Glu->supno;
lsub = Glu->lsub;
xlsub = Glu->xlsub;
ucol = Glu->ucol;
usub = Glu->usub;
xusub = Glu->xusub;
nzumax = Glu->nzumax;
*sum = zero;
if (drop_rule == NODROP) {
drop_tol = -1.0, quota = Glu->n;
}
jsupno = supno[jcol];
nextu = xusub[jcol];
k = nseg - 1;
for (ksub = 0; ksub < nseg; ksub++) {
krep = segrep[k--];
ksupno = supno[krep];
if ( ksupno != jsupno ) { /* Should go into ucol[] */
kfnz = repfnz[krep];
if ( kfnz != EMPTY ) { /* Nonzero U-segment */
fsupc = xsup[ksupno];
isub = xlsub[fsupc] + kfnz - fsupc;
segsze = krep - kfnz + 1;
new_next = nextu + segsze;
while ( new_next > nzumax ) {
if ((mem_error = cLUMemXpand(jcol, nextu, UCOL, &nzumax,
Glu)) != 0)
return (mem_error);
ucol = Glu->ucol;
if ((mem_error = cLUMemXpand(jcol, nextu, USUB, &nzumax,
Glu)) != 0)
return (mem_error);
usub = Glu->usub;
lsub = Glu->lsub;
}
for (i = 0; i < segsze; i++) {
irow = lsub[isub++];
tmp = c_abs1(&dense[irow]);
/* first dropping rule */
if (quota > 0 && tmp >= drop_tol) {
if (tmp > d_max) d_max = tmp;
if (tmp < d_min) d_min = tmp;
usub[nextu] = perm_r[irow];
ucol[nextu] = dense[irow];
nextu++;
} else {
switch (milu) {
case SMILU_1:
case SMILU_2:
c_add(sum, sum, &dense[irow]);
break;
case SMILU_3:
/* *sum += fabs(dense[irow]);*/
sum->r += tmp;
break;
case SILU:
default:
break;
}
#ifdef DEBUG
num_drop_U++;
#endif
}
dense[irow] = zero;
}
}
}
} /* for each segment... */
xusub[jcol + 1] = nextu; /* Close U[*,jcol] */
m = xusub[jcol + 1] - xusub[jcol];
/* second dropping rule */
if (drop_rule & DROP_SECONDARY && m > quota) {
register double tol = d_max;
register int m0 = xusub[jcol] + m - 1;
if (quota > 0) {
if (drop_rule & DROP_INTERP) {
d_max = 1.0 / d_max; d_min = 1.0 / d_min;
tol = 1.0 / (d_max + (d_min - d_max) * quota / m);
} else {
i_1 = xusub[jcol];
for (i = 0; i < m; ++i, ++i_1) work[i] = c_abs1(&ucol[i_1]);
tol = sqselect(m, work, quota);
#if 0
A = &ucol[xusub[jcol]];
for (i = 0; i < m; i++) work[i] = i;
qsort(work, m, sizeof(int), _compare_);
tol = fabs(usub[xusub[jcol] + work[quota]]);
#endif
}
}
for (i = xusub[jcol]; i <= m0; ) {
if (c_abs1(&ucol[i]) <= tol) {
switch (milu) {
case SMILU_1:
case SMILU_2:
c_add(sum, sum, &ucol[i]);
break;
case SMILU_3:
sum->r += tmp;
break;
case SILU:
default:
break;
}
ucol[i] = ucol[m0];
usub[i] = usub[m0];
m0--;
m--;
#ifdef DEBUG
num_drop_U++;
#endif
xusub[jcol + 1]--;
continue;
}
i++;
}
}
if (milu == SMILU_2) {
sum->r = c_abs1(sum); sum->i = 0.0;
}
if (milu == SMILU_3) sum->i = 0.0;
*nnzUj += m;
return 0;
}
