int sfill_diag(int n, NCformat *Astore)
/* fill explicit zeros on the diagonal entries, so that the matrix is not
structurally singular. */
{
float *nzval = (float *)Astore->nzval;
int *rowind = Astore->rowind;
int *colptr = Astore->colptr;
int nnz = colptr[n];
int fill = 0;
float *nzval_new;
float zero = 0.0;
int *rowind_new;
int i, j, diag;
for (i = 0; i < n; i++)
{
diag = -1;
for (j = colptr[i]; j < colptr[i + 1]; j++)
if (rowind[j] == i) diag = j;
if (diag < 0) fill++;
}
if (fill)
{
nzval_new = floatMalloc(nnz + fill);
rowind_new = intMalloc(nnz + fill);
fill = 0;
for (i = 0; i < n; i++)
{
diag = -1;
for (j = colptr[i] - fill; j < colptr[i + 1]; j++)
{
if ((rowind_new[j + fill] = rowind[j]) == i) diag = j;
nzval_new[j + fill] = nzval[j];
}
if (diag < 0)
{
rowind_new[colptr[i + 1] + fill] = i;
nzval_new[colptr[i + 1] + fill] = zero;
fill++;
}
colptr[i + 1] += fill;
}
Astore->nzval = nzval_new;
Astore->rowind = rowind_new;
SUPERLU_FREE(nzval);
SUPERLU_FREE(rowind);
}
Astore->nnz += fill;
return fill;
}
/*
* Convert a row compressed storage into a column compressed storage.
*/
void
sCompRow_to_CompCol(int m, int n, int nnz,
float *a, int *colind, int *rowptr,
float **at, int **rowind, int **colptr)
{
register int i, j, col, relpos;
int *marker;
/* Allocate storage for another copy of the matrix. */
*at = (float *) floatMalloc(nnz);
*rowind = (int *) intMalloc(nnz);
*colptr = (int *) intMalloc(n+1);
marker = (int *) intCalloc(n);
/* Get counts of each column of A, and set up column pointers */
for (i = 0; i < m; ++i)
for (j = rowptr[i]; j < rowptr[i+1]; ++j) ++marker[colind[j]];
(*colptr)[0] = 0;
for (j = 0; j < n; ++j) {
(*colptr)[j+1] = (*colptr)[j] + marker[j];
marker[j] = (*colptr)[j];
}
/* Transfer the matrix into the compressed column storage. */
for (i = 0; i < m; ++i) {
for (j = rowptr[i]; j < rowptr[i+1]; ++j) {
col = colind[j];
relpos = marker[col];
(*rowind)[relpos] = i;
(*at)[relpos] = a[j];
++marker[col];
}
}
SUPERLU_FREE(marker);
}
int main(int argc, char *argv[])
{
char equed[1];
yes_no_t equil;
trans_t trans;
SuperMatrix A, L, U;
SuperMatrix B, X;
NCformat *Astore;
NCformat *Ustore;
SCformat *Lstore;
float *a;
int *asub, *xa;
int *perm_r; /* row permutations from partial pivoting */
int *perm_c; /* column permutation vector */
int *etree;
void *work;
int info, lwork, nrhs, ldx;
int i, m, n, nnz;
float *rhsb, *rhsx, *xact;
float *R, *C;
float *ferr, *berr;
float u, rpg, rcond;
mem_usage_t mem_usage;
superlu_options_t options;
SuperLUStat_t stat;
extern void parse_command_line();
#if ( DEBUGlevel>=1 )
CHECK_MALLOC("Enter main()");
#endif
/* Defaults */
lwork = 0;
nrhs = 1;
equil = YES;
u = 1.0;
trans = NOTRANS;
/* Set the default input options:
options.Fact = DOFACT;
options.Equil = YES;
options.ColPerm = COLAMD;
options.DiagPivotThresh = 1.0;
options.Trans = NOTRANS;
options.IterRefine = NOREFINE;
options.SymmetricMode = NO;
options.PivotGrowth = NO;
options.ConditionNumber = NO;
options.PrintStat = YES;
*/
set_default_options(&options);
/* Can use command line input to modify the defaults. */
parse_command_line(argc, argv, &lwork, &u, &equil, &trans);
options.Equil = equil;
options.DiagPivotThresh = u;
options.Trans = trans;
/* Add more functionalities that the defaults. */
options.PivotGrowth = YES; /* Compute reciprocal pivot growth */
options.ConditionNumber = YES;/* Compute reciprocal condition number */
options.IterRefine = SLU_SINGLE; /* Perform single-precision refinement */
if ( lwork > 0 ) {
work = SUPERLU_MALLOC(lwork);
if ( !work ) {
ABORT("SLINSOLX: cannot allocate work[]");
}
}
/* Read matrix A from a file in Harwell-Boeing format.*/
sreadhb(&m, &n, &nnz, &a, &asub, &xa);
sCreate_CompCol_Matrix(&A, m, n, nnz, a, asub, xa, SLU_NC, SLU_S, SLU_GE);
Astore = A.Store;
printf("Dimension %dx%d; # nonzeros %d\n", A.nrow, A.ncol, Astore->nnz);
if ( !(rhsb = floatMalloc(m * nrhs)) ) ABORT("Malloc fails for rhsb[].");
if ( !(rhsx = floatMalloc(m * nrhs)) ) ABORT("Malloc fails for rhsx[].");
sCreate_Dense_Matrix(&B, m, nrhs, rhsb, m, SLU_DN, SLU_S, SLU_GE);
sCreate_Dense_Matrix(&X, m, nrhs, rhsx, m, SLU_DN, SLU_S, SLU_GE);
xact = floatMalloc(n * nrhs);
ldx = n;
sGenXtrue(n, nrhs, xact, ldx);
sFillRHS(trans, nrhs, xact, ldx, &A, &B);
if ( !(etree = intMalloc(n)) ) ABORT("Malloc fails for etree[].");
if ( !(perm_r = intMalloc(m)) ) ABORT("Malloc fails for perm_r[].");
if ( !(perm_c = intMalloc(n)) ) ABORT("Malloc fails for perm_c[].");
if ( !(R = (float *) SUPERLU_MALLOC(A.nrow * sizeof(float))) )
ABORT("SUPERLU_MALLOC fails for R[].");
if ( !(C = (float *) SUPERLU_MALLOC(A.ncol * sizeof(float))) )
ABORT("SUPERLU_MALLOC fails for C[].");
if ( !(ferr = (float *) SUPERLU_MALLOC(nrhs * sizeof(float))) )
ABORT("SUPERLU_MALLOC fails for ferr[].");
if ( !(berr = (float *) SUPERLU_MALLOC(nrhs * sizeof(float))) )
ABORT("SUPERLU_MALLOC fails for berr[].");
/* Initialize the statistics variables. */
StatInit(&stat);
/* Solve the system and compute the condition number
and error bounds using dgssvx. */
sgssvx(&options, &A, perm_c, perm_r, etree, equed, R, C,
&L, &U, work, lwork, &B, &X, &rpg, &rcond, ferr, berr,
&mem_usage, &stat, &info);
printf("sgssvx(): info %d\n", info);
if ( info == 0 || info == n+1 ) {
/* This is how you could access the solution matrix. */
float *sol = (float*) ((DNformat*) X.Store)->nzval;
if ( options.PivotGrowth == YES )
printf("Recip. pivot growth = %e\n", rpg);
if ( options.ConditionNumber == YES )
printf("Recip. condition number = %e\n", rcond);
if ( options.IterRefine != NOREFINE ) {
printf("Iterative Refinement:\n");
printf("%8s%8s%16s%16s\n", "rhs", "Steps", "FERR", "BERR");
for (i = 0; i < nrhs; ++i)
printf("%8d%8d%16e%16e\n", i+1, stat.RefineSteps, ferr[i], berr[i]);
}
Lstore = (SCformat *) L.Store;
Ustore = (NCformat *) U.Store;
printf("No of nonzeros in factor L = %d\n", Lstore->nnz);
printf("No of nonzeros in factor U = %d\n", Ustore->nnz);
printf("No of nonzeros in L+U = %d\n", Lstore->nnz + Ustore->nnz - n);
printf("FILL ratio = %.1f\n", (float)(Lstore->nnz + Ustore->nnz - n)/nnz);
printf("L\\U MB %.3f\ttotal MB needed %.3f\n",
mem_usage.for_lu/1e6, mem_usage.total_needed/1e6);
fflush(stdout);
} else if ( info > 0 && lwork == -1 ) {
printf("** Estimated memory: %d bytes\n", info - n);
}
if ( options.PrintStat ) StatPrint(&stat);
StatFree(&stat);
SUPERLU_FREE (rhsb);
SUPERLU_FREE (rhsx);
SUPERLU_FREE (xact);
SUPERLU_FREE (etree);
SUPERLU_FREE (perm_r);
SUPERLU_FREE (perm_c);
SUPERLU_FREE (R);
SUPERLU_FREE (C);
SUPERLU_FREE (ferr);
SUPERLU_FREE (berr);
Destroy_CompCol_Matrix(&A);
Destroy_SuperMatrix_Store(&B);
Destroy_SuperMatrix_Store(&X);
if ( lwork == 0 ) {
Destroy_SuperNode_Matrix(&L);
Destroy_CompCol_Matrix(&U);
} else if ( lwork > 0 ) {
SUPERLU_FREE(work);
}
#if ( DEBUGlevel>=1 )
CHECK_MALLOC("Exit main()");
#endif
}
void
cgsitrf(superlu_options_t *options, SuperMatrix *A, int relax, int panel_size,
int *etree, void *work, int lwork, int *perm_c, int *perm_r,
SuperMatrix *L, SuperMatrix *U, SuperLUStat_t *stat, int *info)
{
/* Local working arrays */
NCPformat *Astore;
int *iperm_r = NULL; /* inverse of perm_r; used when
options->Fact == SamePattern_SameRowPerm */
int *iperm_c; /* inverse of perm_c */
int *swap, *iswap; /* swap is used to store the row permutation
during the factorization. Initially, it is set
to iperm_c (row indeces of Pc*A*Pc').
iswap is the inverse of swap. After the
factorization, it is equal to perm_r. */
int *iwork;
complex *cwork;
int *segrep, *repfnz, *parent, *xplore;
int *panel_lsub; /* dense[]/panel_lsub[] pair forms a w-wide SPA */
int *marker, *marker_relax;
complex *dense, *tempv;
float *stempv;
int *relax_end, *relax_fsupc;
complex *a;
int *asub;
int *xa_begin, *xa_end;
int *xsup, *supno;
int *xlsub, *xlusup, *xusub;
int nzlumax;
float *amax;
complex drop_sum;
float alpha, omega; /* used in MILU, mimicing DRIC */
static GlobalLU_t Glu; /* persistent to facilitate multiple factors. */
float *swork2; /* used by the second dropping rule */
/* Local scalars */
fact_t fact = options->Fact;
double diag_pivot_thresh = options->DiagPivotThresh;
double drop_tol = options->ILU_DropTol; /* tau */
double fill_ini = options->ILU_FillTol; /* tau^hat */
double gamma = options->ILU_FillFactor;
int drop_rule = options->ILU_DropRule;
milu_t milu = options->ILU_MILU;
double fill_tol;
int pivrow; /* pivotal row number in the original matrix A */
int nseg1; /* no of segments in U-column above panel row jcol */
int nseg; /* no of segments in each U-column */
register int jcol;
register int kcol; /* end column of a relaxed snode */
register int icol;
register int i, k, jj, new_next, iinfo;
int m, n, min_mn, jsupno, fsupc, nextlu, nextu;
int w_def; /* upper bound on panel width */
int usepr, iperm_r_allocated = 0;
int nnzL, nnzU;
int *panel_histo = stat->panel_histo;
flops_t *ops = stat->ops;
int last_drop;/* the last column which the dropping rules applied */
int quota;
int nnzAj; /* number of nonzeros in A(:,1:j) */
int nnzLj, nnzUj;
double tol_L = drop_tol, tol_U = drop_tol;
complex zero = {0.0, 0.0};
float one = 1.0;
/* Executable */
iinfo = 0;
m = A->nrow;
n = A->ncol;
min_mn = SUPERLU_MIN(m, n);
Astore = A->Store;
a = Astore->nzval;
asub = Astore->rowind;
xa_begin = Astore->colbeg;
xa_end = Astore->colend;
/* Allocate storage common to the factor routines */
*info = cLUMemInit(fact, work, lwork, m, n, Astore->nnz, panel_size,
gamma, L, U, &Glu, &iwork, &cwork);
if ( *info ) return;
xsup = Glu.xsup;
supno = Glu.supno;
xlsub = Glu.xlsub;
xlusup = Glu.xlusup;
xusub = Glu.xusub;
SetIWork(m, n, panel_size, iwork, &segrep, &parent, &xplore,
&repfnz, &panel_lsub, &marker_relax, &marker);
cSetRWork(m, panel_size, cwork, &dense, &tempv);
usepr = (fact == SamePattern_SameRowPerm);
if ( usepr ) {
/* Compute the inverse of perm_r */
iperm_r = (int *) intMalloc(m);
for (k = 0; k < m; ++k) iperm_r[perm_r[k]] = k;
iperm_r_allocated = 1;
}
iperm_c = (int *) intMalloc(n);
for (k = 0; k < n; ++k) iperm_c[perm_c[k]] = k;
swap = (int *)intMalloc(n);
for (k = 0; k < n; k++) swap[k] = iperm_c[k];
iswap = (int *)intMalloc(n);
for (k = 0; k < n; k++) iswap[k] = perm_c[k];
amax = (float *) floatMalloc(panel_size);
if (drop_rule & DROP_SECONDARY)
swork2 = (float *)floatMalloc(n);
else
swork2 = NULL;
nnzAj = 0;
nnzLj = 0;
nnzUj = 0;
last_drop = SUPERLU_MAX(min_mn - 2 * sp_ienv(7), (int)(min_mn * 0.95));
alpha = pow((double)n, -1.0 / options->ILU_MILU_Dim);
/* Identify relaxed snodes */
relax_end = (int *) intMalloc(n);
relax_fsupc = (int *) intMalloc(n);
if ( options->SymmetricMode == YES )
ilu_heap_relax_snode(n, etree, relax, marker, relax_end, relax_fsupc);
else
ilu_relax_snode(n, etree, relax, marker, relax_end, relax_fsupc);
ifill (perm_r, m, EMPTY);
ifill (marker, m * NO_MARKER, EMPTY);
supno[0] = -1;
xsup[0] = xlsub[0] = xusub[0] = xlusup[0] = 0;
w_def = panel_size;
/* Mark the rows used by relaxed supernodes */
ifill (marker_relax, m, EMPTY);
i = mark_relax(m, relax_end, relax_fsupc, xa_begin, xa_end,
asub, marker_relax);
#if ( PRNTlevel >= 1)
printf("%d relaxed supernodes.\n", i);
#endif
/*
* Work on one "panel" at a time. A panel is one of the following:
* (a) a relaxed supernode at the bottom of the etree, or
* (b) panel_size contiguous columns, defined by the user
*/
for (jcol = 0; jcol < min_mn; ) {
if ( relax_end[jcol] != EMPTY ) { /* start of a relaxed snode */
kcol = relax_end[jcol]; /* end of the relaxed snode */
panel_histo[kcol-jcol+1]++;
/* Drop small rows in the previous supernode. */
if (jcol > 0 && jcol < last_drop) {
int first = xsup[supno[jcol - 1]];
int last = jcol - 1;
int quota;
/* Compute the quota */
if (drop_rule & DROP_PROWS)
quota = gamma * Astore->nnz / m * (m - first) / m
* (last - first + 1);
else if (drop_rule & DROP_COLUMN) {
int i;
quota = 0;
for (i = first; i <= last; i++)
quota += xa_end[i] - xa_begin[i];
quota = gamma * quota * (m - first) / m;
} else if (drop_rule & DROP_AREA)
quota = gamma * nnzAj * (1.0 - 0.5 * (last + 1.0) / m)
- nnzLj;
else
quota = m * n;
fill_tol = pow(fill_ini, 1.0 - 0.5 * (first + last) / min_mn);
/* Drop small rows */
stempv = (float *) tempv;
i = ilu_cdrop_row(options, first, last, tol_L, quota, &nnzLj,
&fill_tol, &Glu, stempv, swork2, 0);
/* Reset the parameters */
if (drop_rule & DROP_DYNAMIC) {
if (gamma * nnzAj * (1.0 - 0.5 * (last + 1.0) / m)
< nnzLj)
tol_L = SUPERLU_MIN(1.0, tol_L * 2.0);
else
tol_L = SUPERLU_MAX(drop_tol, tol_L * 0.5);
}
if (fill_tol < 0) iinfo -= (int)fill_tol;
#ifdef DEBUG
num_drop_L += i * (last - first + 1);
#endif
}
/* --------------------------------------
* Factorize the relaxed supernode(jcol:kcol)
* -------------------------------------- */
/* Determine the union of the row structure of the snode */
if ( (*info = ilu_csnode_dfs(jcol, kcol, asub, xa_begin, xa_end,
marker, &Glu)) != 0 )
return;
nextu = xusub[jcol];
nextlu = xlusup[jcol];
jsupno = supno[jcol];
fsupc = xsup[jsupno];
new_next = nextlu + (xlsub[fsupc+1]-xlsub[fsupc])*(kcol-jcol+1);
nzlumax = Glu.nzlumax;
while ( new_next > nzlumax ) {
if ((*info = cLUMemXpand(jcol, nextlu, LUSUP, &nzlumax, &Glu)))
return;
}
for (icol = jcol; icol <= kcol; icol++) {
xusub[icol+1] = nextu;
amax[0] = 0.0;
/* Scatter into SPA dense[*] */
for (k = xa_begin[icol]; k < xa_end[icol]; k++) {
register float tmp = c_abs1 (&a[k]);
if (tmp > amax[0]) amax[0] = tmp;
dense[asub[k]] = a[k];
}
nnzAj += xa_end[icol] - xa_begin[icol];
if (amax[0] == 0.0) {
amax[0] = fill_ini;
#if ( PRNTlevel >= 1)
printf("Column %d is entirely zero!\n", icol);
fflush(stdout);
#endif
}
/* Numeric update within the snode */
csnode_bmod(icol, jsupno, fsupc, dense, tempv, &Glu, stat);
if (usepr) pivrow = iperm_r[icol];
fill_tol = pow(fill_ini, 1.0 - (double)icol / (double)min_mn);
if ( (*info = ilu_cpivotL(icol, diag_pivot_thresh, &usepr,
perm_r, iperm_c[icol], swap, iswap,
marker_relax, &pivrow,
amax[0] * fill_tol, milu, zero,
&Glu, stat)) ) {
iinfo++;
marker[pivrow] = kcol;
}
}
jcol = kcol + 1;
} else { /* Work on one panel of panel_size columns */
/* Adjust panel_size so that a panel won't overlap with the next
* relaxed snode.
*/
panel_size = w_def;
for (k = jcol + 1; k < SUPERLU_MIN(jcol+panel_size, min_mn); k++)
if ( relax_end[k] != EMPTY ) {
panel_size = k - jcol;
break;
}
if ( k == min_mn ) panel_size = min_mn - jcol;
panel_histo[panel_size]++;
/* symbolic factor on a panel of columns */
ilu_cpanel_dfs(m, panel_size, jcol, A, perm_r, &nseg1,
dense, amax, panel_lsub, segrep, repfnz,
marker, parent, xplore, &Glu);
/* numeric sup-panel updates in topological order */
cpanel_bmod(m, panel_size, jcol, nseg1, dense,
tempv, segrep, repfnz, &Glu, stat);
/* Sparse LU within the panel, and below panel diagonal */
for (jj = jcol; jj < jcol + panel_size; jj++) {
k = (jj - jcol) * m; /* column index for w-wide arrays */
nseg = nseg1; /* Begin after all the panel segments */
nnzAj += xa_end[jj] - xa_begin[jj];
if ((*info = ilu_ccolumn_dfs(m, jj, perm_r, &nseg,
&panel_lsub[k], segrep, &repfnz[k],
marker, parent, xplore, &Glu)))
return;
/* Numeric updates */
if ((*info = ccolumn_bmod(jj, (nseg - nseg1), &dense[k],
tempv, &segrep[nseg1], &repfnz[k],
jcol, &Glu, stat)) != 0) return;
/* Make a fill-in position if the column is entirely zero */
if (xlsub[jj + 1] == xlsub[jj]) {
register int i, row;
int nextl;
int nzlmax = Glu.nzlmax;
int *lsub = Glu.lsub;
int *marker2 = marker + 2 * m;
/* Allocate memory */
nextl = xlsub[jj] + 1;
if (nextl >= nzlmax) {
int error = cLUMemXpand(jj, nextl, LSUB, &nzlmax, &Glu);
if (error) { *info = error; return; }
lsub = Glu.lsub;
}
xlsub[jj + 1]++;
assert(xlusup[jj]==xlusup[jj+1]);
xlusup[jj + 1]++;
Glu.lusup[xlusup[jj]] = zero;
/* Choose a row index (pivrow) for fill-in */
for (i = jj; i < n; i++)
if (marker_relax[swap[i]] <= jj) break;
row = swap[i];
marker2[row] = jj;
lsub[xlsub[jj]] = row;
#ifdef DEBUG
printf("Fill col %d.\n", jj);
fflush(stdout);
#endif
}
/* Computer the quota */
if (drop_rule & DROP_PROWS)
quota = gamma * Astore->nnz / m * jj / m;
else if (drop_rule & DROP_COLUMN)
quota = gamma * (xa_end[jj] - xa_begin[jj]) *
(jj + 1) / m;
else if (drop_rule & DROP_AREA)
quota = gamma * 0.9 * nnzAj * 0.5 - nnzUj;
else
quota = m;
/* Copy the U-segments to ucol[*] and drop small entries */
if ((*info = ilu_ccopy_to_ucol(jj, nseg, segrep, &repfnz[k],
perm_r, &dense[k], drop_rule,
milu, amax[jj - jcol] * tol_U,
quota, &drop_sum, &nnzUj, &Glu,
swork2)) != 0)
return;
/* Reset the dropping threshold if required */
if (drop_rule & DROP_DYNAMIC) {
if (gamma * 0.9 * nnzAj * 0.5 < nnzLj)
tol_U = SUPERLU_MIN(1.0, tol_U * 2.0);
else
tol_U = SUPERLU_MAX(drop_tol, tol_U * 0.5);
}
if (drop_sum.r != 0.0 && drop_sum.i != 0.0)
{
omega = SUPERLU_MIN(2.0*(1.0-alpha)/c_abs1(&drop_sum), 1.0);
cs_mult(&drop_sum, &drop_sum, omega);
}
if (usepr) pivrow = iperm_r[jj];
fill_tol = pow(fill_ini, 1.0 - (double)jj / (double)min_mn);
if ( (*info = ilu_cpivotL(jj, diag_pivot_thresh, &usepr, perm_r,
iperm_c[jj], swap, iswap,
marker_relax, &pivrow,
amax[jj - jcol] * fill_tol, milu,
drop_sum, &Glu, stat)) ) {
iinfo++;
marker[m + pivrow] = jj;
marker[2 * m + pivrow] = jj;
}
/* Reset repfnz[] for this column */
resetrep_col (nseg, segrep, &repfnz[k]);
/* Start a new supernode, drop the previous one */
if (jj > 0 && supno[jj] > supno[jj - 1] && jj < last_drop) {
int first = xsup[supno[jj - 1]];
int last = jj - 1;
int quota;
/* Compute the quota */
if (drop_rule & DROP_PROWS)
quota = gamma * Astore->nnz / m * (m - first) / m
* (last - first + 1);
else if (drop_rule & DROP_COLUMN) {
int i;
quota = 0;
for (i = first; i <= last; i++)
quota += xa_end[i] - xa_begin[i];
quota = gamma * quota * (m - first) / m;
} else if (drop_rule & DROP_AREA)
quota = gamma * nnzAj * (1.0 - 0.5 * (last + 1.0)
/ m) - nnzLj;
else
quota = m * n;
fill_tol = pow(fill_ini, 1.0 - 0.5 * (first + last) /
(double)min_mn);
/* Drop small rows */
stempv = (float *) tempv;
i = ilu_cdrop_row(options, first, last, tol_L, quota,
&nnzLj, &fill_tol, &Glu, stempv, swork2,
1);
/* Reset the parameters */
if (drop_rule & DROP_DYNAMIC) {
if (gamma * nnzAj * (1.0 - 0.5 * (last + 1.0) / m)
< nnzLj)
tol_L = SUPERLU_MIN(1.0, tol_L * 2.0);
else
tol_L = SUPERLU_MAX(drop_tol, tol_L * 0.5);
}
if (fill_tol < 0) iinfo -= (int)fill_tol;
#ifdef DEBUG
num_drop_L += i * (last - first + 1);
#endif
} /* if start a new supernode */
} /* for */
jcol += panel_size; /* Move to the next panel */
} /* else */
} /* for */
*info = iinfo;
if ( m > n ) {
k = 0;
for (i = 0; i < m; ++i)
if ( perm_r[i] == EMPTY ) {
perm_r[i] = n + k;
++k;
}
}
ilu_countnz(min_mn, &nnzL, &nnzU, &Glu);
fixupL(min_mn, perm_r, &Glu);
cLUWorkFree(iwork, cwork, &Glu); /* Free work space and compress storage */
if ( fact == SamePattern_SameRowPerm ) {
/* L and U structures may have changed due to possibly different
pivoting, even though the storage is available.
There could also be memory expansions, so the array locations
may have changed, */
((SCformat *)L->Store)->nnz = nnzL;
((SCformat *)L->Store)->nsuper = Glu.supno[n];
((SCformat *)L->Store)->nzval = Glu.lusup;
((SCformat *)L->Store)->nzval_colptr = Glu.xlusup;
((SCformat *)L->Store)->rowind = Glu.lsub;
((SCformat *)L->Store)->rowind_colptr = Glu.xlsub;
((NCformat *)U->Store)->nnz = nnzU;
((NCformat *)U->Store)->nzval = Glu.ucol;
((NCformat *)U->Store)->rowind = Glu.usub;
((NCformat *)U->Store)->colptr = Glu.xusub;
} else {
cCreate_SuperNode_Matrix(L, A->nrow, min_mn, nnzL, Glu.lusup,
Glu.xlusup, Glu.lsub, Glu.xlsub, Glu.supno,
Glu.xsup, SLU_SC, SLU_C, SLU_TRLU);
cCreate_CompCol_Matrix(U, min_mn, min_mn, nnzU, Glu.ucol,
Glu.usub, Glu.xusub, SLU_NC, SLU_C, SLU_TRU);
}
ops[FACT] += ops[TRSV] + ops[GEMV];
stat->expansions = --(Glu.num_expansions);
if ( iperm_r_allocated ) SUPERLU_FREE (iperm_r);
SUPERLU_FREE (iperm_c);
SUPERLU_FREE (relax_end);
SUPERLU_FREE (swap);
SUPERLU_FREE (iswap);
SUPERLU_FREE (relax_fsupc);
SUPERLU_FREE (amax);
if ( swork2 ) SUPERLU_FREE (swork2);
}
main(int argc, char *argv[])
{
/*
* Purpose
* =======
*
* SDRIVE is the main test program for the FLOAT linear
* equation driver routines SGSSV and SGSSVX.
*
* The program is invoked by a shell script file -- stest.csh.
* The output from the tests are written into a file -- stest.out.
*
* =====================================================================
*/
float *a, *a_save;
int *asub, *asub_save;
int *xa, *xa_save;
SuperMatrix A, B, X, L, U;
SuperMatrix ASAV, AC;
GlobalLU_t Glu; /* Not needed on return. */
mem_usage_t mem_usage;
int *perm_r; /* row permutation from partial pivoting */
int *perm_c, *pc_save; /* column permutation */
int *etree;
float zero = 0.0;
float *R, *C;
float *ferr, *berr;
float *rwork;
float *wwork;
void *work;
int info, lwork, nrhs, panel_size, relax;
int m, n, nnz;
float *xact;
float *rhsb, *solx, *bsav;
int ldb, ldx;
float rpg, rcond;
int i, j, k1;
float rowcnd, colcnd, amax;
int maxsuper, rowblk, colblk;
int prefact, nofact, equil, iequed;
int nt, nrun, nfail, nerrs, imat, fimat, nimat;
int nfact, ifact, itran;
int kl, ku, mode, lda;
int zerot, izero, ioff;
double u;
float anorm, cndnum;
float *Afull;
float result[NTESTS];
superlu_options_t options;
fact_t fact;
trans_t trans;
SuperLUStat_t stat;
static char matrix_type[8];
static char equed[1], path[4], sym[1], dist[1];
FILE *fp;
/* Fixed set of parameters */
int iseed[] = {1988, 1989, 1990, 1991};
static char equeds[] = {'N', 'R', 'C', 'B'};
static fact_t facts[] = {FACTORED, DOFACT, SamePattern,
SamePattern_SameRowPerm};
static trans_t transs[] = {NOTRANS, TRANS, CONJ};
/* Some function prototypes */
extern int sgst01(int, int, SuperMatrix *, SuperMatrix *,
SuperMatrix *, int *, int *, float *);
extern int sgst02(trans_t, int, int, int, SuperMatrix *, float *,
int, float *, int, float *resid);
extern int sgst04(int, int, float *, int,
float *, int, float rcond, float *resid);
extern int sgst07(trans_t, int, int, SuperMatrix *, float *, int,
float *, int, float *, int,
float *, float *, float *);
extern int slatb4_slu(char *, int *, int *, int *, char *, int *, int *,
float *, int *, float *, char *);
extern int slatms_slu(int *, int *, char *, int *, char *, float *d,
int *, float *, float *, int *, int *,
char *, float *, int *, float *, int *);
extern int sp_sconvert(int, int, float *, int, int, int,
float *a, int *, int *, int *);
/* Executable statements */
strcpy(path, "SGE");
nrun = 0;
nfail = 0;
nerrs = 0;
/* Defaults */
lwork = 0;
n = 1;
nrhs = 1;
panel_size = sp_ienv(1);
relax = sp_ienv(2);
u = 1.0;
strcpy(matrix_type, "LA");
parse_command_line(argc, argv, matrix_type, &n,
&panel_size, &relax, &nrhs, &maxsuper,
&rowblk, &colblk, &lwork, &u, &fp);
if ( lwork > 0 ) {
work = SUPERLU_MALLOC(lwork);
if ( !work ) {
fprintf(stderr, "expert: cannot allocate %d bytes\n", lwork);
exit (-1);
}
}
/* Set the default input options. */
set_default_options(&options);
options.DiagPivotThresh = u;
options.PrintStat = NO;
options.PivotGrowth = YES;
options.ConditionNumber = YES;
options.IterRefine = SLU_SINGLE;
if ( strcmp(matrix_type, "LA") == 0 ) {
/* Test LAPACK matrix suite. */
m = n;
lda = SUPERLU_MAX(n, 1);
nnz = n * n; /* upper bound */
fimat = 1;
nimat = NTYPES;
Afull = floatCalloc(lda * n);
sallocateA(n, nnz, &a, &asub, &xa);
} else {
/* Read a sparse matrix */
fimat = nimat = 0;
sreadhb(fp, &m, &n, &nnz, &a, &asub, &xa);
}
sallocateA(n, nnz, &a_save, &asub_save, &xa_save);
rhsb = floatMalloc(m * nrhs);
bsav = floatMalloc(m * nrhs);
solx = floatMalloc(n * nrhs);
ldb = m;
ldx = n;
sCreate_Dense_Matrix(&B, m, nrhs, rhsb, ldb, SLU_DN, SLU_S, SLU_GE);
sCreate_Dense_Matrix(&X, n, nrhs, solx, ldx, SLU_DN, SLU_S, SLU_GE);
xact = floatMalloc(n * nrhs);
etree = intMalloc(n);
perm_r = intMalloc(n);
perm_c = intMalloc(n);
pc_save = intMalloc(n);
R = (float *) SUPERLU_MALLOC(m*sizeof(float));
C = (float *) SUPERLU_MALLOC(n*sizeof(float));
ferr = (float *) SUPERLU_MALLOC(nrhs*sizeof(float));
berr = (float *) SUPERLU_MALLOC(nrhs*sizeof(float));
j = SUPERLU_MAX(m,n) * SUPERLU_MAX(4,nrhs);
rwork = (float *) SUPERLU_MALLOC(j*sizeof(float));
for (i = 0; i < j; ++i) rwork[i] = 0.;
if ( !R ) ABORT("SUPERLU_MALLOC fails for R");
if ( !C ) ABORT("SUPERLU_MALLOC fails for C");
if ( !ferr ) ABORT("SUPERLU_MALLOC fails for ferr");
if ( !berr ) ABORT("SUPERLU_MALLOC fails for berr");
if ( !rwork ) ABORT("SUPERLU_MALLOC fails for rwork");
wwork = floatCalloc( SUPERLU_MAX(m,n) * SUPERLU_MAX(4,nrhs) );
for (i = 0; i < n; ++i) perm_c[i] = pc_save[i] = i;
options.ColPerm = MY_PERMC;
for (imat = fimat; imat <= nimat; ++imat) { /* All matrix types */
if ( imat ) {
/* Skip types 5, 6, or 7 if the matrix size is too small. */
zerot = (imat >= 5 && imat <= 7);
if ( zerot && n < imat-4 )
continue;
/* Set up parameters with SLATB4 and generate a test matrix
with SLATMS. */
slatb4_slu(path, &imat, &n, &n, sym, &kl, &ku, &anorm, &mode,
&cndnum, dist);
slatms_slu(&n, &n, dist, iseed, sym, &rwork[0], &mode, &cndnum,
&anorm, &kl, &ku, "No packing", Afull, &lda,
&wwork[0], &info);
if ( info ) {
printf(FMT3, "SLATMS", info, izero, n, nrhs, imat, nfail);
continue;
}
/* For types 5-7, zero one or more columns of the matrix
to test that INFO is returned correctly. */
if ( zerot ) {
if ( imat == 5 ) izero = 1;
else if ( imat == 6 ) izero = n;
else izero = n / 2 + 1;
ioff = (izero - 1) * lda;
if ( imat < 7 ) {
for (i = 0; i < n; ++i) Afull[ioff + i] = zero;
} else {
for (j = 0; j < n - izero + 1; ++j)
for (i = 0; i < n; ++i)
Afull[ioff + i + j*lda] = zero;
}
} else {
izero = 0;
}
/* Convert to sparse representation. */
sp_sconvert(n, n, Afull, lda, kl, ku, a, asub, xa, &nnz);
} else {
izero = 0;
zerot = 0;
}
sCreate_CompCol_Matrix(&A, m, n, nnz, a, asub, xa, SLU_NC, SLU_S, SLU_GE);
/* Save a copy of matrix A in ASAV */
sCreate_CompCol_Matrix(&ASAV, m, n, nnz, a_save, asub_save, xa_save,
SLU_NC, SLU_S, SLU_GE);
sCopy_CompCol_Matrix(&A, &ASAV);
/* Form exact solution. */
sGenXtrue(n, nrhs, xact, ldx);
StatInit(&stat);
for (iequed = 0; iequed < 4; ++iequed) {
*equed = equeds[iequed];
if (iequed == 0) nfact = 4;
else nfact = 1; /* Only test factored, pre-equilibrated matrix */
for (ifact = 0; ifact < nfact; ++ifact) {
fact = facts[ifact];
options.Fact = fact;
for (equil = 0; equil < 2; ++equil) {
options.Equil = equil;
prefact = ( options.Fact == FACTORED ||
options.Fact == SamePattern_SameRowPerm );
/* Need a first factor */
nofact = (options.Fact != FACTORED); /* Not factored */
/* Restore the matrix A. */
sCopy_CompCol_Matrix(&ASAV, &A);
if ( zerot ) {
if ( prefact ) continue;
} else if ( options.Fact == FACTORED ) {
if ( equil || iequed ) {
/* Compute row and column scale factors to
equilibrate matrix A. */
sgsequ(&A, R, C, &rowcnd, &colcnd, &amax, &info);
/* Force equilibration. */
if ( !info && n > 0 ) {
if ( strncmp(equed, "R", 1)==0 ) {
rowcnd = 0.;
colcnd = 1.;
} else if ( strncmp(equed, "C", 1)==0 ) {
rowcnd = 1.;
colcnd = 0.;
} else if ( strncmp(equed, "B", 1)==0 ) {
rowcnd = 0.;
colcnd = 0.;
}
}
/* Equilibrate the matrix. */
slaqgs(&A, R, C, rowcnd, colcnd, amax, equed);
}
}
if ( prefact ) { /* Need a factor for the first time */
/* Save Fact option. */
fact = options.Fact;
options.Fact = DOFACT;
/* Preorder the matrix, obtain the column etree. */
sp_preorder(&options, &A, perm_c, etree, &AC);
/* Factor the matrix AC. */
sgstrf(&options, &AC, relax, panel_size,
etree, work, lwork, perm_c, perm_r, &L, &U,
&Glu, &stat, &info);
if ( info ) {
printf("** First factor: info %d, equed %c\n",
info, *equed);
if ( lwork == -1 ) {
printf("** Estimated memory: %d bytes\n",
info - n);
exit(0);
}
}
Destroy_CompCol_Permuted(&AC);
/* Restore Fact option. */
options.Fact = fact;
} /* if .. first time factor */
for (itran = 0; itran < NTRAN; ++itran) {
trans = transs[itran];
options.Trans = trans;
/* Restore the matrix A. */
sCopy_CompCol_Matrix(&ASAV, &A);
/* Set the right hand side. */
sFillRHS(trans, nrhs, xact, ldx, &A, &B);
sCopy_Dense_Matrix(m, nrhs, rhsb, ldb, bsav, ldb);
/*----------------
* Test sgssv
*----------------*/
if ( options.Fact == DOFACT && itran == 0) {
/* Not yet factored, and untransposed */
sCopy_Dense_Matrix(m, nrhs, rhsb, ldb, solx, ldx);
sgssv(&options, &A, perm_c, perm_r, &L, &U, &X,
&stat, &info);
if ( info && info != izero ) {
printf(FMT3, "sgssv",
info, izero, n, nrhs, imat, nfail);
} else {
/* Reconstruct matrix from factors and
compute residual. */
sgst01(m, n, &A, &L, &U, perm_c, perm_r,
&result[0]);
nt = 1;
if ( izero == 0 ) {
/* Compute residual of the computed
solution. */
sCopy_Dense_Matrix(m, nrhs, rhsb, ldb,
wwork, ldb);
sgst02(trans, m, n, nrhs, &A, solx,
ldx, wwork,ldb, &result[1]);
nt = 2;
}
/* Print information about the tests that
did not pass the threshold. */
for (i = 0; i < nt; ++i) {
if ( result[i] >= THRESH ) {
printf(FMT1, "sgssv", n, i,
result[i]);
++nfail;
}
}
nrun += nt;
} /* else .. info == 0 */
/* Restore perm_c. */
for (i = 0; i < n; ++i) perm_c[i] = pc_save[i];
if (lwork == 0) {
Destroy_SuperNode_Matrix(&L);
Destroy_CompCol_Matrix(&U);
}
} /* if .. end of testing sgssv */
/*----------------
* Test sgssvx
*----------------*/
/* Equilibrate the matrix if fact = FACTORED and
equed = 'R', 'C', or 'B'. */
if ( options.Fact == FACTORED &&
(equil || iequed) && n > 0 ) {
slaqgs(&A, R, C, rowcnd, colcnd, amax, equed);
}
/* Solve the system and compute the condition number
and error bounds using sgssvx. */
sgssvx(&options, &A, perm_c, perm_r, etree,
equed, R, C, &L, &U, work, lwork, &B, &X, &rpg,
&rcond, ferr, berr, &Glu,
&mem_usage, &stat, &info);
if ( info && info != izero ) {
printf(FMT3, "sgssvx",
info, izero, n, nrhs, imat, nfail);
if ( lwork == -1 ) {
printf("** Estimated memory: %.0f bytes\n",
mem_usage.total_needed);
exit(0);
}
} else {
if ( !prefact ) {
/* Reconstruct matrix from factors and
compute residual. */
sgst01(m, n, &A, &L, &U, perm_c, perm_r,
&result[0]);
k1 = 0;
} else {
k1 = 1;
}
if ( !info ) {
/* Compute residual of the computed solution.*/
sCopy_Dense_Matrix(m, nrhs, bsav, ldb,
wwork, ldb);
sgst02(trans, m, n, nrhs, &ASAV, solx, ldx,
wwork, ldb, &result[1]);
/* Check solution from generated exact
solution. */
sgst04(n, nrhs, solx, ldx, xact, ldx, rcond,
&result[2]);
/* Check the error bounds from iterative
refinement. */
sgst07(trans, n, nrhs, &ASAV, bsav, ldb,
solx, ldx, xact, ldx, ferr, berr,
&result[3]);
/* Print information about the tests that did
not pass the threshold. */
for (i = k1; i < NTESTS; ++i) {
if ( result[i] >= THRESH ) {
printf(FMT2, "sgssvx",
options.Fact, trans, *equed,
n, imat, i, result[i]);
++nfail;
}
}
nrun += NTESTS;
} /* if .. info == 0 */
} /* else .. end of testing sgssvx */
} /* for itran ... */
if ( lwork == 0 ) {
Destroy_SuperNode_Matrix(&L);
Destroy_CompCol_Matrix(&U);
}
} /* for equil ... */
} /* for ifact ... */
} /* for iequed ... */
#if 0
if ( !info ) {
PrintPerf(&L, &U, &mem_usage, rpg, rcond, ferr, berr, equed);
}
#endif
Destroy_SuperMatrix_Store(&A);
Destroy_SuperMatrix_Store(&ASAV);
StatFree(&stat);
} /* for imat ... */
/* Print a summary of the results. */
PrintSumm("SGE", nfail, nrun, nerrs);
if ( strcmp(matrix_type, "LA") == 0 ) SUPERLU_FREE (Afull);
SUPERLU_FREE (rhsb);
SUPERLU_FREE (bsav);
SUPERLU_FREE (solx);
SUPERLU_FREE (xact);
SUPERLU_FREE (etree);
SUPERLU_FREE (perm_r);
SUPERLU_FREE (perm_c);
SUPERLU_FREE (pc_save);
SUPERLU_FREE (R);
SUPERLU_FREE (C);
SUPERLU_FREE (ferr);
SUPERLU_FREE (berr);
SUPERLU_FREE (rwork);
SUPERLU_FREE (wwork);
Destroy_SuperMatrix_Store(&B);
Destroy_SuperMatrix_Store(&X);
#if 0
Destroy_CompCol_Matrix(&A);
Destroy_CompCol_Matrix(&ASAV);
#else
SUPERLU_FREE(a); SUPERLU_FREE(asub); SUPERLU_FREE(xa);
SUPERLU_FREE(a_save); SUPERLU_FREE(asub_save); SUPERLU_FREE(xa_save);
#endif
if ( lwork > 0 ) {
SUPERLU_FREE (work);
Destroy_SuperMatrix_Store(&L);
Destroy_SuperMatrix_Store(&U);
}
return 0;
}
int sfgmr(int n,
void (*smatvec) (float, float[], float, float[]),
void (*spsolve) (int, float[], float[]),
float *rhs, float *sol, double tol, int im, int *itmax, FILE * fits)
{
/*----------------------------------------------------------------------
| *** Preconditioned FGMRES ***
+-----------------------------------------------------------------------
| This is a simple version of the ARMS preconditioned FGMRES algorithm.
+-----------------------------------------------------------------------
| Y. S. Dec. 2000. -- Apr. 2008
+-----------------------------------------------------------------------
| on entry:
|----------
|
| rhs = real vector of length n containing the right hand side.
| sol = real vector of length n containing an initial guess to the
| solution on input.
| tol = tolerance for stopping iteration
| im = Krylov subspace dimension
| (itmax) = max number of iterations allowed.
| fits = NULL: no output
| != NULL: file handle to output " resid vs time and its"
|
| on return:
|----------
| fgmr int = 0 --> successful return.
| int = 1 --> convergence not achieved in itmax iterations.
| sol = contains an approximate solution (upon successful return).
| itmax = has changed. It now contains the number of steps required
| to converge --
+-----------------------------------------------------------------------
| internal work arrays:
|----------
| vv = work array of length [im+1][n] (used to store the Arnoldi
| basis)
| hh = work array of length [im][im+1] (Householder matrix)
| z = work array of length [im][n] to store preconditioned vectors
+-----------------------------------------------------------------------
| subroutines called :
| matvec - matrix-vector multiplication operation
| psolve - (right) preconditionning operation
| psolve can be a NULL pointer (GMRES without preconditioner)
+---------------------------------------------------------------------*/
int maxits = *itmax;
int i, i1, ii, j, k, k1, its, retval, i_1 = 1, i_2 = 2;
float beta, eps1 = 0.0, t, t0, gam;
float **hh, *c, *s, *rs;
float **vv, **z, tt;
float zero = 0.0;
float one = 1.0;
its = 0;
vv = (float **)SUPERLU_MALLOC((im + 1) * sizeof(float *));
for (i = 0; i <= im; i++) vv[i] = floatMalloc(n);
z = (float **)SUPERLU_MALLOC(im * sizeof(float *));
hh = (float **)SUPERLU_MALLOC(im * sizeof(float *));
for (i = 0; i < im; i++)
{
hh[i] = floatMalloc(i + 2);
z[i] = floatMalloc(n);
}
c = floatMalloc(im);
s = floatMalloc(im);
rs = floatMalloc(im + 1);
/*---- outer loop starts here ----*/
do
{
/*---- compute initial residual vector ----*/
smatvec(one, sol, zero, vv[0]);
for (j = 0; j < n; j++)
vv[0][j] = rhs[j] - vv[0][j]; /* vv[0]= initial residual */
beta = snrm2_(&n, vv[0], &i_1);
/*---- print info if fits != null ----*/
if (fits != NULL && its == 0)
fprintf(fits, "%8d %10.2e\n", its, beta);
/*if ( beta <= tol * dnrm2_(&n, rhs, &i_1) )*/
if ( !(beta > tol * snrm2_(&n, rhs, &i_1)) )
break;
t = 1.0 / beta;
/*---- normalize: vv[0] = vv[0] / beta ----*/
for (j = 0; j < n; j++)
vv[0][j] = vv[0][j] * t;
if (its == 0)
eps1 = tol * beta;
/*---- initialize 1-st term of rhs of hessenberg system ----*/
rs[0] = beta;
for (i = 0; i < im; i++)
{
its++;
i1 = i + 1;
/*------------------------------------------------------------
| (Right) Preconditioning Operation z_{j} = M^{-1} v_{j}
+-----------------------------------------------------------*/
if (spsolve)
spsolve(n, z[i], vv[i]);
else
scopy_(&n, vv[i], &i_1, z[i], &i_1);
/*---- matvec operation w = A z_{j} = A M^{-1} v_{j} ----*/
smatvec(one, z[i], zero, vv[i1]);
/*------------------------------------------------------------
| modified gram - schmidt...
| h_{i,j} = (w,v_{i})
| w = w - h_{i,j} v_{i}
+------------------------------------------------------------*/
t0 = snrm2_(&n, vv[i1], &i_1);
for (j = 0; j <= i; j++)
{
float negt;
tt = sdot_(&n, vv[j], &i_1, vv[i1], &i_1);
hh[i][j] = tt;
negt = -tt;
saxpy_(&n, &negt, vv[j], &i_1, vv[i1], &i_1);
}
/*---- h_{j+1,j} = ||w||_{2} ----*/
t = snrm2_(&n, vv[i1], &i_1);
while (t < 0.5 * t0)
{
t0 = t;
for (j = 0; j <= i; j++)
{
float negt;
tt = sdot_(&n, vv[j], &i_1, vv[i1], &i_1);
hh[i][j] += tt;
negt = -tt;
saxpy_(&n, &negt, vv[j], &i_1, vv[i1], &i_1);
}
t = snrm2_(&n, vv[i1], &i_1);
}
hh[i][i1] = t;
if (t != 0.0)
{
/*---- v_{j+1} = w / h_{j+1,j} ----*/
t = 1.0 / t;
for (k = 0; k < n; k++)
vv[i1][k] = vv[i1][k] * t;
}
/*---------------------------------------------------
| done with modified gram schimdt and arnoldi step
| now update factorization of hh
+--------------------------------------------------*/
/*--------------------------------------------------------
| perform previous transformations on i-th column of h
+-------------------------------------------------------*/
for (k = 1; k <= i; k++)
{
k1 = k - 1;
tt = hh[i][k1];
hh[i][k1] = c[k1] * tt + s[k1] * hh[i][k];
hh[i][k] = -s[k1] * tt + c[k1] * hh[i][k];
}
gam = sqrt(pow(hh[i][i], 2) + pow(hh[i][i1], 2));
/*---------------------------------------------------
| if gamma is zero then any small value will do
| affect only residual estimate
+--------------------------------------------------*/
/* if (gam == 0.0) gam = epsmac; */
/*---- get next plane rotation ---*/
if (gam == 0.0)
{
c[i] = one;
s[i] = zero;
}
else
{
c[i] = hh[i][i] / gam;
s[i] = hh[i][i1] / gam;
}
rs[i1] = -s[i] * rs[i];
rs[i] = c[i] * rs[i];
/*----------------------------------------------------
| determine residual norm and test for convergence
+---------------------------------------------------*/
hh[i][i] = c[i] * hh[i][i] + s[i] * hh[i][i1];
beta = fabs(rs[i1]);
if (fits != NULL)
fprintf(fits, "%8d %10.2e\n", its, beta);
if (beta <= eps1 || its >= maxits)
break;
}
if (i == im) i--;
/*---- now compute solution. 1st, solve upper triangular system ----*/
rs[i] = rs[i] / hh[i][i];
for (ii = 1; ii <= i; ii++)
{
k = i - ii;
k1 = k + 1;
tt = rs[k];
for (j = k1; j <= i; j++)
tt = tt - hh[j][k] * rs[j];
rs[k] = tt / hh[k][k];
}
/*---- linear combination of v[i]'s to get sol. ----*/
for (j = 0; j <= i; j++)
{
tt = rs[j];
for (k = 0; k < n; k++)
sol[k] += tt * z[j][k];
}
/* calculate the residual and output */
smatvec(one, sol, zero, vv[0]);
for (j = 0; j < n; j++)
vv[0][j] = rhs[j] - vv[0][j]; /* vv[0]= initial residual */
/*---- print info if fits != null ----*/
beta = snrm2_(&n, vv[0], &i_1);
/*---- restart outer loop if needed ----*/
/*if (beta >= eps1 / tol)*/
if ( !(beta < eps1 / tol) )
{
its = maxits + 10;
break;
}
if (beta <= eps1)
break;
} while(its < maxits);
retval = (its >= maxits);
for (i = 0; i <= im; i++)
SUPERLU_FREE(vv[i]);
SUPERLU_FREE(vv);
for (i = 0; i < im; i++)
{
SUPERLU_FREE(hh[i]);
SUPERLU_FREE(z[i]);
}
SUPERLU_FREE(hh);
SUPERLU_FREE(z);
SUPERLU_FREE(c);
SUPERLU_FREE(s);
SUPERLU_FREE(rs);
*itmax = its;
return retval;
} /*----end of fgmr ----*/
void
sgstrs (trans_t trans, SuperMatrix *L, SuperMatrix *U,
int *perm_c, int *perm_r, SuperMatrix *B,
SuperLUStat_t *stat, int *info)
{
/*
* Purpose
* =======
*
* SGSTRS solves a system of linear equations A*X=B or A'*X=B
* with A sparse and B dense, using the LU factorization computed by
* SGSTRF.
*
* See supermatrix.h for the definition of 'SuperMatrix' structure.
*
* Arguments
* =========
*
* trans (input) trans_t
* Specifies the form of the system of equations:
* = NOTRANS: A * X = B (No transpose)
* = TRANS: A'* X = B (Transpose)
* = CONJ: A**H * X = B (Conjugate transpose)
*
* L (input) SuperMatrix*
* The factor L from the factorization Pr*A*Pc=L*U as computed by
* sgstrf(). Use compressed row subscripts storage for supernodes,
* i.e., L has types: Stype = SLU_SC, Dtype = SLU_S, Mtype = SLU_TRLU.
*
* U (input) SuperMatrix*
* The factor U from the factorization Pr*A*Pc=L*U as computed by
* sgstrf(). Use column-wise storage scheme, i.e., U has types:
* Stype = SLU_NC, Dtype = SLU_S, Mtype = SLU_TRU.
*
* perm_c (input) int*, dimension (L->ncol)
* Column permutation vector, which defines the
* permutation matrix Pc; perm_c[i] = j means column i of A is
* in position j in A*Pc.
*
* perm_r (input) int*, dimension (L->nrow)
* Row permutation vector, which defines the permutation matrix Pr;
* perm_r[i] = j means row i of A is in position j in Pr*A.
*
* B (input/output) SuperMatrix*
* B has types: Stype = SLU_DN, Dtype = SLU_S, Mtype = SLU_GE.
* On entry, the right hand side matrix.
* On exit, the solution matrix if info = 0;
*
* stat (output) SuperLUStat_t*
* Record the statistics on runtime and floating-point operation count.
* See util.h for the definition of 'SuperLUStat_t'.
*
* info (output) int*
* = 0: successful exit
* < 0: if info = -i, the i-th argument had an illegal value
*
*/
#ifdef _CRAY
_fcd ftcs1, ftcs2, ftcs3, ftcs4;
#endif
int incx = 1, incy = 1;
#ifdef USE_VENDOR_BLAS
float alpha = 1.0, beta = 1.0;
float *work_col;
#endif
DNformat *Bstore;
float *Bmat;
SCformat *Lstore;
NCformat *Ustore;
float *Lval, *Uval;
int fsupc, nrow, nsupr, nsupc, luptr, istart, irow;
int i, j, k, iptr, jcol, n, ldb, nrhs;
float *work, *rhs_work, *soln;
flops_t solve_ops;
void sprint_soln();
/* Test input parameters ... */
*info = 0;
Bstore = B->Store;
ldb = Bstore->lda;
nrhs = B->ncol;
if ( trans != NOTRANS && trans != TRANS && trans != CONJ ) *info = -1;
else if ( L->nrow != L->ncol || L->nrow < 0 ||
L->Stype != SLU_SC || L->Dtype != SLU_S || L->Mtype != SLU_TRLU )
*info = -2;
else if ( U->nrow != U->ncol || U->nrow < 0 ||
U->Stype != SLU_NC || U->Dtype != SLU_S || U->Mtype != SLU_TRU )
*info = -3;
else if ( ldb < SUPERLU_MAX(0, L->nrow) ||
B->Stype != SLU_DN || B->Dtype != SLU_S || B->Mtype != SLU_GE )
*info = -6;
if ( *info ) {
i = -(*info);
xerbla_("sgstrs", &i);
return;
}
n = L->nrow;
work = floatCalloc(n * nrhs);
if ( !work ) ABORT("Malloc fails for local work[].");
soln = floatMalloc(n);
if ( !soln ) ABORT("Malloc fails for local soln[].");
Bmat = Bstore->nzval;
Lstore = L->Store;
Lval = Lstore->nzval;
Ustore = U->Store;
Uval = Ustore->nzval;
solve_ops = 0;
if ( trans == NOTRANS ) {
/* Permute right hand sides to form Pr*B */
for (i = 0; i < nrhs; i++) {
rhs_work = &Bmat[i*ldb];
for (k = 0; k < n; k++) soln[perm_r[k]] = rhs_work[k];
for (k = 0; k < n; k++) rhs_work[k] = soln[k];
}
/* Forward solve PLy=Pb. */
for (k = 0; k <= Lstore->nsuper; k++) {
fsupc = L_FST_SUPC(k);
istart = L_SUB_START(fsupc);
nsupr = L_SUB_START(fsupc+1) - istart;
nsupc = L_FST_SUPC(k+1) - fsupc;
nrow = nsupr - nsupc;
solve_ops += nsupc * (nsupc - 1) * nrhs;
solve_ops += 2 * nrow * nsupc * nrhs;
if ( nsupc == 1 ) {
for (j = 0; j < nrhs; j++) {
rhs_work = &Bmat[j*ldb];
luptr = L_NZ_START(fsupc);
for (iptr=istart+1; iptr < L_SUB_START(fsupc+1); iptr++){
irow = L_SUB(iptr);
++luptr;
rhs_work[irow] -= rhs_work[fsupc] * Lval[luptr];
}
}
} else {
luptr = L_NZ_START(fsupc);
#ifdef USE_VENDOR_BLAS
#ifdef _CRAY
ftcs1 = _cptofcd("L", strlen("L"));
ftcs2 = _cptofcd("N", strlen("N"));
ftcs3 = _cptofcd("U", strlen("U"));
STRSM( ftcs1, ftcs1, ftcs2, ftcs3, &nsupc, &nrhs, &alpha,
&Lval[luptr], &nsupr, &Bmat[fsupc], &ldb);
SGEMM( ftcs2, ftcs2, &nrow, &nrhs, &nsupc, &alpha,
&Lval[luptr+nsupc], &nsupr, &Bmat[fsupc], &ldb,
&beta, &work[0], &n );
#else
strsm_("L", "L", "N", "U", &nsupc, &nrhs, &alpha,
&Lval[luptr], &nsupr, &Bmat[fsupc], &ldb);
sgemm_( "N", "N", &nrow, &nrhs, &nsupc, &alpha,
&Lval[luptr+nsupc], &nsupr, &Bmat[fsupc], &ldb,
&beta, &work[0], &n );
#endif
for (j = 0; j < nrhs; j++) {
rhs_work = &Bmat[j*ldb];
work_col = &work[j*n];
iptr = istart + nsupc;
for (i = 0; i < nrow; i++) {
irow = L_SUB(iptr);
rhs_work[irow] -= work_col[i]; /* Scatter */
work_col[i] = 0.0;
iptr++;
}
}
#else
for (j = 0; j < nrhs; j++) {
rhs_work = &Bmat[j*ldb];
slsolve (nsupr, nsupc, &Lval[luptr], &rhs_work[fsupc]);
smatvec (nsupr, nrow, nsupc, &Lval[luptr+nsupc],
&rhs_work[fsupc], &work[0] );
iptr = istart + nsupc;
for (i = 0; i < nrow; i++) {
irow = L_SUB(iptr);
rhs_work[irow] -= work[i];
work[i] = 0.0;
iptr++;
}
}
#endif
} /* else ... */
} /* for L-solve */
#ifdef DEBUG
printf("After L-solve: y=\n");
sprint_soln(n, nrhs, Bmat);
#endif
/*
* Back solve Ux=y.
*/
for (k = Lstore->nsuper; k >= 0; k--) {
fsupc = L_FST_SUPC(k);
istart = L_SUB_START(fsupc);
nsupr = L_SUB_START(fsupc+1) - istart;
nsupc = L_FST_SUPC(k+1) - fsupc;
luptr = L_NZ_START(fsupc);
solve_ops += nsupc * (nsupc + 1) * nrhs;
if ( nsupc == 1 ) {
rhs_work = &Bmat[0];
for (j = 0; j < nrhs; j++) {
rhs_work[fsupc] /= Lval[luptr];
rhs_work += ldb;
}
} else {
#ifdef USE_VENDOR_BLAS
#ifdef _CRAY
ftcs1 = _cptofcd("L", strlen("L"));
ftcs2 = _cptofcd("U", strlen("U"));
ftcs3 = _cptofcd("N", strlen("N"));
STRSM( ftcs1, ftcs2, ftcs3, ftcs3, &nsupc, &nrhs, &alpha,
&Lval[luptr], &nsupr, &Bmat[fsupc], &ldb);
#else
strsm_("L", "U", "N", "N", &nsupc, &nrhs, &alpha,
&Lval[luptr], &nsupr, &Bmat[fsupc], &ldb);
#endif
#else
for (j = 0; j < nrhs; j++)
susolve ( nsupr, nsupc, &Lval[luptr], &Bmat[fsupc+j*ldb] );
#endif
}
for (j = 0; j < nrhs; ++j) {
rhs_work = &Bmat[j*ldb];
for (jcol = fsupc; jcol < fsupc + nsupc; jcol++) {
solve_ops += 2*(U_NZ_START(jcol+1) - U_NZ_START(jcol));
for (i = U_NZ_START(jcol); i < U_NZ_START(jcol+1); i++ ){
irow = U_SUB(i);
rhs_work[irow] -= rhs_work[jcol] * Uval[i];
}
}
}
} /* for U-solve */
#ifdef DEBUG
printf("After U-solve: x=\n");
sprint_soln(n, nrhs, Bmat);
#endif
/* Compute the final solution X := Pc*X. */
for (i = 0; i < nrhs; i++) {
rhs_work = &Bmat[i*ldb];
for (k = 0; k < n; k++) soln[k] = rhs_work[perm_c[k]];
for (k = 0; k < n; k++) rhs_work[k] = soln[k];
}
stat->ops[SOLVE] = solve_ops;
} else { /* Solve A'*X=B or CONJ(A)*X=B */
/* Permute right hand sides to form Pc'*B. */
for (i = 0; i < nrhs; i++) {
rhs_work = &Bmat[i*ldb];
for (k = 0; k < n; k++) soln[perm_c[k]] = rhs_work[k];
for (k = 0; k < n; k++) rhs_work[k] = soln[k];
}
stat->ops[SOLVE] = 0;
for (k = 0; k < nrhs; ++k) {
/* Multiply by inv(U'). */
sp_strsv("U", "T", "N", L, U, &Bmat[k*ldb], stat, info);
/* Multiply by inv(L'). */
sp_strsv("L", "T", "U", L, U, &Bmat[k*ldb], stat, info);
}
/* Compute the final solution X := Pr'*X (=inv(Pr)*X) */
for (i = 0; i < nrhs; i++) {
rhs_work = &Bmat[i*ldb];
for (k = 0; k < n; k++) soln[k] = rhs_work[perm_r[k]];
for (k = 0; k < n; k++) rhs_work[k] = soln[k];
}
}
SUPERLU_FREE(work);
SUPERLU_FREE(soln);
}
int main ( int argc, char *argv[] )
/**********************************************************************/
/*
Purpose:
SUPER_LU_S3 solves a sparse system read from a file using SGSSVX.
Discussion:
The sparse matrix is stored in a file using the Harwell-Boeing
sparse matrix format. The file should be assigned to the standard
input of this program. For instance, if the matrix is stored
in the file "g10_rua.txt", the execution command might be:
super_lu_s3 < g10_rua.txt
Modified:
25 April 2004
Reference:
James Demmel, John Gilbert, Xiaoye Li,
SuperLU Users's Guide,
Sections 1 and 2.
Local parameters:
SuperMatrix L, the computed L factor.
int *perm_c, the column permutation vector.
int *perm_r, the row permutations from partial pivoting.
SuperMatrix U, the computed U factor.
*/
{
SuperMatrix A;
NCformat *Astore;
float *a;
int *asub;
SuperMatrix B;
float *berr;
float *C;
char equed[1];
yes_no_t equil;
int *etree;
float *ferr;
int i;
int info;
SuperMatrix L;
int ldx;
SCformat *Lstore;
int lwork;
int m;
mem_usage_t mem_usage;
int n;
int nnz;
int nrhs;
superlu_options_t options;
int *perm_c;
int *perm_r;
float *R;
float rcond;
float *rhsb;
float *rhsx;
float rpg;
float *sol;
SuperLUStat_t stat;
trans_t trans;
SuperMatrix U;
float u;
NCformat *Ustore;
void *work;
SuperMatrix X;
int *xa;
float *xact;
/*
Say hello.
*/
printf ( "\n" );
printf ( "SUPER_LU_S3:\n" );
printf ( " Read a sparse matrix A from standard input,\n");
printf ( " stored in Harwell-Boeing Sparse Matrix format.\n" );
printf ( "\n" );
printf ( " Solve a linear system A * X = B using SGSSVX.\n" );
/*
Defaults
*/
lwork = 0;
nrhs = 1;
equil = YES;
u = 1.0;
trans = NOTRANS;
/*
Set the default input options:
options.Fact = DOFACT;
options.Equil = YES;
options.ColPerm = COLAMD;
options.DiagPivotThresh = 1.0;
options.Trans = NOTRANS;
options.IterRefine = NOREFINE;
options.SymmetricMode = NO;
options.PivotGrowth = NO;
options.ConditionNumber = NO;
options.PrintStat = YES;
*/
set_default_options ( &options );
/*
Can use command line input to modify the defaults.
*/
parse_command_line ( argc, argv, &lwork, &u, &equil, &trans );
options.Equil = equil;
options.DiagPivotThresh = u;
options.Trans = trans;
printf ( "\n" );
printf ( " Length of work array LWORK = %d\n", lwork );
printf ( " Equilibration option EQUIL = %d\n", equil );
printf ( " Diagonal pivot threshhold value U = %f\n", u );
printf ( " Tranpose option TRANS = %d\n", trans );
/*
Add more functionalities that the defaults.
Compute reciprocal pivot growth
*/
options.PivotGrowth = YES;
/*
Compute reciprocal condition number
*/
options.ConditionNumber = YES;
/*
Perform single-precision refinement
*/
options.IterRefine = SINGLE;
if ( 0 < lwork )
{
work = SUPERLU_MALLOC(lwork);
if ( !work )
{
ABORT ( "SUPERLU_MALLOC cannot allocate work[]" );
}
}
/*
Read matrix A from a file in Harwell-Boeing format.
*/
sreadhb ( &m, &n, &nnz, &a, &asub, &xa );
/*
Create storage for a compressed column matrix.
*/
sCreate_CompCol_Matrix ( &A, m, n, nnz, a, asub, xa, SLU_NC, SLU_S, SLU_GE );
Astore = A.Store;
printf ( "\n" );
printf ( " Dimension %dx%d; # nonzeros %d\n", A.nrow, A.ncol, Astore->nnz );
rhsb = floatMalloc ( m * nrhs );
if ( !rhsb )
{
ABORT ( "Malloc fails for rhsb[]." );
}
rhsx = floatMalloc ( m * nrhs );
if ( !rhsx )
{
ABORT ( "Malloc fails for rhsx[]." );
}
sCreate_Dense_Matrix ( &B, m, nrhs, rhsb, m, SLU_DN, SLU_S, SLU_GE );
sCreate_Dense_Matrix ( &X, m, nrhs, rhsx, m, SLU_DN, SLU_S, SLU_GE );
xact = floatMalloc ( n * nrhs );
if ( !xact )
{
ABORT ( "SUPERLU_MALLOC cannot allocate xact[]" );
}
ldx = n;
sGenXtrue ( n, nrhs, xact, ldx );
sFillRHS ( trans, nrhs, xact, ldx, &A, &B );
etree = intMalloc ( n );
if ( !etree )
{
ABORT ( "Malloc fails for etree[]." );
}
perm_c = intMalloc ( n );
if ( !perm_c )
{
ABORT ( "Malloc fails for perm_c[]." );
}
perm_r = intMalloc ( m );
if ( !perm_r )
{
ABORT ( "Malloc fails for perm_r[]." );
}
R = (float *) SUPERLU_MALLOC ( A.nrow * sizeof(float) );
if ( !R )
{
ABORT ( "SUPERLU_MALLOC fails for R[]." );
}
C = (float *) SUPERLU_MALLOC ( A.ncol * sizeof(float) );
if ( !C )
{
ABORT ( "SUPERLU_MALLOC fails for C[]." );
}
ferr = (float *) SUPERLU_MALLOC ( nrhs * sizeof(float) );
if ( !ferr )
{
ABORT ( "SUPERLU_MALLOC fails for ferr[]." );
}
berr = (float *) SUPERLU_MALLOC ( nrhs * sizeof(float) );
if ( !berr )
{
ABORT ( "SUPERLU_MALLOC fails for berr[]." );
}
/*
Initialize the statistics variables.
*/
StatInit(&stat);
/*
Solve the system and compute the condition number and error bounds using SGSSVX.
*/
sgssvx ( &options, &A, perm_c, perm_r, etree, equed, R, C,
&L, &U, work, lwork, &B, &X, &rpg, &rcond, ferr, berr,
&mem_usage, &stat, &info );
printf ( "\n" );
printf ( " SGSSVX returns INFO = %d\n", info );
if ( info == 0 || info == n+1 )
{
sol = (float*) ((DNformat*) X.Store)->nzval;
if ( options.PivotGrowth == YES )
{
printf ( "\n" );
printf ( " Reciprocal pivot growth = %e\n", rpg);
}
if ( options.ConditionNumber == YES )
{
printf ( "\n" );
printf ( " Reciprocal condition number = %e\n", rcond);
}
if ( options.IterRefine != NOREFINE )
{
printf ( "\n" );
printf ( " Iterative Refinement:\n");
printf ( "%8s%8s%16s%16s\n", "rhs", "Steps", "FERR", "BERR");
for ( i = 0; i < nrhs; i++ )
{
printf ( "%8d%8d%16e%16e\n", i+1, stat.RefineSteps, ferr[i], berr[i]);
}
}
Lstore = (SCformat *) L.Store;
Ustore = (NCformat *) U.Store;
printf ( "\n" );
printf ( " Number of nonzeros in factor L = %d\n", Lstore->nnz );
printf ( " Number of nonzeros in factor U = %d\n", Ustore->nnz );
printf ( " Number of nonzeros in L+U = %d\n",
Lstore->nnz + Ustore->nnz - n );
printf ( "\n" );
printf ( " L\\U MB %.3f\ttotal MB needed %.3f\texpansions %d\n",
mem_usage.for_lu/1e6, mem_usage.total_needed/1e6,
mem_usage.expansions );
fflush ( stdout );
}
else if ( info > 0 && lwork == -1 )
{
printf ( "\n" );
printf ( " Estimated memory: %d bytes\n", info - n );
}
if ( options.PrintStat )
{
StatPrint ( &stat );
}
StatFree ( &stat );
SUPERLU_FREE ( rhsb );
SUPERLU_FREE ( rhsx );
SUPERLU_FREE ( xact );
SUPERLU_FREE ( etree );
SUPERLU_FREE ( perm_r );
SUPERLU_FREE ( perm_c );
SUPERLU_FREE ( R );
SUPERLU_FREE ( C );
SUPERLU_FREE ( ferr );
SUPERLU_FREE ( berr );
Destroy_CompCol_Matrix ( &A );
Destroy_SuperMatrix_Store ( &B );
Destroy_SuperMatrix_Store ( &X );
if ( 0 <= lwork )
{
Destroy_SuperNode_Matrix ( &L );
Destroy_CompCol_Matrix ( &U );
}
/*
Say goodbye.
*/
printf ( "\n" );
printf ( "SUPER_LU_S3:\n" );
printf ( " Normal end of execution.\n");
return 0;
}
int main(int argc, char *argv[])
{
SuperMatrix A;
NCformat *Astore;
float *a;
int *asub, *xa;
int *perm_c; /* column permutation vector */
int *perm_r; /* row permutations from partial pivoting */
SuperMatrix L; /* factor L */
SCformat *Lstore;
SuperMatrix U; /* factor U */
NCformat *Ustore;
SuperMatrix B;
int nrhs, ldx, info, m, n, nnz;
float *xact, *rhs;
mem_usage_t mem_usage;
superlu_options_t options;
SuperLUStat_t stat;
FILE *fp = stdin;
#if ( DEBUGlevel>=1 )
CHECK_MALLOC("Enter main()");
#endif
/* Set the default input options:
options.Fact = DOFACT;
options.Equil = YES;
options.ColPerm = COLAMD;
options.DiagPivotThresh = 1.0;
options.Trans = NOTRANS;
options.IterRefine = NOREFINE;
options.SymmetricMode = NO;
options.PivotGrowth = NO;
options.ConditionNumber = NO;
options.PrintStat = YES;
*/
set_default_options(&options);
/* Read the matrix in Harwell-Boeing format. */
sreadhb(fp, &m, &n, &nnz, &a, &asub, &xa);
sCreate_CompCol_Matrix(&A, m, n, nnz, a, asub, xa, SLU_NC, SLU_S, SLU_GE);
Astore = A.Store;
printf("Dimension %dx%d; # nonzeros %d\n", A.nrow, A.ncol, Astore->nnz);
nrhs = 1;
if ( !(rhs = floatMalloc(m * nrhs)) ) ABORT("Malloc fails for rhs[].");
sCreate_Dense_Matrix(&B, m, nrhs, rhs, m, SLU_DN, SLU_S, SLU_GE);
xact = floatMalloc(n * nrhs);
ldx = n;
sGenXtrue(n, nrhs, xact, ldx);
sFillRHS(options.Trans, nrhs, xact, ldx, &A, &B);
if ( !(perm_c = intMalloc(n)) ) ABORT("Malloc fails for perm_c[].");
if ( !(perm_r = intMalloc(m)) ) ABORT("Malloc fails for perm_r[].");
/* Initialize the statistics variables. */
StatInit(&stat);
sgssv(&options, &A, perm_c, perm_r, &L, &U, &B, &stat, &info);
if ( info == 0 ) {
/* This is how you could access the solution matrix. */
float *sol = (float*) ((DNformat*) B.Store)->nzval;
/* Compute the infinity norm of the error. */
sinf_norm_error(nrhs, &B, xact);
Lstore = (SCformat *) L.Store;
Ustore = (NCformat *) U.Store;
printf("No of nonzeros in factor L = %d\n", Lstore->nnz);
printf("No of nonzeros in factor U = %d\n", Ustore->nnz);
printf("No of nonzeros in L+U = %d\n", Lstore->nnz + Ustore->nnz - n);
printf("FILL ratio = %.1f\n", (float)(Lstore->nnz + Ustore->nnz - n)/nnz);
sQuerySpace(&L, &U, &mem_usage);
printf("L\\U MB %.3f\ttotal MB needed %.3f\n",
mem_usage.for_lu/1e6, mem_usage.total_needed/1e6);
} else {
printf("sgssv() error returns INFO= %d\n", info);
if ( info <= n ) { /* factorization completes */
sQuerySpace(&L, &U, &mem_usage);
printf("L\\U MB %.3f\ttotal MB needed %.3f\n",
mem_usage.for_lu/1e6, mem_usage.total_needed/1e6);
}
}
if ( options.PrintStat ) StatPrint(&stat);
StatFree(&stat);
SUPERLU_FREE (rhs);
SUPERLU_FREE (xact);
SUPERLU_FREE (perm_r);
SUPERLU_FREE (perm_c);
Destroy_CompCol_Matrix(&A);
Destroy_SuperMatrix_Store(&B);
Destroy_SuperNode_Matrix(&L);
Destroy_CompCol_Matrix(&U);
#if ( DEBUGlevel>=1 )
CHECK_MALLOC("Exit main()");
#endif
}
int sdominate(int n, NCformat *Astore)
/* make the matrix diagonally dominant */
{
float *nzval = (float *)Astore->nzval;
int *rowind = Astore->rowind;
int *colptr = Astore->colptr;
int nnz = colptr[n];
int fill = 0;
float *nzval_new;
int *rowind_new;
int i, j, diag;
double s;
for (i = 0; i < n; i++)
{
diag = -1;
for (j = colptr[i]; j < colptr[i + 1]; j++)
if (rowind[j] == i) diag = j;
if (diag < 0) fill++;
}
if (fill)
{
nzval_new = floatMalloc(nnz + fill);
rowind_new = intMalloc(nnz+ fill);
fill = 0;
for (i = 0; i < n; i++)
{
s = 1e-6;
diag = -1;
for (j = colptr[i] - fill; j < colptr[i + 1]; j++)
{
if ((rowind_new[j + fill] = rowind[j]) == i) diag = j;
s += fabs(nzval_new[j + fill] = nzval[j]);
}
if (diag >= 0) {
nzval_new[diag+fill] = s * 3.0;
} else {
rowind_new[colptr[i + 1] + fill] = i;
nzval_new[colptr[i + 1] + fill] = s * 3.0;
fill++;
}
colptr[i + 1] += fill;
}
Astore->nzval = nzval_new;
Astore->rowind = rowind_new;
SUPERLU_FREE(nzval);
SUPERLU_FREE(rowind);
}
else
{
for (i = 0; i < n; i++)
{
s = 1e-6;
diag = -1;
for (j = colptr[i]; j < colptr[i + 1]; j++)
{
if (rowind[j] == i) diag = j;
s += fabs(nzval[j]);
}
nzval[diag] = s * 3.0;
}
}
Astore->nnz += fill;
return fill;
}
main(int argc, char *argv[])
{
/*
* Purpose
* =======
*
* The driver program SLINSOLX1.
*
* This example illustrates how to use SGSSVX to solve systems with the same
* A but different right-hand side.
* In this case, we factorize A only once in the first call to DGSSVX,
* and reuse the following data structures in the subsequent call to SGSSVX:
* perm_c, perm_r, R, C, L, U.
*
*/
char equed[1];
yes_no_t equil;
trans_t trans;
SuperMatrix A, L, U;
SuperMatrix B, X;
NCformat *Astore;
NCformat *Ustore;
SCformat *Lstore;
float *a;
int *asub, *xa;
int *perm_c; /* column permutation vector */
int *perm_r; /* row permutations from partial pivoting */
int *etree;
void *work;
int info, lwork, nrhs, ldx;
int i, m, n, nnz;
float *rhsb, *rhsx, *xact;
float *R, *C;
float *ferr, *berr;
float u, rpg, rcond;
mem_usage_t mem_usage;
superlu_options_t options;
SuperLUStat_t stat;
extern void parse_command_line();
#if ( DEBUGlevel>=1 )
CHECK_MALLOC("Enter main()");
#endif
/* Defaults */
lwork = 0;
nrhs = 1;
equil = YES;
u = 1.0;
trans = NOTRANS;
/* Set the default values for options argument:
options.Fact = DOFACT;
options.Equil = YES;
options.ColPerm = COLAMD;
options.DiagPivotThresh = 1.0;
options.Trans = NOTRANS;
options.IterRefine = NOREFINE;
options.SymmetricMode = NO;
options.PivotGrowth = NO;
options.ConditionNumber = NO;
options.PrintStat = YES;
*/
set_default_options(&options);
/* Can use command line input to modify the defaults. */
parse_command_line(argc, argv, &lwork, &u, &equil, &trans);
options.Equil = equil;
options.DiagPivotThresh = u;
options.Trans = trans;
if ( lwork > 0 ) {
work = SUPERLU_MALLOC(lwork);
if ( !work ) {
ABORT("SLINSOLX: cannot allocate work[]");
}
}
/* Read matrix A from a file in Harwell-Boeing format.*/
sreadhb(&m, &n, &nnz, &a, &asub, &xa);
sCreate_CompCol_Matrix(&A, m, n, nnz, a, asub, xa, SLU_NC, SLU_S, SLU_GE);
Astore = A.Store;
printf("Dimension %dx%d; # nonzeros %d\n", A.nrow, A.ncol, Astore->nnz);
if ( !(rhsb = floatMalloc(m * nrhs)) ) ABORT("Malloc fails for rhsb[].");
if ( !(rhsx = floatMalloc(m * nrhs)) ) ABORT("Malloc fails for rhsx[].");
sCreate_Dense_Matrix(&B, m, nrhs, rhsb, m, SLU_DN, SLU_S, SLU_GE);
sCreate_Dense_Matrix(&X, m, nrhs, rhsx, m, SLU_DN, SLU_S, SLU_GE);
xact = floatMalloc(n * nrhs);
ldx = n;
sGenXtrue(n, nrhs, xact, ldx);
sFillRHS(trans, nrhs, xact, ldx, &A, &B);
if ( !(etree = intMalloc(n)) ) ABORT("Malloc fails for etree[].");
if ( !(perm_r = intMalloc(m)) ) ABORT("Malloc fails for perm_r[].");
if ( !(perm_c = intMalloc(n)) ) ABORT("Malloc fails for perm_c[].");
if ( !(R = (float *) SUPERLU_MALLOC(A.nrow * sizeof(float))) )
ABORT("SUPERLU_MALLOC fails for R[].");
if ( !(C = (float *) SUPERLU_MALLOC(A.ncol * sizeof(float))) )
ABORT("SUPERLU_MALLOC fails for C[].");
if ( !(ferr = (float *) SUPERLU_MALLOC(nrhs * sizeof(float))) )
ABORT("SUPERLU_MALLOC fails for ferr[].");
if ( !(berr = (float *) SUPERLU_MALLOC(nrhs * sizeof(float))) )
ABORT("SUPERLU_MALLOC fails for berr[].");
/* Initialize the statistics variables. */
StatInit(&stat);
/* ONLY PERFORM THE LU DECOMPOSITION */
B.ncol = 0; /* Indicate not to solve the system */
sgssvx(&options, &A, perm_c, perm_r, etree, equed, R, C,
&L, &U, work, lwork, &B, &X, &rpg, &rcond, ferr, berr,
&mem_usage, &stat, &info);
printf("LU factorization: sgssvx() returns info %d\n", info);
if ( info == 0 || info == n+1 ) {
if ( options.PivotGrowth ) printf("Recip. pivot growth = %e\n", rpg);
if ( options.ConditionNumber )
printf("Recip. condition number = %e\n", rcond);
Lstore = (SCformat *) L.Store;
Ustore = (NCformat *) U.Store;
printf("No of nonzeros in factor L = %d\n", Lstore->nnz);
printf("No of nonzeros in factor U = %d\n", Ustore->nnz);
printf("No of nonzeros in L+U = %d\n", Lstore->nnz + Ustore->nnz - n);
printf("FILL ratio = %.1f\n", (float)(Lstore->nnz + Ustore->nnz - n)/nnz);
printf("L\\U MB %.3f\ttotal MB needed %.3f\n",
mem_usage.for_lu/1e6, mem_usage.total_needed/1e6);
fflush(stdout);
} else if ( info > 0 && lwork == -1 ) {
printf("** Estimated memory: %d bytes\n", info - n);
}
if ( options.PrintStat ) StatPrint(&stat);
StatFree(&stat);
/* ------------------------------------------------------------
NOW WE SOLVE THE LINEAR SYSTEM USING THE FACTORED FORM OF A.
------------------------------------------------------------*/
options.Fact = FACTORED; /* Indicate the factored form of A is supplied. */
B.ncol = nrhs; /* Set the number of right-hand side */
/* Initialize the statistics variables. */
StatInit(&stat);
sgssvx(&options, &A, perm_c, perm_r, etree, equed, R, C,
&L, &U, work, lwork, &B, &X, &rpg, &rcond, ferr, berr,
&mem_usage, &stat, &info);
printf("Triangular solve: sgssvx() returns info %d\n", info);
if ( info == 0 || info == n+1 ) {
/* This is how you could access the solution matrix. */
float *sol = (float*) ((DNformat*) X.Store)->nzval;
if ( options.IterRefine ) {
printf("Iterative Refinement:\n");
printf("%8s%8s%16s%16s\n", "rhs", "Steps", "FERR", "BERR");
for (i = 0; i < nrhs; ++i)
printf("%8d%8d%16e%16e\n", i+1, stat.RefineSteps, ferr[i], berr[i]);
}
fflush(stdout);
} else if ( info > 0 && lwork == -1 ) {
printf("** Estimated memory: %d bytes\n", info - n);
}
if ( options.PrintStat ) StatPrint(&stat);
StatFree(&stat);
SUPERLU_FREE (rhsb);
SUPERLU_FREE (rhsx);
SUPERLU_FREE (xact);
SUPERLU_FREE (etree);
SUPERLU_FREE (perm_r);
SUPERLU_FREE (perm_c);
SUPERLU_FREE (R);
SUPERLU_FREE (C);
SUPERLU_FREE (ferr);
SUPERLU_FREE (berr);
Destroy_CompCol_Matrix(&A);
Destroy_SuperMatrix_Store(&B);
Destroy_SuperMatrix_Store(&X);
if ( lwork >= 0 ) {
Destroy_SuperNode_Matrix(&L);
Destroy_CompCol_Matrix(&U);
}
#if ( DEBUGlevel>=1 )
CHECK_MALLOC("Exit main()");
#endif
}
void
sgsisx(superlu_options_t *options, SuperMatrix *A, int *perm_c, int *perm_r,
int *etree, char *equed, float *R, float *C,
SuperMatrix *L, SuperMatrix *U, void *work, int lwork,
SuperMatrix *B, SuperMatrix *X,
float *recip_pivot_growth, float *rcond,
mem_usage_t *mem_usage, SuperLUStat_t *stat, int *info)
{
DNformat *Bstore, *Xstore;
float *Bmat, *Xmat;
int ldb, ldx, nrhs;
SuperMatrix *AA;/* A in SLU_NC format used by the factorization routine.*/
SuperMatrix AC; /* Matrix postmultiplied by Pc */
int colequ, equil, nofact, notran, rowequ, permc_spec, mc64;
trans_t trant;
char norm[1];
int i, j, info1;
float amax, anorm, bignum, smlnum, colcnd, rowcnd, rcmax, rcmin;
int relax, panel_size;
float diag_pivot_thresh;
double t0; /* temporary time */
double *utime;
int *perm = NULL;
/* External functions */
extern float slangs(char *, SuperMatrix *);
Bstore = B->Store;
Xstore = X->Store;
Bmat = Bstore->nzval;
Xmat = Xstore->nzval;
ldb = Bstore->lda;
ldx = Xstore->lda;
nrhs = B->ncol;
*info = 0;
nofact = (options->Fact != FACTORED);
equil = (options->Equil == YES);
notran = (options->Trans == NOTRANS);
mc64 = (options->RowPerm == LargeDiag);
if ( nofact ) {
*(unsigned char *)equed = 'N';
rowequ = FALSE;
colequ = FALSE;
} else {
rowequ = lsame_(equed, "R") || lsame_(equed, "B");
colequ = lsame_(equed, "C") || lsame_(equed, "B");
smlnum = slamch_("Safe minimum");
bignum = 1. / smlnum;
}
/* Test the input parameters */
if (!nofact && options->Fact != DOFACT && options->Fact != SamePattern &&
options->Fact != SamePattern_SameRowPerm &&
!notran && options->Trans != TRANS && options->Trans != CONJ &&
!equil && options->Equil != NO)
*info = -1;
else if ( A->nrow != A->ncol || A->nrow < 0 ||
(A->Stype != SLU_NC && A->Stype != SLU_NR) ||
A->Dtype != SLU_S || A->Mtype != SLU_GE )
*info = -2;
else if (options->Fact == FACTORED &&
!(rowequ || colequ || lsame_(equed, "N")))
*info = -6;
else {
if (rowequ) {
rcmin = bignum;
rcmax = 0.;
for (j = 0; j < A->nrow; ++j) {
rcmin = SUPERLU_MIN(rcmin, R[j]);
rcmax = SUPERLU_MAX(rcmax, R[j]);
}
if (rcmin <= 0.) *info = -7;
else if ( A->nrow > 0)
rowcnd = SUPERLU_MAX(rcmin,smlnum) / SUPERLU_MIN(rcmax,bignum);
else rowcnd = 1.;
}
if (colequ && *info == 0) {
rcmin = bignum;
rcmax = 0.;
for (j = 0; j < A->nrow; ++j) {
rcmin = SUPERLU_MIN(rcmin, C[j]);
rcmax = SUPERLU_MAX(rcmax, C[j]);
}
if (rcmin <= 0.) *info = -8;
else if (A->nrow > 0)
colcnd = SUPERLU_MAX(rcmin,smlnum) / SUPERLU_MIN(rcmax,bignum);
else colcnd = 1.;
}
if (*info == 0) {
if ( lwork < -1 ) *info = -12;
else if ( B->ncol < 0 || Bstore->lda < SUPERLU_MAX(0, A->nrow) ||
B->Stype != SLU_DN || B->Dtype != SLU_S ||
B->Mtype != SLU_GE )
*info = -13;
else if ( X->ncol < 0 || Xstore->lda < SUPERLU_MAX(0, A->nrow) ||
(B->ncol != 0 && B->ncol != X->ncol) ||
X->Stype != SLU_DN ||
X->Dtype != SLU_S || X->Mtype != SLU_GE )
*info = -14;
}
}
if (*info != 0) {
i = -(*info);
xerbla_("sgsisx", &i);
return;
}
/* Initialization for factor parameters */
panel_size = sp_ienv(1);
relax = sp_ienv(2);
diag_pivot_thresh = options->DiagPivotThresh;
utime = stat->utime;
/* Convert A to SLU_NC format when necessary. */
if ( A->Stype == SLU_NR ) {
NRformat *Astore = A->Store;
AA = (SuperMatrix *) SUPERLU_MALLOC( sizeof(SuperMatrix) );
sCreate_CompCol_Matrix(AA, A->ncol, A->nrow, Astore->nnz,
Astore->nzval, Astore->colind, Astore->rowptr,
SLU_NC, A->Dtype, A->Mtype);
if ( notran ) { /* Reverse the transpose argument. */
trant = TRANS;
notran = 0;
} else {
trant = NOTRANS;
notran = 1;
}
} else { /* A->Stype == SLU_NC */
trant = options->Trans;
AA = A;
}
if ( nofact ) {
register int i, j;
NCformat *Astore = AA->Store;
int nnz = Astore->nnz;
int *colptr = Astore->colptr;
int *rowind = Astore->rowind;
float *nzval = (float *)Astore->nzval;
int n = AA->nrow;
if ( mc64 ) {
*equed = 'B';
/*rowequ = colequ = 1;*/
t0 = SuperLU_timer_();
if ((perm = intMalloc(n)) == NULL)
ABORT("SUPERLU_MALLOC fails for perm[]");
info1 = sldperm(5, n, nnz, colptr, rowind, nzval, perm, R, C);
if (info1 > 0) { /* MC64 fails, call sgsequ() later */
mc64 = 0;
SUPERLU_FREE(perm);
perm = NULL;
} else {
rowequ = colequ = 1;
for (i = 0; i < n; i++) {
R[i] = exp(R[i]);
C[i] = exp(C[i]);
}
/* permute and scale the matrix */
for (j = 0; j < n; j++) {
for (i = colptr[j]; i < colptr[j + 1]; i++) {
nzval[i] *= R[rowind[i]] * C[j];
rowind[i] = perm[rowind[i]];
}
}
}
utime[EQUIL] = SuperLU_timer_() - t0;
}
if ( !mc64 & equil ) {
t0 = SuperLU_timer_();
/* Compute row and column scalings to equilibrate the matrix A. */
sgsequ(AA, R, C, &rowcnd, &colcnd, &amax, &info1);
if ( info1 == 0 ) {
/* Equilibrate matrix A. */
slaqgs(AA, R, C, rowcnd, colcnd, amax, equed);
rowequ = lsame_(equed, "R") || lsame_(equed, "B");
colequ = lsame_(equed, "C") || lsame_(equed, "B");
}
utime[EQUIL] = SuperLU_timer_() - t0;
}
}
if ( nofact ) {
t0 = SuperLU_timer_();
/*
* Gnet column permutation vector perm_c[], according to permc_spec:
* permc_spec = NATURAL: natural ordering
* permc_spec = MMD_AT_PLUS_A: minimum degree on structure of A'+A
* permc_spec = MMD_ATA: minimum degree on structure of A'*A
* permc_spec = COLAMD: approximate minimum degree column ordering
* permc_spec = MY_PERMC: the ordering already supplied in perm_c[]
*/
permc_spec = options->ColPerm;
if ( permc_spec != MY_PERMC && options->Fact == DOFACT )
get_perm_c(permc_spec, AA, perm_c);
utime[COLPERM] = SuperLU_timer_() - t0;
t0 = SuperLU_timer_();
sp_preorder(options, AA, perm_c, etree, &AC);
utime[ETREE] = SuperLU_timer_() - t0;
/* Compute the LU factorization of A*Pc. */
t0 = SuperLU_timer_();
sgsitrf(options, &AC, relax, panel_size, etree, work, lwork,
perm_c, perm_r, L, U, stat, info);
utime[FACT] = SuperLU_timer_() - t0;
if ( lwork == -1 ) {
mem_usage->total_needed = *info - A->ncol;
return;
}
}
if ( options->PivotGrowth ) {
if ( *info > 0 ) return;
/* Compute the reciprocal pivot growth factor *recip_pivot_growth. */
*recip_pivot_growth = sPivotGrowth(A->ncol, AA, perm_c, L, U);
}
if ( options->ConditionNumber ) {
/* Estimate the reciprocal of the condition number of A. */
t0 = SuperLU_timer_();
if ( notran ) {
*(unsigned char *)norm = '1';
} else {
*(unsigned char *)norm = 'I';
}
anorm = slangs(norm, AA);
sgscon(norm, L, U, anorm, rcond, stat, &info1);
utime[RCOND] = SuperLU_timer_() - t0;
}
if ( nrhs > 0 ) { /* Solve the system */
float *tmp, *rhs_work;
int n = A->nrow;
if ( mc64 ) {
if ((tmp = floatMalloc(n)) == NULL)
ABORT("SUPERLU_MALLOC fails for tmp[]");
}
/* Scale and permute the right-hand side if equilibration
and permutation from MC64 were performed. */
if ( notran ) {
if ( rowequ ) {
for (j = 0; j < nrhs; ++j)
for (i = 0; i < n; ++i)
Bmat[i + j*ldb] *= R[i];
}
if ( mc64 ) {
for (j = 0; j < nrhs; ++j) {
rhs_work = &Bmat[j*ldb];
for (i = 0; i < n; i++) tmp[perm[i]] = rhs_work[i];
for (i = 0; i < n; i++) rhs_work[i] = tmp[i];
}
}
} else if ( colequ ) {
for (j = 0; j < nrhs; ++j)
for (i = 0; i < n; ++i) {
Bmat[i + j*ldb] *= C[i];
}
}
/* Compute the solution matrix X. */
for (j = 0; j < nrhs; j++) /* Save a copy of the right hand sides */
for (i = 0; i < B->nrow; i++)
Xmat[i + j*ldx] = Bmat[i + j*ldb];
t0 = SuperLU_timer_();
sgstrs (trant, L, U, perm_c, perm_r, X, stat, &info1);
utime[SOLVE] = SuperLU_timer_() - t0;
/* Transform the solution matrix X to a solution of the original
system. */
if ( notran ) {
if ( colequ ) {
for (j = 0; j < nrhs; ++j)
for (i = 0; i < n; ++i) {
Xmat[i + j*ldx] *= C[i];
}
}
} else { /* transposed system */
if ( rowequ ) {
if ( mc64 ) {
for (j = 0; j < nrhs; j++) {
for (i = 0; i < n; i++)
tmp[i] = Xmat[i + j * ldx]; /*dcopy*/
for (i = 0; i < n; i++)
Xmat[i + j * ldx] = R[i] * tmp[perm[i]];
}
} else {
for (j = 0; j < nrhs; ++j)
for (i = 0; i < A->nrow; ++i) {
Xmat[i + j*ldx] *= R[i];
}
}
}
}
if ( mc64 ) SUPERLU_FREE(tmp);
} /* end if nrhs > 0 */
if ( options->ConditionNumber ) {
/* Set INFO = A->ncol+1 if the matrix is singular to working precision. */
if ( *rcond < slamch_("E") && *info == 0) *info = A->ncol + 1;
}
if (perm) SUPERLU_FREE(perm);
if ( nofact ) {
ilu_sQuerySpace(L, U, mem_usage);
Destroy_CompCol_Permuted(&AC);
}
if ( A->Stype == SLU_NR ) {
Destroy_SuperMatrix_Store(AA);
SUPERLU_FREE(AA);
}
}
main(int argc, char *argv[])
{
/*
* Purpose
* =======
*
* The driver program SLINSOLX2.
*
* This example illustrates how to use SGSSVX to solve systems repeatedly
* with the same sparsity pattern of matrix A.
* In this case, the column permutation vector perm_c is computed once.
* The following data structures will be reused in the subsequent call to
* SGSSVX: perm_c, etree
*
*/
char equed[1];
yes_no_t equil;
trans_t trans;
SuperMatrix A, A1, L, U;
SuperMatrix B, B1, X;
NCformat *Astore;
NCformat *Ustore;
SCformat *Lstore;
float *a, *a1;
int *asub, *xa, *asub1, *xa1;
int *perm_r; /* row permutations from partial pivoting */
int *perm_c; /* column permutation vector */
int *etree;
void *work;
int info, lwork, nrhs, ldx;
int i, j, m, n, nnz;
float *rhsb, *rhsb1, *rhsx, *xact;
float *R, *C;
float *ferr, *berr;
float u, rpg, rcond;
mem_usage_t mem_usage;
superlu_options_t options;
SuperLUStat_t stat;
extern void parse_command_line();
#if ( DEBUGlevel>=1 )
CHECK_MALLOC("Enter main()");
#endif
/* Defaults */
lwork = 0;
nrhs = 1;
equil = YES;
u = 1.0;
trans = NOTRANS;
/* Set the default input options:
options.Fact = DOFACT;
options.Equil = YES;
options.ColPerm = COLAMD;
options.DiagPivotThresh = 1.0;
options.Trans = NOTRANS;
options.IterRefine = NOREFINE;
options.SymmetricMode = NO;
options.PivotGrowth = NO;
options.ConditionNumber = NO;
options.PrintStat = YES;
*/
set_default_options(&options);
/* Can use command line input to modify the defaults. */
parse_command_line(argc, argv, &lwork, &u, &equil, &trans);
options.Equil = equil;
options.DiagPivotThresh = u;
options.Trans = trans;
if ( lwork > 0 ) {
work = SUPERLU_MALLOC(lwork);
if ( !work ) {
ABORT("DLINSOLX: cannot allocate work[]");
}
}
/* Read matrix A from a file in Harwell-Boeing format.*/
sreadhb(&m, &n, &nnz, &a, &asub, &xa);
if ( !(a1 = floatMalloc(nnz)) ) ABORT("Malloc fails for a1[].");
if ( !(asub1 = intMalloc(nnz)) ) ABORT("Malloc fails for asub1[].");
if ( !(xa1 = intMalloc(n+1)) ) ABORT("Malloc fails for xa1[].");
for (i = 0; i < nnz; ++i) {
a1[i] = a[i];
asub1[i] = asub[i];
}
for (i = 0; i < n+1; ++i) xa1[i] = xa[i];
sCreate_CompCol_Matrix(&A, m, n, nnz, a, asub, xa, SLU_NC, SLU_S, SLU_GE);
Astore = A.Store;
printf("Dimension %dx%d; # nonzeros %d\n", A.nrow, A.ncol, Astore->nnz);
if ( !(rhsb = floatMalloc(m * nrhs)) ) ABORT("Malloc fails for rhsb[].");
if ( !(rhsb1 = floatMalloc(m * nrhs)) ) ABORT("Malloc fails for rhsb1[].");
if ( !(rhsx = floatMalloc(m * nrhs)) ) ABORT("Malloc fails for rhsx[].");
sCreate_Dense_Matrix(&B, m, nrhs, rhsb, m, SLU_DN, SLU_S, SLU_GE);
sCreate_Dense_Matrix(&X, m, nrhs, rhsx, m, SLU_DN, SLU_S, SLU_GE);
xact = floatMalloc(n * nrhs);
ldx = n;
sGenXtrue(n, nrhs, xact, ldx);
sFillRHS(trans, nrhs, xact, ldx, &A, &B);
for (j = 0; j < nrhs; ++j)
for (i = 0; i < m; ++i) rhsb1[i+j*m] = rhsb[i+j*m];
if ( !(perm_c = intMalloc(n)) ) ABORT("Malloc fails for perm_c[].");
if ( !(perm_r = intMalloc(m)) ) ABORT("Malloc fails for perm_r[].");
if ( !(etree = intMalloc(n)) ) ABORT("Malloc fails for etree[].");
if ( !(R = (float *) SUPERLU_MALLOC(A.nrow * sizeof(float))) )
ABORT("SUPERLU_MALLOC fails for R[].");
if ( !(C = (float *) SUPERLU_MALLOC(A.ncol * sizeof(float))) )
ABORT("SUPERLU_MALLOC fails for C[].");
if ( !(ferr = (float *) SUPERLU_MALLOC(nrhs * sizeof(float))) )
ABORT("SUPERLU_MALLOC fails for ferr[].");
if ( !(berr = (float *) SUPERLU_MALLOC(nrhs * sizeof(float))) )
ABORT("SUPERLU_MALLOC fails for berr[].");
/* Initialize the statistics variables. */
StatInit(&stat);
/* ------------------------------------------------------------
WE SOLVE THE LINEAR SYSTEM FOR THE FIRST TIME: AX = B
------------------------------------------------------------*/
sgssvx(&options, &A, perm_c, perm_r, etree, equed, R, C,
&L, &U, work, lwork, &B, &X, &rpg, &rcond, ferr, berr,
&mem_usage, &stat, &info);
printf("First system: sgssvx() returns info %d\n", info);
if ( info == 0 || info == n+1 ) {
/* This is how you could access the solution matrix. */
float *sol = (float*) ((DNformat*) X.Store)->nzval;
if ( options.PivotGrowth ) printf("Recip. pivot growth = %e\n", rpg);
if ( options.ConditionNumber )
printf("Recip. condition number = %e\n", rcond);
Lstore = (SCformat *) L.Store;
Ustore = (NCformat *) U.Store;
printf("No of nonzeros in factor L = %d\n", Lstore->nnz);
printf("No of nonzeros in factor U = %d\n", Ustore->nnz);
printf("No of nonzeros in L+U = %d\n", Lstore->nnz + Ustore->nnz - n);
printf("FILL ratio = %.1f\n", (float)(Lstore->nnz + Ustore->nnz - n)/nnz);
printf("L\\U MB %.3f\ttotal MB needed %.3f\n",
mem_usage.for_lu/1e6, mem_usage.total_needed/1e6);
if ( options.IterRefine ) {
printf("Iterative Refinement:\n");
printf("%8s%8s%16s%16s\n", "rhs", "Steps", "FERR", "BERR");
for (i = 0; i < nrhs; ++i)
printf("%8d%8d%16e%16e\n", i+1, stat.RefineSteps, ferr[i], berr[i]);
}
fflush(stdout);
} else if ( info > 0 && lwork == -1 ) {
printf("** Estimated memory: %d bytes\n", info - n);
}
if ( options.PrintStat ) StatPrint(&stat);
StatFree(&stat);
Destroy_CompCol_Matrix(&A);
Destroy_Dense_Matrix(&B);
if ( lwork >= 0 ) { /* Deallocate storage associated with L and U. */
Destroy_SuperNode_Matrix(&L);
Destroy_CompCol_Matrix(&U);
}
/* ------------------------------------------------------------
NOW WE SOLVE ANOTHER LINEAR SYSTEM: A1*X = B1
ONLY THE SPARSITY PATTERN OF A1 IS THE SAME AS THAT OF A.
------------------------------------------------------------*/
options.Fact = SamePattern;
StatInit(&stat); /* Initialize the statistics variables. */
sCreate_CompCol_Matrix(&A1, m, n, nnz, a1, asub1, xa1,
SLU_NC, SLU_S, SLU_GE);
sCreate_Dense_Matrix(&B1, m, nrhs, rhsb1, m, SLU_DN, SLU_S, SLU_GE);
sgssvx(&options, &A1, perm_c, perm_r, etree, equed, R, C,
&L, &U, work, lwork, &B1, &X, &rpg, &rcond, ferr, berr,
&mem_usage, &stat, &info);
printf("\nSecond system: sgssvx() returns info %d\n", info);
if ( info == 0 || info == n+1 ) {
/* This is how you could access the solution matrix. */
float *sol = (float*) ((DNformat*) X.Store)->nzval;
if ( options.PivotGrowth ) printf("Recip. pivot growth = %e\n", rpg);
if ( options.ConditionNumber )
printf("Recip. condition number = %e\n", rcond);
Lstore = (SCformat *) L.Store;
Ustore = (NCformat *) U.Store;
printf("No of nonzeros in factor L = %d\n", Lstore->nnz);
printf("No of nonzeros in factor U = %d\n", Ustore->nnz);
printf("No of nonzeros in L+U = %d\n", Lstore->nnz + Ustore->nnz - n);
printf("L\\U MB %.3f\ttotal MB needed %.3f\n",
mem_usage.for_lu/1e6, mem_usage.total_needed/1e6);
if ( options.IterRefine ) {
printf("Iterative Refinement:\n");
printf("%8s%8s%16s%16s\n", "rhs", "Steps", "FERR", "BERR");
for (i = 0; i < nrhs; ++i)
printf("%8d%8d%16e%16e\n", i+1, stat.RefineSteps, ferr[i], berr[i]);
}
fflush(stdout);
} else if ( info > 0 && lwork == -1 ) {
printf("** Estimated memory: %d bytes\n", info - n);
}
if ( options.PrintStat ) StatPrint(&stat);
StatFree(&stat);
SUPERLU_FREE (xact);
SUPERLU_FREE (etree);
SUPERLU_FREE (perm_r);
SUPERLU_FREE (perm_c);
SUPERLU_FREE (R);
SUPERLU_FREE (C);
SUPERLU_FREE (ferr);
SUPERLU_FREE (berr);
Destroy_CompCol_Matrix(&A1);
Destroy_Dense_Matrix(&B1);
Destroy_Dense_Matrix(&X);
if ( lwork == 0 ) {
Destroy_SuperNode_Matrix(&L);
Destroy_CompCol_Matrix(&U);
} else if ( lwork > 0 ) {
SUPERLU_FREE(work);
}
#if ( DEBUGlevel>=1 )
CHECK_MALLOC("Exit main()");
#endif
}
void
sgsrfs(trans_t trans, SuperMatrix *A, SuperMatrix *L, SuperMatrix *U,
int *perm_c, int *perm_r, char *equed, float *R, float *C,
SuperMatrix *B, SuperMatrix *X, float *ferr, float *berr,
SuperLUStat_t *stat, int *info)
{
/*
* Purpose
* =======
*
* SGSRFS improves the computed solution to a system of linear
* equations and provides error bounds and backward error estimates for
* the solution.
*
* If equilibration was performed, the system becomes:
* (diag(R)*A_original*diag(C)) * X = diag(R)*B_original.
*
* See supermatrix.h for the definition of 'SuperMatrix' structure.
*
* Arguments
* =========
*
* trans (input) trans_t
* Specifies the form of the system of equations:
* = NOTRANS: A * X = B (No transpose)
* = TRANS: A'* X = B (Transpose)
* = CONJ: A**H * X = B (Conjugate transpose)
*
* A (input) SuperMatrix*
* The original matrix A in the system, or the scaled A if
* equilibration was done. The type of A can be:
* Stype = SLU_NC, Dtype = SLU_S, Mtype = SLU_GE.
*
* L (input) SuperMatrix*
* The factor L from the factorization Pr*A*Pc=L*U. Use
* compressed row subscripts storage for supernodes,
* i.e., L has types: Stype = SLU_SC, Dtype = SLU_S, Mtype = SLU_TRLU.
*
* U (input) SuperMatrix*
* The factor U from the factorization Pr*A*Pc=L*U as computed by
* sgstrf(). Use column-wise storage scheme,
* i.e., U has types: Stype = SLU_NC, Dtype = SLU_S, Mtype = SLU_TRU.
*
* perm_c (input) int*, dimension (A->ncol)
* Column permutation vector, which defines the
* permutation matrix Pc; perm_c[i] = j means column i of A is
* in position j in A*Pc.
*
* perm_r (input) int*, dimension (A->nrow)
* Row permutation vector, which defines the permutation matrix Pr;
* perm_r[i] = j means row i of A is in position j in Pr*A.
*
* equed (input) Specifies the form of equilibration that was done.
* = 'N': No equilibration.
* = 'R': Row equilibration, i.e., A was premultiplied by diag(R).
* = 'C': Column equilibration, i.e., A was postmultiplied by
* diag(C).
* = 'B': Both row and column equilibration, i.e., A was replaced
* by diag(R)*A*diag(C).
*
* R (input) float*, dimension (A->nrow)
* The row scale factors for A.
* If equed = 'R' or 'B', A is premultiplied by diag(R).
* If equed = 'N' or 'C', R is not accessed.
*
* C (input) float*, dimension (A->ncol)
* The column scale factors for A.
* If equed = 'C' or 'B', A is postmultiplied by diag(C).
* If equed = 'N' or 'R', C is not accessed.
*
* B (input) SuperMatrix*
* B has types: Stype = SLU_DN, Dtype = SLU_S, Mtype = SLU_GE.
* The right hand side matrix B.
* if equed = 'R' or 'B', B is premultiplied by diag(R).
*
* X (input/output) SuperMatrix*
* X has types: Stype = SLU_DN, Dtype = SLU_S, Mtype = SLU_GE.
* On entry, the solution matrix X, as computed by sgstrs().
* On exit, the improved solution matrix X.
* if *equed = 'C' or 'B', X should be premultiplied by diag(C)
* in order to obtain the solution to the original system.
*
* FERR (output) float*, dimension (B->ncol)
* The estimated forward error bound for each solution vector
* X(j) (the j-th column of the solution matrix X).
* If XTRUE is the true solution corresponding to X(j), FERR(j)
* is an estimated upper bound for the magnitude of the largest
* element in (X(j) - XTRUE) divided by the magnitude of the
* largest element in X(j). The estimate is as reliable as
* the estimate for RCOND, and is almost always a slight
* overestimate of the true error.
*
* BERR (output) float*, dimension (B->ncol)
* The componentwise relative backward error of each solution
* vector X(j) (i.e., the smallest relative change in
* any element of A or B that makes X(j) an exact solution).
*
* stat (output) SuperLUStat_t*
* Record the statistics on runtime and floating-point operation count.
* See util.h for the definition of 'SuperLUStat_t'.
*
* info (output) int*
* = 0: successful exit
* < 0: if INFO = -i, the i-th argument had an illegal value
*
* Internal Parameters
* ===================
*
* ITMAX is the maximum number of steps of iterative refinement.
*
*/
#define ITMAX 5
/* Table of constant values */
int ione = 1;
float ndone = -1.;
float done = 1.;
/* Local variables */
NCformat *Astore;
float *Aval;
SuperMatrix Bjcol;
DNformat *Bstore, *Xstore, *Bjcol_store;
float *Bmat, *Xmat, *Bptr, *Xptr;
int kase;
float safe1, safe2;
int i, j, k, irow, nz, count, notran, rowequ, colequ;
int ldb, ldx, nrhs;
float s, xk, lstres, eps, safmin;
char transc[1];
trans_t transt;
float *work;
float *rwork;
int *iwork;
extern double slamch_(char *);
extern int slacon_(int *, float *, float *, int *, float *, int *);
#ifdef _CRAY
extern int SCOPY(int *, float *, int *, float *, int *);
extern int SSAXPY(int *, float *, float *, int *, float *, int *);
#else
extern int scopy_(int *, float *, int *, float *, int *);
extern int saxpy_(int *, float *, float *, int *, float *, int *);
#endif
Astore = A->Store;
Aval = Astore->nzval;
Bstore = B->Store;
Xstore = X->Store;
Bmat = Bstore->nzval;
Xmat = Xstore->nzval;
ldb = Bstore->lda;
ldx = Xstore->lda;
nrhs = B->ncol;
/* Test the input parameters */
*info = 0;
notran = (trans == NOTRANS);
if ( !notran && trans != TRANS && trans != CONJ ) *info = -1;
else if ( A->nrow != A->ncol || A->nrow < 0 ||
A->Stype != SLU_NC || A->Dtype != SLU_S || A->Mtype != SLU_GE )
*info = -2;
else if ( L->nrow != L->ncol || L->nrow < 0 ||
L->Stype != SLU_SC || L->Dtype != SLU_S || L->Mtype != SLU_TRLU )
*info = -3;
else if ( U->nrow != U->ncol || U->nrow < 0 ||
U->Stype != SLU_NC || U->Dtype != SLU_S || U->Mtype != SLU_TRU )
*info = -4;
else if ( ldb < SUPERLU_MAX(0, A->nrow) ||
B->Stype != SLU_DN || B->Dtype != SLU_S || B->Mtype != SLU_GE )
*info = -10;
else if ( ldx < SUPERLU_MAX(0, A->nrow) ||
X->Stype != SLU_DN || X->Dtype != SLU_S || X->Mtype != SLU_GE )
*info = -11;
if (*info != 0) {
i = -(*info);
xerbla_("sgsrfs", &i);
return;
}
/* Quick return if possible */
if ( A->nrow == 0 || nrhs == 0) {
for (j = 0; j < nrhs; ++j) {
ferr[j] = 0.;
berr[j] = 0.;
}
return;
}
rowequ = lsame_(equed, "R") || lsame_(equed, "B");
colequ = lsame_(equed, "C") || lsame_(equed, "B");
/* Allocate working space */
work = floatMalloc(2*A->nrow);
rwork = (float *) SUPERLU_MALLOC( A->nrow * sizeof(float) );
iwork = intMalloc(2*A->nrow);
if ( !work || !rwork || !iwork )
ABORT("Malloc fails for work/rwork/iwork.");
if ( notran ) {
*(unsigned char *)transc = 'N';
transt = TRANS;
} else {
*(unsigned char *)transc = 'T';
transt = NOTRANS;
}
/* NZ = maximum number of nonzero elements in each row of A, plus 1 */
nz = A->ncol + 1;
eps = slamch_("Epsilon");
safmin = slamch_("Safe minimum");
safe1 = nz * safmin;
safe2 = safe1 / eps;
/* Compute the number of nonzeros in each row (or column) of A */
for (i = 0; i < A->nrow; ++i) iwork[i] = 0;
if ( notran ) {
for (k = 0; k < A->ncol; ++k)
for (i = Astore->colptr[k]; i < Astore->colptr[k+1]; ++i)
++iwork[Astore->rowind[i]];
} else {
for (k = 0; k < A->ncol; ++k)
iwork[k] = Astore->colptr[k+1] - Astore->colptr[k];
}
/* Copy one column of RHS B into Bjcol. */
Bjcol.Stype = B->Stype;
Bjcol.Dtype = B->Dtype;
Bjcol.Mtype = B->Mtype;
Bjcol.nrow = B->nrow;
Bjcol.ncol = 1;
Bjcol.Store = (void *) SUPERLU_MALLOC( sizeof(DNformat) );
if ( !Bjcol.Store ) ABORT("SUPERLU_MALLOC fails for Bjcol.Store");
Bjcol_store = Bjcol.Store;
Bjcol_store->lda = ldb;
Bjcol_store->nzval = work; /* address aliasing */
/* Do for each right hand side ... */
for (j = 0; j < nrhs; ++j) {
count = 0;
lstres = 3.;
Bptr = &Bmat[j*ldb];
Xptr = &Xmat[j*ldx];
while (1) { /* Loop until stopping criterion is satisfied. */
/* Compute residual R = B - op(A) * X,
where op(A) = A, A**T, or A**H, depending on TRANS. */
#ifdef _CRAY
SCOPY(&A->nrow, Bptr, &ione, work, &ione);
#else
scopy_(&A->nrow, Bptr, &ione, work, &ione);
#endif
sp_sgemv(transc, ndone, A, Xptr, ione, done, work, ione);
/* Compute componentwise relative backward error from formula
max(i) ( abs(R(i)) / ( abs(op(A))*abs(X) + abs(B) )(i) )
where abs(Z) is the componentwise absolute value of the matrix
or vector Z. If the i-th component of the denominator is less
than SAFE2, then SAFE1 is added to the i-th component of the
numerator and denominator before dividing. */
for (i = 0; i < A->nrow; ++i) rwork[i] = fabs( Bptr[i] );
/* Compute abs(op(A))*abs(X) + abs(B). */
if (notran) {
for (k = 0; k < A->ncol; ++k) {
xk = fabs( Xptr[k] );
for (i = Astore->colptr[k]; i < Astore->colptr[k+1]; ++i)
rwork[Astore->rowind[i]] += fabs(Aval[i]) * xk;
}
} else {
for (k = 0; k < A->ncol; ++k) {
s = 0.;
for (i = Astore->colptr[k]; i < Astore->colptr[k+1]; ++i) {
irow = Astore->rowind[i];
s += fabs(Aval[i]) * fabs(Xptr[irow]);
}
rwork[k] += s;
}
}
s = 0.;
for (i = 0; i < A->nrow; ++i) {
if (rwork[i] > safe2)
s = SUPERLU_MAX( s, fabs(work[i]) / rwork[i] );
else
s = SUPERLU_MAX( s, (fabs(work[i]) + safe1) /
(rwork[i] + safe1) );
}
berr[j] = s;
/* Test stopping criterion. Continue iterating if
1) The residual BERR(J) is larger than machine epsilon, and
2) BERR(J) decreased by at least a factor of 2 during the
last iteration, and
3) At most ITMAX iterations tried. */
if (berr[j] > eps && berr[j] * 2. <= lstres && count < ITMAX) {
/* Update solution and try again. */
sgstrs (trans, L, U, perm_c, perm_r, &Bjcol, stat, info);
#ifdef _CRAY
SAXPY(&A->nrow, &done, work, &ione,
&Xmat[j*ldx], &ione);
#else
saxpy_(&A->nrow, &done, work, &ione,
&Xmat[j*ldx], &ione);
#endif
lstres = berr[j];
++count;
} else {
break;
}
} /* end while */
stat->RefineSteps = count;
/* Bound error from formula:
norm(X - XTRUE) / norm(X) .le. FERR = norm( abs(inv(op(A)))*
( abs(R) + NZ*EPS*( abs(op(A))*abs(X)+abs(B) ))) / norm(X)
where
norm(Z) is the magnitude of the largest component of Z
inv(op(A)) is the inverse of op(A)
abs(Z) is the componentwise absolute value of the matrix or
vector Z
NZ is the maximum number of nonzeros in any row of A, plus 1
EPS is machine epsilon
The i-th component of abs(R)+NZ*EPS*(abs(op(A))*abs(X)+abs(B))
is incremented by SAFE1 if the i-th component of
abs(op(A))*abs(X) + abs(B) is less than SAFE2.
Use SLACON to estimate the infinity-norm of the matrix
inv(op(A)) * diag(W),
where W = abs(R) + NZ*EPS*( abs(op(A))*abs(X)+abs(B) ))) */
for (i = 0; i < A->nrow; ++i) rwork[i] = fabs( Bptr[i] );
/* Compute abs(op(A))*abs(X) + abs(B). */
if ( notran ) {
for (k = 0; k < A->ncol; ++k) {
xk = fabs( Xptr[k] );
for (i = Astore->colptr[k]; i < Astore->colptr[k+1]; ++i)
rwork[Astore->rowind[i]] += fabs(Aval[i]) * xk;
}
} else {
for (k = 0; k < A->ncol; ++k) {
s = 0.;
for (i = Astore->colptr[k]; i < Astore->colptr[k+1]; ++i) {
irow = Astore->rowind[i];
xk = fabs( Xptr[irow] );
s += fabs(Aval[i]) * xk;
}
rwork[k] += s;
}
}
for (i = 0; i < A->nrow; ++i)
if (rwork[i] > safe2)
rwork[i] = fabs(work[i]) + (iwork[i]+1)*eps*rwork[i];
else
rwork[i] = fabs(work[i])+(iwork[i]+1)*eps*rwork[i]+safe1;
kase = 0;
do {
slacon_(&A->nrow, &work[A->nrow], work,
&iwork[A->nrow], &ferr[j], &kase);
if (kase == 0) break;
if (kase == 1) {
/* Multiply by diag(W)*inv(op(A)**T)*(diag(C) or diag(R)). */
if ( notran && colequ )
for (i = 0; i < A->ncol; ++i) work[i] *= C[i];
else if ( !notran && rowequ )
for (i = 0; i < A->nrow; ++i) work[i] *= R[i];
sgstrs (transt, L, U, perm_c, perm_r, &Bjcol, stat, info);
for (i = 0; i < A->nrow; ++i) work[i] *= rwork[i];
} else {
/* Multiply by (diag(C) or diag(R))*inv(op(A))*diag(W). */
for (i = 0; i < A->nrow; ++i) work[i] *= rwork[i];
sgstrs (trans, L, U, perm_c, perm_r, &Bjcol, stat, info);
if ( notran && colequ )
for (i = 0; i < A->ncol; ++i) work[i] *= C[i];
else if ( !notran && rowequ )
for (i = 0; i < A->ncol; ++i) work[i] *= R[i];
}
} while ( kase != 0 );
/* Normalize error. */
lstres = 0.;
if ( notran && colequ ) {
for (i = 0; i < A->nrow; ++i)
lstres = SUPERLU_MAX( lstres, C[i] * fabs( Xptr[i]) );
} else if ( !notran && rowequ ) {
for (i = 0; i < A->nrow; ++i)
lstres = SUPERLU_MAX( lstres, R[i] * fabs( Xptr[i]) );
} else {
for (i = 0; i < A->nrow; ++i)
lstres = SUPERLU_MAX( lstres, fabs( Xptr[i]) );
}
if ( lstres != 0. )
ferr[j] /= lstres;
} /* for each RHS j ... */
SUPERLU_FREE(work);
SUPERLU_FREE(rwork);
SUPERLU_FREE(iwork);
SUPERLU_FREE(Bjcol.Store);
return;
} /* sgsrfs */
/*! \brief
*
* <pre>
* Purpose
* =======
*
* SGSRFS improves the computed solution to a system of linear
* equations and provides error bounds and backward error estimates for
* the solution.
*
* If equilibration was performed, the system becomes:
* (diag(R)*A_original*diag(C)) * X = diag(R)*B_original.
*
* See supermatrix.h for the definition of 'SuperMatrix' structure.
*
* Arguments
* =========
*
* trans (input) trans_t
* Specifies the form of the system of equations:
* = NOTRANS: A * X = B (No transpose)
* = TRANS: A'* X = B (Transpose)
* = CONJ: A**H * X = B (Conjugate transpose)
*
* A (input) SuperMatrix*
* The original matrix A in the system, or the scaled A if
* equilibration was done. The type of A can be:
* Stype = SLU_NC, Dtype = SLU_S, Mtype = SLU_GE.
*
* L (input) SuperMatrix*
* The factor L from the factorization Pr*A*Pc=L*U. Use
* compressed row subscripts storage for supernodes,
* i.e., L has types: Stype = SLU_SC, Dtype = SLU_S, Mtype = SLU_TRLU.
*
* U (input) SuperMatrix*
* The factor U from the factorization Pr*A*Pc=L*U as computed by
* sgstrf(). Use column-wise storage scheme,
* i.e., U has types: Stype = SLU_NC, Dtype = SLU_S, Mtype = SLU_TRU.
*
* perm_c (input) int*, dimension (A->ncol)
* Column permutation vector, which defines the
* permutation matrix Pc; perm_c[i] = j means column i of A is
* in position j in A*Pc.
*
* perm_r (input) int*, dimension (A->nrow)
* Row permutation vector, which defines the permutation matrix Pr;
* perm_r[i] = j means row i of A is in position j in Pr*A.
*
* equed (input) Specifies the form of equilibration that was done.
* = 'N': No equilibration.
* = 'R': Row equilibration, i.e., A was premultiplied by diag(R).
* = 'C': Column equilibration, i.e., A was postmultiplied by
* diag(C).
* = 'B': Both row and column equilibration, i.e., A was replaced
* by diag(R)*A*diag(C).
*
* R (input) float*, dimension (A->nrow)
* The row scale factors for A.
* If equed = 'R' or 'B', A is premultiplied by diag(R).
* If equed = 'N' or 'C', R is not accessed.
*
* C (input) float*, dimension (A->ncol)
* The column scale factors for A.
* If equed = 'C' or 'B', A is postmultiplied by diag(C).
* If equed = 'N' or 'R', C is not accessed.
*
* B (input) SuperMatrix*
* B has types: Stype = SLU_DN, Dtype = SLU_S, Mtype = SLU_GE.
* The right hand side matrix B.
* if equed = 'R' or 'B', B is premultiplied by diag(R).
*
* X (input/output) SuperMatrix*
* X has types: Stype = SLU_DN, Dtype = SLU_S, Mtype = SLU_GE.
* On entry, the solution matrix X, as computed by sgstrs().
* On exit, the improved solution matrix X.
* if *equed = 'C' or 'B', X should be premultiplied by diag(C)
* in order to obtain the solution to the original system.
*
* FERR (output) float*, dimension (B->ncol)
* The estimated forward error bound for each solution vector
* X(j) (the j-th column of the solution matrix X).
* If XTRUE is the true solution corresponding to X(j), FERR(j)
* is an estimated upper bound for the magnitude of the largest
* element in (X(j) - XTRUE) divided by the magnitude of the
* largest element in X(j). The estimate is as reliable as
* the estimate for RCOND, and is almost always a slight
* overestimate of the true error.
*
* BERR (output) float*, dimension (B->ncol)
* The componentwise relative backward error of each solution
* vector X(j) (i.e., the smallest relative change in
* any element of A or B that makes X(j) an exact solution).
*
* stat (output) SuperLUStat_t*
* Record the statistics on runtime and floating-point operation count.
* See util.h for the definition of 'SuperLUStat_t'.
*
* info (output) int*
* = 0: successful exit
* < 0: if INFO = -i, the i-th argument had an illegal value
*
* Internal Parameters
* ===================
*
* ITMAX is the maximum number of steps of iterative refinement.
*
* </pre>
*/
void
sgsrfs(trans_t trans, SuperMatrix *A, SuperMatrix *L, SuperMatrix *U,
int *perm_c, int *perm_r, char *equed, float *R, float *C,
SuperMatrix *B, SuperMatrix *X, float *ferr, float *berr,
SuperLUStat_t *stat, int *info)
{
#define ITMAX 5
/* Table of constant values */
int ione = 1;
float ndone = -1.;
float done = 1.;
/* Local variables */
NCformat *Astore;
float *Aval;
SuperMatrix Bjcol;
DNformat *Bstore, *Xstore, *Bjcol_store;
float *Bmat, *Xmat, *Bptr, *Xptr;
int kase;
float safe1, safe2;
int i, j, k, irow, nz, count, notran, rowequ, colequ;
int ldb, ldx, nrhs;
float s, xk, lstres, eps, safmin;
char transc[1];
trans_t transt;
float *work;
float *rwork;
int *iwork;
extern int slacon_(int *, float *, float *, int *, float *, int *);
#ifdef _CRAY
extern int SCOPY(int *, float *, int *, float *, int *);
extern int SSAXPY(int *, float *, float *, int *, float *, int *);
#else
extern int scopy_(int *, float *, int *, float *, int *);
extern int saxpy_(int *, float *, float *, int *, float *, int *);
#endif
Astore = A->Store;
Aval = Astore->nzval;
Bstore = B->Store;
Xstore = X->Store;
Bmat = Bstore->nzval;
Xmat = Xstore->nzval;
ldb = Bstore->lda;
ldx = Xstore->lda;
nrhs = B->ncol;
/* Test the input parameters */
*info = 0;
notran = (trans == NOTRANS);
if ( !notran && trans != TRANS && trans != CONJ ) *info = -1;
else if ( A->nrow != A->ncol || A->nrow < 0 ||
A->Stype != SLU_NC || A->Dtype != SLU_S || A->Mtype != SLU_GE )
*info = -2;
else if ( L->nrow != L->ncol || L->nrow < 0 ||
L->Stype != SLU_SC || L->Dtype != SLU_S || L->Mtype != SLU_TRLU )
*info = -3;
else if ( U->nrow != U->ncol || U->nrow < 0 ||
U->Stype != SLU_NC || U->Dtype != SLU_S || U->Mtype != SLU_TRU )
*info = -4;
else if ( ldb < SUPERLU_MAX(0, A->nrow) ||
B->Stype != SLU_DN || B->Dtype != SLU_S || B->Mtype != SLU_GE )
*info = -10;
else if ( ldx < SUPERLU_MAX(0, A->nrow) ||
X->Stype != SLU_DN || X->Dtype != SLU_S || X->Mtype != SLU_GE )
*info = -11;
if (*info != 0) {
i = -(*info);
xerbla_("sgsrfs", &i);
return;
}
/* Quick return if possible */
if ( A->nrow == 0 || nrhs == 0) {
for (j = 0; j < nrhs; ++j) {
ferr[j] = 0.;
berr[j] = 0.;
}
return;
}
rowequ = lsame_(equed, "R") || lsame_(equed, "B");
colequ = lsame_(equed, "C") || lsame_(equed, "B");
/* Allocate working space */
work = floatMalloc(2*A->nrow);
rwork = (float *) SUPERLU_MALLOC( A->nrow * sizeof(float) );
iwork = intMalloc(2*A->nrow);
if ( !work || !rwork || !iwork )
ABORT("Malloc fails for work/rwork/iwork.");
if ( notran ) {
*(unsigned char *)transc = 'N';
transt = TRANS;
} else {
*(unsigned char *)transc = 'T';
transt = NOTRANS;
}
/* NZ = maximum number of nonzero elements in each row of A, plus 1 */
nz = A->ncol + 1;
eps = slamch_("Epsilon");
safmin = slamch_("Safe minimum");
/* Set SAFE1 essentially to be the underflow threshold times the
number of additions in each row. */
safe1 = nz * safmin;
safe2 = safe1 / eps;
/* Compute the number of nonzeros in each row (or column) of A */
for (i = 0; i < A->nrow; ++i) iwork[i] = 0;
if ( notran ) {
for (k = 0; k < A->ncol; ++k)
for (i = Astore->colptr[k]; i < Astore->colptr[k+1]; ++i)
++iwork[Astore->rowind[i]];
} else {
for (k = 0; k < A->ncol; ++k)
iwork[k] = Astore->colptr[k+1] - Astore->colptr[k];
}
/* Copy one column of RHS B into Bjcol. */
Bjcol.Stype = B->Stype;
Bjcol.Dtype = B->Dtype;
Bjcol.Mtype = B->Mtype;
Bjcol.nrow = B->nrow;
Bjcol.ncol = 1;
Bjcol.Store = (void *) SUPERLU_MALLOC( sizeof(DNformat) );
if ( !Bjcol.Store ) ABORT("SUPERLU_MALLOC fails for Bjcol.Store");
Bjcol_store = Bjcol.Store;
Bjcol_store->lda = ldb;
Bjcol_store->nzval = work; /* address aliasing */
/* Do for each right hand side ... */
for (j = 0; j < nrhs; ++j) {
count = 0;
lstres = 3.;
Bptr = &Bmat[j*ldb];
Xptr = &Xmat[j*ldx];
while (1) { /* Loop until stopping criterion is satisfied. */
/* Compute residual R = B - op(A) * X,
where op(A) = A, A**T, or A**H, depending on TRANS. */
#ifdef _CRAY
SCOPY(&A->nrow, Bptr, &ione, work, &ione);
#else
scopy_(&A->nrow, Bptr, &ione, work, &ione);
#endif
sp_sgemv(transc, ndone, A, Xptr, ione, done, work, ione);
/* Compute componentwise relative backward error from formula
max(i) ( abs(R(i)) / ( abs(op(A))*abs(X) + abs(B) )(i) )
where abs(Z) is the componentwise absolute value of the matrix
or vector Z. If the i-th component of the denominator is less
than SAFE2, then SAFE1 is added to the i-th component of the
numerator before dividing. */
for (i = 0; i < A->nrow; ++i) rwork[i] = fabs( Bptr[i] );
/* Compute abs(op(A))*abs(X) + abs(B). */
if (notran) {
for (k = 0; k < A->ncol; ++k) {
xk = fabs( Xptr[k] );
for (i = Astore->colptr[k]; i < Astore->colptr[k+1]; ++i)
rwork[Astore->rowind[i]] += fabs(Aval[i]) * xk;
}
} else {
for (k = 0; k < A->ncol; ++k) {
s = 0.;
for (i = Astore->colptr[k]; i < Astore->colptr[k+1]; ++i) {
irow = Astore->rowind[i];
s += fabs(Aval[i]) * fabs(Xptr[irow]);
}
rwork[k] += s;
}
}
s = 0.;
for (i = 0; i < A->nrow; ++i) {
if (rwork[i] > safe2) {
s = SUPERLU_MAX( s, fabs(work[i]) / rwork[i] );
} else if ( rwork[i] != 0.0 ) {
/* Adding SAFE1 to the numerator guards against
spuriously zero residuals (underflow). */
s = SUPERLU_MAX( s, (safe1 + fabs(work[i])) / rwork[i] );
}
/* If rwork[i] is exactly 0.0, then we know the true
residual also must be exactly 0.0. */
}
berr[j] = s;
/* Test stopping criterion. Continue iterating if
1) The residual BERR(J) is larger than machine epsilon, and
2) BERR(J) decreased by at least a factor of 2 during the
last iteration, and
3) At most ITMAX iterations tried. */
if (berr[j] > eps && berr[j] * 2. <= lstres && count < ITMAX) {
/* Update solution and try again. */
sgstrs (trans, L, U, perm_c, perm_r, &Bjcol, stat, info);
#ifdef _CRAY
SAXPY(&A->nrow, &done, work, &ione,
&Xmat[j*ldx], &ione);
#else
saxpy_(&A->nrow, &done, work, &ione,
&Xmat[j*ldx], &ione);
#endif
lstres = berr[j];
++count;
} else {
break;
}
} /* end while */
stat->RefineSteps = count;
/* Bound error from formula:
norm(X - XTRUE) / norm(X) .le. FERR = norm( abs(inv(op(A)))*
( abs(R) + NZ*EPS*( abs(op(A))*abs(X)+abs(B) ))) / norm(X)
where
norm(Z) is the magnitude of the largest component of Z
inv(op(A)) is the inverse of op(A)
abs(Z) is the componentwise absolute value of the matrix or
vector Z
NZ is the maximum number of nonzeros in any row of A, plus 1
EPS is machine epsilon
The i-th component of abs(R)+NZ*EPS*(abs(op(A))*abs(X)+abs(B))
is incremented by SAFE1 if the i-th component of
abs(op(A))*abs(X) + abs(B) is less than SAFE2.
Use SLACON to estimate the infinity-norm of the matrix
inv(op(A)) * diag(W),
where W = abs(R) + NZ*EPS*( abs(op(A))*abs(X)+abs(B) ))) */
for (i = 0; i < A->nrow; ++i) rwork[i] = fabs( Bptr[i] );
/* Compute abs(op(A))*abs(X) + abs(B). */
if ( notran ) {
for (k = 0; k < A->ncol; ++k) {
xk = fabs( Xptr[k] );
for (i = Astore->colptr[k]; i < Astore->colptr[k+1]; ++i)
rwork[Astore->rowind[i]] += fabs(Aval[i]) * xk;
}
} else {
for (k = 0; k < A->ncol; ++k) {
s = 0.;
for (i = Astore->colptr[k]; i < Astore->colptr[k+1]; ++i) {
irow = Astore->rowind[i];
xk = fabs( Xptr[irow] );
s += fabs(Aval[i]) * xk;
}
rwork[k] += s;
}
}
for (i = 0; i < A->nrow; ++i)
if (rwork[i] > safe2)
rwork[i] = fabs(work[i]) + (iwork[i]+1)*eps*rwork[i];
else
rwork[i] = fabs(work[i])+(iwork[i]+1)*eps*rwork[i]+safe1;
kase = 0;
do {
slacon_(&A->nrow, &work[A->nrow], work,
&iwork[A->nrow], &ferr[j], &kase);
if (kase == 0) break;
if (kase == 1) {
/* Multiply by diag(W)*inv(op(A)**T)*(diag(C) or diag(R)). */
if ( notran && colequ )
for (i = 0; i < A->ncol; ++i) work[i] *= C[i];
else if ( !notran && rowequ )
for (i = 0; i < A->nrow; ++i) work[i] *= R[i];
sgstrs (transt, L, U, perm_c, perm_r, &Bjcol, stat, info);
for (i = 0; i < A->nrow; ++i) work[i] *= rwork[i];
} else {
/* Multiply by (diag(C) or diag(R))*inv(op(A))*diag(W). */
for (i = 0; i < A->nrow; ++i) work[i] *= rwork[i];
sgstrs (trans, L, U, perm_c, perm_r, &Bjcol, stat, info);
if ( notran && colequ )
for (i = 0; i < A->ncol; ++i) work[i] *= C[i];
else if ( !notran && rowequ )
for (i = 0; i < A->ncol; ++i) work[i] *= R[i];
}
} while ( kase != 0 );
/* Normalize error. */
lstres = 0.;
if ( notran && colequ ) {
for (i = 0; i < A->nrow; ++i)
lstres = SUPERLU_MAX( lstres, C[i] * fabs( Xptr[i]) );
} else if ( !notran && rowequ ) {
for (i = 0; i < A->nrow; ++i)
lstres = SUPERLU_MAX( lstres, R[i] * fabs( Xptr[i]) );
} else {
for (i = 0; i < A->nrow; ++i)
lstres = SUPERLU_MAX( lstres, fabs( Xptr[i]) );
}
if ( lstres != 0. )
ferr[j] /= lstres;
} /* for each RHS j ... */
SUPERLU_FREE(work);
SUPERLU_FREE(rwork);
SUPERLU_FREE(iwork);
SUPERLU_FREE(Bjcol.Store);
return;
} /* sgsrfs */
int main(int argc, char *argv[])
{
void smatvec_mult(float alpha, float x[], float beta, float y[]);
void spsolve(int n, float x[], float y[]);
extern int sfgmr( int n,
void (*matvec_mult)(float, float [], float, float []),
void (*psolve)(int n, float [], float[]),
float *rhs, float *sol, double tol, int restrt, int *itmax,
FILE *fits);
extern int sfill_diag(int n, NCformat *Astore);
char equed[1] = {'B'};
yes_no_t equil;
trans_t trans;
SuperMatrix A, L, U;
SuperMatrix B, X;
NCformat *Astore;
NCformat *Ustore;
SCformat *Lstore;
GlobalLU_t Glu; /* facilitate multiple factorizations with
SamePattern_SameRowPerm */
float *a;
int *asub, *xa;
int *etree;
int *perm_c; /* column permutation vector */
int *perm_r; /* row permutations from partial pivoting */
int nrhs, ldx, lwork, info, m, n, nnz;
float *rhsb, *rhsx, *xact;
float *work = NULL;
float *R, *C;
float u, rpg, rcond;
float zero = 0.0;
float one = 1.0;
mem_usage_t mem_usage;
superlu_options_t options;
SuperLUStat_t stat;
FILE *fp = stdin;
int restrt, iter, maxit, i;
double resid;
float *x, *b;
#ifdef DEBUG
extern int num_drop_L, num_drop_U;
#endif
#if ( DEBUGlevel>=1 )
CHECK_MALLOC("Enter main()");
#endif
/* Defaults */
lwork = 0;
nrhs = 1;
trans = NOTRANS;
/* Set the default input options:
options.Fact = DOFACT;
options.Equil = YES;
options.ColPerm = COLAMD;
options.DiagPivotThresh = 0.1; //different from complete LU
options.Trans = NOTRANS;
options.IterRefine = NOREFINE;
options.SymmetricMode = NO;
options.PivotGrowth = NO;
options.ConditionNumber = NO;
options.PrintStat = YES;
options.RowPerm = LargeDiag;
options.ILU_DropTol = 1e-4;
options.ILU_FillTol = 1e-2;
options.ILU_FillFactor = 10.0;
options.ILU_DropRule = DROP_BASIC | DROP_AREA;
options.ILU_Norm = INF_NORM;
options.ILU_MILU = SILU;
*/
ilu_set_default_options(&options);
/* Modify the defaults. */
options.PivotGrowth = YES; /* Compute reciprocal pivot growth */
options.ConditionNumber = YES;/* Compute reciprocal condition number */
if ( lwork > 0 ) {
work = SUPERLU_MALLOC(lwork);
if ( !work ) ABORT("Malloc fails for work[].");
}
/* Read matrix A from a file in Harwell-Boeing format.*/
if (argc < 2)
{
printf("Usage:\n%s [OPTION] < [INPUT] > [OUTPUT]\nOPTION:\n"
"-h -hb:\n\t[INPUT] is a Harwell-Boeing format matrix.\n"
"-r -rb:\n\t[INPUT] is a Rutherford-Boeing format matrix.\n"
"-t -triplet:\n\t[INPUT] is a triplet format matrix.\n",
argv[0]);
return 0;
}
else
{
switch (argv[1][1])
{
case 'H':
case 'h':
printf("Input a Harwell-Boeing format matrix:\n");
sreadhb(fp, &m, &n, &nnz, &a, &asub, &xa);
break;
case 'R':
case 'r':
printf("Input a Rutherford-Boeing format matrix:\n");
sreadrb(&m, &n, &nnz, &a, &asub, &xa);
break;
case 'T':
case 't':
printf("Input a triplet format matrix:\n");
sreadtriple(&m, &n, &nnz, &a, &asub, &xa);
break;
default:
printf("Unrecognized format.\n");
return 0;
}
}
sCreate_CompCol_Matrix(&A, m, n, nnz, a, asub, xa,
SLU_NC, SLU_S, SLU_GE);
Astore = A.Store;
sfill_diag(n, Astore);
printf("Dimension %dx%d; # nonzeros %d\n", A.nrow, A.ncol, Astore->nnz);
fflush(stdout);
/* Generate the right-hand side */
if ( !(rhsb = floatMalloc(m * nrhs)) ) ABORT("Malloc fails for rhsb[].");
if ( !(rhsx = floatMalloc(m * nrhs)) ) ABORT("Malloc fails for rhsx[].");
sCreate_Dense_Matrix(&B, m, nrhs, rhsb, m, SLU_DN, SLU_S, SLU_GE);
sCreate_Dense_Matrix(&X, m, nrhs, rhsx, m, SLU_DN, SLU_S, SLU_GE);
xact = floatMalloc(n * nrhs);
ldx = n;
sGenXtrue(n, nrhs, xact, ldx);
sFillRHS(trans, nrhs, xact, ldx, &A, &B);
if ( !(etree = intMalloc(n)) ) ABORT("Malloc fails for etree[].");
if ( !(perm_r = intMalloc(m)) ) ABORT("Malloc fails for perm_r[].");
if ( !(perm_c = intMalloc(n)) ) ABORT("Malloc fails for perm_c[].");
if ( !(R = (float *) SUPERLU_MALLOC(A.nrow * sizeof(float))) )
ABORT("SUPERLU_MALLOC fails for R[].");
if ( !(C = (float *) SUPERLU_MALLOC(A.ncol * sizeof(float))) )
ABORT("SUPERLU_MALLOC fails for C[].");
info = 0;
#ifdef DEBUG
num_drop_L = 0;
num_drop_U = 0;
#endif
/* Initialize the statistics variables. */
StatInit(&stat);
/* Compute the incomplete factorization and compute the condition number
and pivot growth using dgsisx. */
B.ncol = 0; /* not to perform triangular solution */
sgsisx(&options, &A, perm_c, perm_r, etree, equed, R, C, &L, &U, work,
lwork, &B, &X, &rpg, &rcond, &Glu, &mem_usage, &stat, &info);
/* Set RHS for GMRES. */
if (!(b = floatMalloc(m))) ABORT("Malloc fails for b[].");
if (*equed == 'R' || *equed == 'B') {
for (i = 0; i < n; ++i) b[i] = rhsb[i] * R[i];
} else {
for (i = 0; i < m; i++) b[i] = rhsb[i];
}
printf("sgsisx(): info %d, equed %c\n", info, equed[0]);
if (info > 0 || rcond < 1e-8 || rpg > 1e8)
printf("WARNING: This preconditioner might be unstable.\n");
if ( info == 0 || info == n+1 ) {
if ( options.PivotGrowth == YES )
printf("Recip. pivot growth = %e\n", rpg);
if ( options.ConditionNumber == YES )
printf("Recip. condition number = %e\n", rcond);
} else if ( info > 0 && lwork == -1 ) {
printf("** Estimated memory: %d bytes\n", info - n);
}
Lstore = (SCformat *) L.Store;
Ustore = (NCformat *) U.Store;
printf("n(A) = %d, nnz(A) = %d\n", n, Astore->nnz);
printf("No of nonzeros in factor L = %d\n", Lstore->nnz);
printf("No of nonzeros in factor U = %d\n", Ustore->nnz);
printf("No of nonzeros in L+U = %d\n", Lstore->nnz + Ustore->nnz - n);
printf("Fill ratio: nnz(F)/nnz(A) = %.3f\n",
((double)(Lstore->nnz) + (double)(Ustore->nnz) - (double)n)
/ (double)Astore->nnz);
printf("L\\U MB %.3f\ttotal MB needed %.3f\n",
mem_usage.for_lu/1e6, mem_usage.total_needed/1e6);
fflush(stdout);
/* Set the global variables. */
GLOBAL_A = &A;
GLOBAL_L = &L;
GLOBAL_U = &U;
GLOBAL_STAT = &stat;
GLOBAL_PERM_C = perm_c;
GLOBAL_PERM_R = perm_r;
GLOBAL_OPTIONS = &options;
GLOBAL_R = R;
GLOBAL_C = C;
GLOBAL_MEM_USAGE = &mem_usage;
/* Set the options to do solve-only. */
options.Fact = FACTORED;
options.PivotGrowth = NO;
options.ConditionNumber = NO;
/* Set the variables used by GMRES. */
restrt = SUPERLU_MIN(n / 3 + 1, 50);
maxit = 1000;
iter = maxit;
resid = 1e-8;
if (!(x = floatMalloc(n))) ABORT("Malloc fails for x[].");
if (info <= n + 1)
{
int i_1 = 1;
double maxferr = 0.0, nrmA, nrmB, res, t;
float temp;
extern float snrm2_(int *, float [], int *);
extern void saxpy_(int *, float *, float [], int *, float [], int *);
/* Initial guess */
for (i = 0; i < n; i++) x[i] = zero;
t = SuperLU_timer_();
/* Call GMRES */
sfgmr(n, smatvec_mult, spsolve, b, x, resid, restrt, &iter, stdout);
t = SuperLU_timer_() - t;
/* Output the result. */
nrmA = snrm2_(&(Astore->nnz), (float *)((DNformat *)A.Store)->nzval,
&i_1);
nrmB = snrm2_(&m, b, &i_1);
sp_sgemv("N", -1.0, &A, x, 1, 1.0, b, 1);
res = snrm2_(&m, b, &i_1);
resid = res / nrmB;
printf("||A||_F = %.1e, ||B||_2 = %.1e, ||B-A*X||_2 = %.1e, "
"relres = %.1e\n", nrmA, nrmB, res, resid);
if (iter >= maxit)
{
if (resid >= 1.0) iter = -180;
else if (resid > 1e-8) iter = -111;
}
printf("iteration: %d\nresidual: %.1e\nGMRES time: %.2f seconds.\n",
iter, resid, t);
/* Scale the solution back if equilibration was performed. */
if (*equed == 'C' || *equed == 'B')
for (i = 0; i < n; i++) x[i] *= C[i];
for (i = 0; i < m; i++) {
maxferr = SUPERLU_MAX(maxferr, fabs(x[i] - xact[i]));
}
printf("||X-X_true||_oo = %.1e\n", maxferr);
}
#ifdef DEBUG
printf("%d entries in L and %d entries in U dropped.\n",
num_drop_L, num_drop_U);
#endif
fflush(stdout);
if ( options.PrintStat ) StatPrint(&stat);
StatFree(&stat);
SUPERLU_FREE (rhsb);
SUPERLU_FREE (rhsx);
SUPERLU_FREE (xact);
SUPERLU_FREE (etree);
SUPERLU_FREE (perm_r);
SUPERLU_FREE (perm_c);
SUPERLU_FREE (R);
SUPERLU_FREE (C);
Destroy_CompCol_Matrix(&A);
Destroy_SuperMatrix_Store(&B);
Destroy_SuperMatrix_Store(&X);
if ( lwork >= 0 ) {
Destroy_SuperNode_Matrix(&L);
Destroy_CompCol_Matrix(&U);
}
SUPERLU_FREE(b);
SUPERLU_FREE(x);
#if ( DEBUGlevel>=1 )
CHECK_MALLOC("Exit main()");
#endif
return 0;
}
int main ( int argc, char *argv[] )
/******************************************************************************/
/*
Purpose:
MAIN is the main program for PSLINSOL.
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
10 February 2014
Author:
Xiaoye Li
*/
{
SuperMatrix A;
NCformat *Astore;
float *a;
int *asub, *xa;
int *perm_r; /* row permutations from partial pivoting */
int *perm_c; /* column permutation vector */
SuperMatrix L; /* factor L */
SCPformat *Lstore;
SuperMatrix U; /* factor U */
NCPformat *Ustore;
SuperMatrix B;
int nrhs, ldx, info, m, n, nnz, b;
int nprocs; /* maximum number of processors to use. */
int panel_size, relax, maxsup;
int permc_spec;
trans_t trans;
float *xact, *rhs;
superlu_memusage_t superlu_memusage;
void parse_command_line();
timestamp ( );
printf ( "\n" );
printf ( "PSLINSOL:\n" );
printf ( " C/OpenMP version\n" );
printf ( " Call the OpenMP version of SuperLU to solve a linear system.\n" );
nrhs = 1;
trans = NOTRANS;
nprocs = 1;
n = 1000;
b = 1;
panel_size = sp_ienv(1);
relax = sp_ienv(2);
maxsup = sp_ienv(3);
/*
Check for any commandline input.
*/
parse_command_line ( argc, argv, &nprocs, &n, &b, &panel_size,
&relax, &maxsup );
#if ( PRNTlevel>=1 || DEBUGlevel>=1 )
cpp_defs();
#endif
#define HB
#if defined( DEN )
m = n;
nnz = n * n;
sband(n, n, nnz, &a, &asub, &xa);
#elif defined( BAND )
m = n;
nnz = (2*b+1) * n;
sband(n, b, nnz, &a, &asub, &xa);
#elif defined( BD )
nb = 5;
bs = 200;
m = n = bs * nb;
nnz = bs * bs * nb;
sblockdiag(nb, bs, nnz, &a, &asub, &xa);
#elif defined( HB )
sreadhb(&m, &n, &nnz, &a, &asub, &xa);
#else
sreadmt(&m, &n, &nnz, &a, &asub, &xa);
#endif
sCreate_CompCol_Matrix(&A, m, n, nnz, a, asub, xa, SLU_NC, SLU_S, SLU_GE);
Astore = A.Store;
printf("Dimension %dx%d; # nonzeros %d\n", A.nrow, A.ncol, Astore->nnz);
if (!(rhs = floatMalloc(m * nrhs))) SUPERLU_ABORT("Malloc fails for rhs[].");
sCreate_Dense_Matrix(&B, m, nrhs, rhs, m, SLU_DN, SLU_S, SLU_GE);
xact = floatMalloc(n * nrhs);
ldx = n;
sGenXtrue(n, nrhs, xact, ldx);
sFillRHS(trans, nrhs, xact, ldx, &A, &B);
if (!(perm_r = intMalloc(m))) SUPERLU_ABORT("Malloc fails for perm_r[].");
if (!(perm_c = intMalloc(n))) SUPERLU_ABORT("Malloc fails for perm_c[].");
/*
* Get column permutation vector perm_c[], according to permc_spec:
* permc_spec = 0: natural ordering
* permc_spec = 1: minimum degree ordering on structure of A'*A
* permc_spec = 2: minimum degree ordering on structure of A'+A
* permc_spec = 3: approximate minimum degree for unsymmetric matrices
*/
permc_spec = 1;
get_perm_c(permc_spec, &A, perm_c);
psgssv(nprocs, &A, perm_c, perm_r, &L, &U, &B, &info);
if ( info == 0 ) {
sinf_norm_error(nrhs, &B, xact); /* Inf. norm of the error */
Lstore = (SCPformat *) L.Store;
Ustore = (NCPformat *) U.Store;
printf("#NZ in factor L = %d\n", Lstore->nnz);
printf("#NZ in factor U = %d\n", Ustore->nnz);
printf("#NZ in L+U = %d\n", Lstore->nnz + Ustore->nnz - L.ncol);
superlu_sQuerySpace(nprocs, &L, &U, panel_size, &superlu_memusage);
printf("L\\U MB %.3f\ttotal MB needed %.3f\texpansions %d\n",
superlu_memusage.for_lu/1024/1024,
superlu_memusage.total_needed/1024/1024,
superlu_memusage.expansions);
}
SUPERLU_FREE (rhs);
SUPERLU_FREE (xact);
SUPERLU_FREE (perm_r);
SUPERLU_FREE (perm_c);
Destroy_CompCol_Matrix(&A);
Destroy_SuperMatrix_Store(&B);
Destroy_SuperNode_SCP(&L);
Destroy_CompCol_NCP(&U);
/*
Terminate.
*/
printf ( "\n" );
printf ( "PSLINSOL:\n" );
printf ( " Normal end of execution.\n" );
printf ( "\n" );
timestamp ( );
return 0;
}
int main ( int argc, char *argv[] )
/**********************************************************************/
/*
Purpose:
SUPER_LU_S2 solves a symmetric sparse system read from a file.
Discussion:
The sparse matrix is stored in a file using the Harwell-Boeing
sparse matrix format. The file should be assigned to the standard
input of this program. For instance, if the matrix is stored
in the file "g10_rua.txt", the execution command might be:
super_lu_s2 < g10_rua.txt
Modified:
25 April 2004
Reference:
James Demmel, John Gilbert, Xiaoye Li,
SuperLU Users's Guide,
Sections 1 and 2.
Local parameters:
SuperMatrix L, the computed L factor.
int *perm_c, the column permutation vector.
int *perm_r, the row permutations from partial pivoting.
SuperMatrix U, the computed U factor.
*/
{
SuperMatrix A;
NCformat *Astore;
float *a;
int *asub;
SuperMatrix B;
int info;
SuperMatrix L;
int ldx;
SCformat *Lstore;
int m;
mem_usage_t mem_usage;
int n;
int nnz;
int nrhs;
superlu_options_t options;
int *perm_c;
int *perm_r;
float *rhs;
float *sol;
SuperLUStat_t stat;
SuperMatrix U;
NCformat *Ustore;
int *xa;
float *xact;
/*
Say hello.
*/
printf ( "\n" );
printf ( "SUPER_LU_S2:\n" );
printf ( " Read a symmetric sparse matrix A from standard input,\n");
printf ( " stored in Harwell-Boeing Sparse Matrix format.\n" );
printf ( "\n" );
printf ( " Solve a linear system A * X = B.\n" );
/*
Set the default input options:
options.Fact = DOFACT;
options.Equil = YES;
options.ColPerm = COLAMD;
options.DiagPivotThresh = 1.0;
options.Trans = NOTRANS;
options.IterRefine = NOREFINE;
options.SymmetricMode = NO;
options.PivotGrowth = NO;
options.ConditionNumber = NO;
options.PrintStat = YES;
*/
set_default_options ( &options );
/*
Now we modify the default options to use the symmetric mode.
*/
options.SymmetricMode = YES;
options.ColPerm = MMD_AT_PLUS_A;
options.DiagPivotThresh = 0.001;
/*
Read the matrix in Harwell-Boeing format.
*/
sreadhb ( &m, &n, &nnz, &a, &asub, &xa );
/*
Create storage for a compressed column matrix.
*/
sCreate_CompCol_Matrix ( &A, m, n, nnz, a, asub, xa, SLU_NC, SLU_S, SLU_GE );
Astore = A.Store;
printf ( "\n" );
printf ( " Dimension %dx%d; # nonzeros %d\n", A.nrow, A.ncol, Astore->nnz );
/*
Set up the right hand side.
*/
nrhs = 1;
rhs = floatMalloc ( m * nrhs );
if ( !rhs )
{
ABORT ( " Malloc fails for rhs[]." );
}
sCreate_Dense_Matrix ( &B, m, nrhs, rhs, m, SLU_DN, SLU_S, SLU_GE );
xact = floatMalloc ( n * nrhs );
if ( !xact )
{
ABORT ( " Malloc fails for rhs[]." );
}
ldx = n;
sGenXtrue ( n, nrhs, xact, ldx );
sFillRHS ( options.Trans, nrhs, xact, ldx, &A, &B );
perm_c = intMalloc ( n );
if ( !perm_c )
{
ABORT ( "Malloc fails for perm_c[]." );
}
perm_r = intMalloc ( m );
if ( !perm_r )
{
ABORT ( "Malloc fails for perm_r[]." );
}
/*
Initialize the statistics variables.
*/
StatInit ( &stat );
/*
Call SGSSV to factor the matrix and solve the linear system.
*/
sgssv ( &options, &A, perm_c, perm_r, &L, &U, &B, &stat, &info );
if ( info == 0 )
{
/*
To conveniently access the solution matrix, you need to get a pointer to it.
*/
sol = (float*) ((DNformat*) B.Store)->nzval;
/*
Compute the infinity norm of the error.
*/
sinf_norm_error ( nrhs, &B, xact );
Lstore = (SCformat *) L.Store;
Ustore = (NCformat *) U.Store;
printf ( "\n" );
printf ( " Number of nonzeros in factor L = %d\n", Lstore->nnz );
printf ( " Number of nonzeros in factor U = %d\n", Ustore->nnz );
printf ( " Number of nonzeros in L+U = %d\n",
Lstore->nnz + Ustore->nnz - n );
sQuerySpace ( &L, &U, &mem_usage );
printf ( "\n" );
printf ( " L\\U MB %.3f\ttotal MB needed %.3f\texpansions %d\n",
mem_usage.for_lu/1e6, mem_usage.total_needed/1e6,
mem_usage.expansions);
}
else
{
printf ( "\n" );
printf ( " SGSSV error returns INFO= %d\n", info );
if ( info <= n )
{
sQuerySpace ( &L, &U, &mem_usage );
printf ( "\n" );
printf (" L\\U MB %.3f\ttotal MB needed %.3f\texpansions %d\n",
mem_usage.for_lu/1e6, mem_usage.total_needed/1e6,
mem_usage.expansions );
}
}
if ( options.PrintStat )
{
StatPrint ( &stat );
}
StatFree ( &stat );
/*
Free the memory.
*/
SUPERLU_FREE ( rhs );
SUPERLU_FREE ( xact );
SUPERLU_FREE ( perm_r );
SUPERLU_FREE ( perm_c );
Destroy_CompCol_Matrix ( &A );
Destroy_SuperMatrix_Store ( &B );
Destroy_SuperNode_Matrix ( &L );
Destroy_CompCol_Matrix ( &U );
/*
Say goodbye.
*/
printf ( "\n" );
printf ( "SUPER_LU_S2:\n" );
printf ( " Normal end of execution.\n");
return 0;
}
