/*
* Check the inf-norm of the error vector
*/
void pdinf_norm_error(int iam, int_t n, int_t nrhs, double x[], int_t ldx,
double xtrue[], int_t ldxtrue, gridinfo_t *grid)
{
double err, xnorm, temperr, tempxnorm;
double *x_work, *xtrue_work;
int i, j;
for (j = 0; j < nrhs; j++) {
x_work = &x[j*ldx];
xtrue_work = &xtrue[j*ldxtrue];
err = xnorm = 0.0;
for (i = 0; i < n; i++) {
err = SUPERLU_MAX(err, fabs(x_work[i] - xtrue_work[i]));
xnorm = SUPERLU_MAX(xnorm, fabs(x_work[i]));
}
/* get the golbal max err & xnrom */
temperr = err;
tempxnorm = xnorm;
MPI_Allreduce( &temperr, &err, 1, MPI_DOUBLE, MPI_MAX, grid->comm);
MPI_Allreduce( &tempxnorm, &xnorm, 1, MPI_DOUBLE, MPI_MAX, grid->comm);
err = err / xnorm;
if ( !iam ) printf("\tSol %2d: ||X-Xtrue||/||X|| = %e\n", j, err);
}
}
/*! \brief
<pre>
Purpose
=======
DLANGS_dist returns the value of the one norm, or the Frobenius norm, or
the infinity norm, or the element of largest absolute value of a
real matrix A.
Description
===========
DLANGE returns the value
DLANGE = ( max(abs(A(i,j))), NORM = 'M' or 'm'
(
( norm1(A), NORM = '1', 'O' or 'o'
(
( normI(A), NORM = 'I' or 'i'
(
( normF(A), NORM = 'F', 'f', 'E' or 'e'
where norm1 denotes the one norm of a matrix (maximum column sum),
normI denotes the infinity norm of a matrix (maximum row sum) and
normF denotes the Frobenius norm of a matrix (square root of sum of
squares). Note that max(abs(A(i,j))) is not a matrix norm.
Arguments
=========
NORM (input) CHARACTER*1
Specifies the value to be returned in DLANGE as described above.
A (input) SuperMatrix*
The M by N sparse matrix A.
=====================================================================
</pre>
*/
double dlangs_dist(char *norm, SuperMatrix *A)
{
/* Local variables */
NCformat *Astore;
double *Aval;
int_t i, j, irow;
double value=0., sum;
double *rwork;
Astore = (NCformat *) A->Store;
Aval = (double *) Astore->nzval;
if ( SUPERLU_MIN(A->nrow, A->ncol) == 0) {
value = 0.;
} else if ( strncmp(norm, "M", 1)==0 ) {
/* Find max(abs(A(i,j))). */
value = 0.;
for (j = 0; j < A->ncol; ++j)
for (i = Astore->colptr[j]; i < Astore->colptr[j+1]; i++)
value = SUPERLU_MAX( value, fabs( Aval[i]) );
} else if ( strncmp(norm, "O", 1)==0 || *(unsigned char *)norm == '1') {
/* Find norm1(A). */
value = 0.;
for (j = 0; j < A->ncol; ++j) {
sum = 0.;
for (i = Astore->colptr[j]; i < Astore->colptr[j+1]; i++)
sum += fabs(Aval[i]);
value = SUPERLU_MAX(value, sum);
}
} else if ( strncmp(norm, "I", 1)==0 ) {
/* Find normI(A). */
if ( !(rwork = (double *) SUPERLU_MALLOC(A->nrow * sizeof(double))) )
ABORT("SUPERLU_MALLOC fails for rwork.");
for (i = 0; i < A->nrow; ++i) rwork[i] = 0.;
for (j = 0; j < A->ncol; ++j)
for (i = Astore->colptr[j]; i < Astore->colptr[j+1]; i++) {
irow = Astore->rowind[i];
rwork[irow] += fabs(Aval[i]);
}
value = 0.;
for (i = 0; i < A->nrow; ++i)
value = SUPERLU_MAX(value, rwork[i]);
SUPERLU_FREE (rwork);
} else if ( strncmp(norm, "F", 1)==0 || strncmp(norm, "E", 1)==0 ) {
/* Find normF(A). */
ABORT("Not implemented.");
} else
ABORT("Illegal norm specified.");
return (value);
} /* dlangs_dist */
/*
* Convert a full matrix into a sparse matrix format.
*/
int
sp_dconvert(int m, int n, double *A, int lda, int kl, int ku,
double *a, int *asub, int *xa, int *nnz)
{
int lasta = 0;
int i, j, ilow, ihigh;
int *row;
double *val;
for (j = 0; j < n; ++j) {
xa[j] = lasta;
val = &a[xa[j]];
row = &asub[xa[j]];
ilow = SUPERLU_MAX(0, j - ku);
ihigh = SUPERLU_MIN(n-1, j + kl);
for (i = ilow; i <= ihigh; ++i) {
val[i-ilow] = A[i + j*lda];
row[i-ilow] = i;
}
lasta += ihigh - ilow + 1;
}
xa[n] = *nnz = lasta;
return 0;
}
void log_memory(long long cur_bytes, SuperLUStat_t *stat) {
stat->current_buffer += (float) cur_bytes;
if (cur_bytes > 0) {
stat->peak_buffer =
SUPERLU_MAX(stat->peak_buffer, stat->current_buffer);
}
}
float sqselect(int n, float A[], int k)
{
register int i, j, p;
register float val;
k = SUPERLU_MAX(k, 0);
k = SUPERLU_MIN(k, n - 1);
while (n > 1)
{
i = 0; j = n-1;
p = j; val = A[p];
while (i < j)
{
for (; A[i] >= val && i < p; i++);
if (A[i] < val) { A[p] = A[i]; p = i; }
for (; A[j] <= val && j > p; j--);
if (A[j] > val) { A[p] = A[j]; p = j; }
}
A[p] = val;
if (p == k) return val;
else if (p > k) n = p;
else
{
p++;
n -= p; A += p; k -= p;
}
}
return A[0];
}
doublecomplex *doublecomplexMalloc_dist(int_t n)
{
doublecomplex *buf;
buf = (doublecomplex *)
SUPERLU_MALLOC(SUPERLU_MAX(1, n) * sizeof(doublecomplex));
return (buf);
}
/*
* Generate a banded square matrix A, with dimension n and semi-bandwidth b.
*/
void
zband(int n, int b, int nonz, doublecomplex **nzval, int **rowind, int **colptr)
{
int iseed[] = {1992,1993,1994,1995};
register int i, j, ub, lb, ilow, ihigh, lasta = 0;
doublecomplex *a;
int *asub, *xa;
doublecomplex *val;
int *row;
extern double dlaran_();
printf("A banded matrix.");
zallocateA(n, nonz, nzval, rowind, colptr); /* Allocate storage */
a = *nzval;
asub = *rowind;
xa = *colptr;
ub = lb = b;
for (i = 0; i < 4; ++i) iseed[i] = abs( iseed[i] ) % 4096;
if ( iseed[3] % 2 != 1 ) ++iseed[3];
for (j = 0; j < n; ++j) {
xa[j] = lasta;
val = &a[lasta];
row = &asub[lasta];
ilow = SUPERLU_MAX(0, j - ub);
ihigh = SUPERLU_MIN(n-1, j + lb);
for (i = ilow; i <= ihigh; ++i) {
val[i-ilow].r = dlaran_(iseed);
row[i-ilow] = i;
}
lasta += ihigh - ilow + 1;
} /* for j ... */
xa[n] = lasta;
}
/*! \brief
*
* <pre>
* Purpose
* =======
*
* GetDiagU extracts the main diagonal of matrix U of the LU factorization.
*
* Arguments
* =========
*
* n (input) int
* Dimension of the matrix.
*
* LUstruct (input) LUstruct_t*
* The data structures to store the distributed L and U factors.
* see superlu_ddefs.h for its definition.
*
* grid (input) gridinfo_t*
* The 2D process mesh. It contains the MPI communicator, the number
* of process rows (NPROW), the number of process columns (NPCOL),
* and my process rank. It is an input argument to all the
* parallel routines.
*
* diagU (output) double*, dimension (n)
* The main diagonal of matrix U.
* On exit, it is available on all processes.
*
*
* Note
* ====
*
* The diagonal blocks of the L and U matrices are stored in the L
* data structures, and are on the diagonal processes of the
* 2D process grid.
*
* This routine is modified from gather_diag_to_all() in pzgstrs_Bglobal.c.
* </pre>
*/
void pzGetDiagU(int_t n, LUstruct_t *LUstruct, gridinfo_t *grid,
doublecomplex *diagU)
{
int_t *xsup;
int iam, knsupc, pkk;
int nsupr; /* number of rows in the block L(:,k) (LDA) */
int_t i, j, jj, k, lk, lwork, nsupers, p;
int_t num_diag_procs, *diag_procs, *diag_len;
Glu_persist_t *Glu_persist = LUstruct->Glu_persist;
LocalLU_t *Llu = LUstruct->Llu;
doublecomplex *zblock, *zwork, *lusup;
iam = grid->iam;
nsupers = Glu_persist->supno[n-1] + 1;
xsup = Glu_persist->xsup;
get_diag_procs(n, Glu_persist, grid, &num_diag_procs,
&diag_procs, &diag_len);
jj = diag_len[0];
for (j = 1; j < num_diag_procs; ++j) jj = SUPERLU_MAX( jj, diag_len[j] );
if ( !(zwork = doublecomplexMalloc_dist(jj)) ) ABORT("Malloc fails for zwork[]");
for (p = 0; p < num_diag_procs; ++p) {
pkk = diag_procs[p];
if ( iam == pkk ) {
/* Copy diagonal into buffer dwork[]. */
lwork = 0;
for (k = p; k < nsupers; k += num_diag_procs) {
knsupc = SuperSize( k );
lk = LBj( k, grid );
nsupr = Llu->Lrowind_bc_ptr[lk][1]; /* LDA of lusup[] */
lusup = Llu->Lnzval_bc_ptr[lk];
for (i = 0; i < knsupc; ++i) /* Copy the diagonal. */
zwork[lwork+i] = lusup[i*(nsupr+1)];
lwork += knsupc;
}
MPI_Bcast( zwork, lwork, SuperLU_MPI_DOUBLE_COMPLEX, pkk, grid->comm );
} else {
MPI_Bcast( zwork, diag_len[p], SuperLU_MPI_DOUBLE_COMPLEX, pkk, grid->comm );
}
/* Scatter zwork[] into global diagU vector. */
lwork = 0;
for (k = p; k < nsupers; k += num_diag_procs) {
knsupc = SuperSize( k );
zblock = &diagU[FstBlockC( k )];
for (i = 0; i < knsupc; ++i) zblock[i] = zwork[lwork+i];
lwork += knsupc;
}
} /* for p = ... */
SUPERLU_FREE(diag_procs);
SUPERLU_FREE(diag_len);
SUPERLU_FREE(zwork);
}
double *doubleCalloc_dist(int_t n)
{
double *buf;
register int_t i;
double zero = 0.0;
buf = (double *) SUPERLU_MALLOC( SUPERLU_MAX(1, n) * sizeof(double));
if ( !buf ) return (buf);
for (i = 0; i < n; ++i) buf[i] = zero;
return (buf);
}
/*
* Check the inf-norm of the error vector
*/
void dinf_norm_error_dist(int_t n, int_t nrhs, double *x, int_t ldx,
double *xtrue, int_t ldxtrue,
gridinfo_t *grid)
{
double err, xnorm;
double *x_work, *xtrue_work;
int i, j;
for (j = 0; j < nrhs; j++) {
x_work = &x[j*ldx];
xtrue_work = &xtrue[j*ldxtrue];
err = xnorm = 0.0;
for (i = 0; i < n; i++) {
err = SUPERLU_MAX(err, fabs(x_work[i] - xtrue_work[i]));
xnorm = SUPERLU_MAX(xnorm, fabs(x_work[i]));
}
err = err / xnorm;
printf("(%d) .. ||X-Xtrue||/||X|| = %e\n", grid->iam, err);
}
}
doublecomplex *doublecomplexCalloc_dist(int_t n)
{
doublecomplex *buf;
register int_t i;
doublecomplex zero = {0.0, 0.0};
buf = (doublecomplex *)
SUPERLU_MALLOC(SUPERLU_MAX(1, n) * sizeof(doublecomplex));
if ( !buf ) return (buf);
for (i = 0; i < n; ++i) buf[i] = zero;
return (buf);
}
/*
* Check the inf-norm of the error vector
*/
void sinf_norm_error(int nrhs, SuperMatrix *X, float *xtrue)
{
DNformat *Xstore;
float err, xnorm;
float *Xmat, *soln_work;
int i, j;
Xstore = X->Store;
Xmat = Xstore->nzval;
for (j = 0; j < nrhs; j++) {
soln_work = &Xmat[j*Xstore->lda];
err = xnorm = 0.0;
for (i = 0; i < X->nrow; i++) {
err = SUPERLU_MAX(err, fabs(soln_work[i] - xtrue[i]));
xnorm = SUPERLU_MAX(xnorm, fabs(soln_work[i]));
}
err = err / xnorm;
printf("||X - Xtrue||/||X|| = %e\n", err);
}
}
/*! \brief Set up pointers for real working arrays.
*/
void
sSetRWork(int m, int panel_size, float *dworkptr,
float **dense, float **tempv)
{
float zero = 0.0;
int maxsuper = SUPERLU_MAX( sp_ienv(3), sp_ienv(7) ),
rowblk = sp_ienv(4);
*dense = dworkptr;
*tempv = *dense + panel_size*m;
sfill (*dense, m * panel_size, zero);
sfill (*tempv, NUM_TEMPV(m,panel_size,maxsuper,rowblk), zero);
}
/*! \brief Set up pointers for real working arrays.
*/
void
zSetRWork(int m, int panel_size, doublecomplex *dworkptr,
doublecomplex **dense, doublecomplex **tempv)
{
doublecomplex zero = {0.0, 0.0};
int maxsuper = SUPERLU_MAX( sp_ienv(3), sp_ienv(7) ),
rowblk = sp_ienv(4);
*dense = dworkptr;
*tempv = *dense + panel_size*m;
zfill (*dense, m * panel_size, zero);
zfill (*tempv, NUM_TEMPV(m,panel_size,maxsuper,rowblk), zero);
}
/*
* Check the inf-norm of the error vector
*/
void zinf_norm_error_dist(int_t n, int_t nrhs, doublecomplex *x, int_t ldx,
doublecomplex *xtrue, int_t ldxtrue,
gridinfo_t *grid)
{
double err, xnorm;
doublecomplex *x_work, *xtrue_work;
doublecomplex temp;
int i, j;
for (j = 0; j < nrhs; j++) {
x_work = &x[j*ldx];
xtrue_work = &xtrue[j*ldxtrue];
err = xnorm = 0.0;
for (i = 0; i < n; i++) {
z_sub(&temp, &x_work[i], &xtrue_work[i]);
err = SUPERLU_MAX(err, z_abs(&temp));
xnorm = SUPERLU_MAX(xnorm, z_abs(&x_work[i]));
}
err = err / xnorm;
printf("\tRHS %2d: ||X-Xtrue||/||X|| = %e\n", j, err);
}
}
/*! \brief Check the inf-norm of the error vector
*/
void cinf_norm_error(int nrhs, SuperMatrix *X, complex *xtrue)
{
DNformat *Xstore;
float err, xnorm;
complex *Xmat, *soln_work;
complex temp;
int i, j;
Xstore = X->Store;
Xmat = Xstore->nzval;
for (j = 0; j < nrhs; j++) {
soln_work = &Xmat[j*Xstore->lda];
err = xnorm = 0.0;
for (i = 0; i < X->nrow; i++) {
c_sub(&temp, &soln_work[i], &xtrue[i]);
err = SUPERLU_MAX(err, c_abs(&temp));
xnorm = SUPERLU_MAX(xnorm, c_abs(&soln_work[i]));
}
err = err / xnorm;
printf("||X - Xtrue||/||X|| = %e\n", err);
}
}
/*! \brief Allocate known working storage. Returns 0 if success, otherwise
returns the number of bytes allocated so far when failure occurred. */
int
sLUWorkInit(int m, int n, int panel_size, int **iworkptr,
float **dworkptr, GlobalLU_t *Glu)
{
int isize, dsize, extra;
float *old_ptr;
int maxsuper = SUPERLU_MAX( sp_ienv(3), sp_ienv(7) ),
rowblk = sp_ienv(4);
isize = ( (2 * panel_size + 3 + NO_MARKER ) * m + n ) * sizeof(int);
dsize = (m * panel_size +
NUM_TEMPV(m,panel_size,maxsuper,rowblk)) * sizeof(float);
if ( Glu->MemModel == SYSTEM )
*iworkptr = (int *) intCalloc(isize/sizeof(int));
else
*iworkptr = (int *) suser_malloc(isize, TAIL, Glu);
if ( ! *iworkptr ) {
fprintf(stderr, "sLUWorkInit: malloc fails for local iworkptr[]\n");
return (isize + n);
}
if ( Glu->MemModel == SYSTEM )
*dworkptr = (float *) SUPERLU_MALLOC(dsize);
else {
*dworkptr = (float *) suser_malloc(dsize, TAIL, Glu);
if ( NotDoubleAlign(*dworkptr) ) {
old_ptr = *dworkptr;
*dworkptr = (float*) DoubleAlign(*dworkptr);
*dworkptr = (float*) ((double*)*dworkptr - 1);
extra = (char*)old_ptr - (char*)*dworkptr;
#ifdef DEBUG
printf("sLUWorkInit: not aligned, extra %d\n", extra);
#endif
Glu->stack.top2 -= extra;
Glu->stack.used += extra;
}
}
if ( ! *dworkptr ) {
fprintf(stderr, "malloc fails for local dworkptr[].");
return (isize + dsize + n);
}
return 0;
}
void
StatInit(SuperLUStat_t *stat)
{
register int i, w, panel_size, relax;
panel_size = sp_ienv(1);
relax = sp_ienv(2);
w = SUPERLU_MAX(panel_size, relax);
stat->panel_histo = intCalloc(w+1);
stat->utime = (double *) SUPERLU_MALLOC(NPHASES * sizeof(double));
if (!stat->utime) ABORT("SUPERLU_MALLOC fails for stat->utime");
stat->ops = (flops_t *) SUPERLU_MALLOC(NPHASES * sizeof(flops_t));
if (!stat->ops) ABORT("SUPERLU_MALLOC fails for stat->ops");
for (i = 0; i < NPHASES; ++i) {
stat->utime[i] = 0.;
stat->ops[i] = 0.;
}
}
/*
* Allocate storage for various statistics.
*/
void
StatAlloc(const int n, const int nprocs, const int panel_size,
const int relax, Gstat_t *Gstat)
{
register int w;
w = SUPERLU_MAX( panel_size, relax ) + 1;
Gstat->panel_histo = intCalloc(w);
Gstat->utime = (double *) doubleMalloc(NPHASES);
Gstat->ops = (flops_t *) SUPERLU_MALLOC(NPHASES * sizeof(flops_t));
if ( !(Gstat->procstat =
(procstat_t *) SUPERLU_MALLOC(nprocs*sizeof(procstat_t))) )
SUPERLU_ABORT( "SUPERLU_MALLOC failed for procstat[]" );
#if (PRNTlevel==1)
printf(".. StatAlloc(): n %d, nprocs %d, panel_size %d, relax %d\n",
n, nprocs, panel_size, relax);
#endif
#ifdef PROFILE
if ( !(Gstat->panstat =
(panstat_t*) SUPERLU_MALLOC(n * sizeof(panstat_t))) )
SUPERLU_ABORT( "SUPERLU_MALLOC failed for panstat[]" );
Gstat->panhows = intCalloc(3);
Gstat->height = intCalloc(n+1);
if ( !(Gstat->flops_by_height =
(float *) SUPERLU_MALLOC(n * sizeof(float))) )
SUPERLU_ABORT("SUPERLU_MALLOC failed for flops_by_height[]");
#endif
#ifdef PREDICT_OPT
if ( !(cp_panel = (cp_panel_t *) SUPERLU_MALLOC(n * sizeof(cp_panel_t))) )
SUPERLU_ABORT( "SUPERLU_MALLOC failed for cp_panel[]" );
if ( !(desc_eft = (desc_eft_t *) SUPERLU_MALLOC(n * sizeof(desc_eft_t))) )
SUPERLU_ABORT( "SUPERLU_MALLOC failed for desc_eft[]" );
cp_firstkid = intMalloc(n+1);
cp_nextkid = intMalloc(n+1);
#endif
}
int
pcgstrf_column_bmod(
const int pnum, /* process number */
const int jcol, /* current column in the panel */
const int fpanelc,/* first column in the panel */
const int nseg, /* number of s-nodes to update jcol */
int *segrep,/* in */
int *repfnz,/* in */
complex *dense, /* modified */
complex *tempv, /* working array */
pxgstrf_shared_t *pxgstrf_shared, /* modified */
Gstat_t *Gstat /* modified */
)
{
/*
* -- SuperLU MT routine (version 2.0) --
* Lawrence Berkeley National Lab, Univ. of California Berkeley,
* and Xerox Palo Alto Research Center.
* September 10, 2007
*
* Purpose:
* ========
* Performs numeric block updates (sup-col) in topological order.
* It features: col-col, 2cols-col, 3cols-col, and sup-col updates.
* Special processing on the supernodal portion of L\U[*,j].
*
* Return value:
* =============
* 0 - successful return
* > 0 - number of bytes allocated when run out of space
*
*/
#if ( MACH==CRAY_PVP )
_fcd ftcs1 = _cptofcd("L", strlen("L")),
ftcs2 = _cptofcd("N", strlen("N")),
ftcs3 = _cptofcd("U", strlen("U"));
#endif
#ifdef USE_VENDOR_BLAS
int incx = 1, incy = 1;
complex alpha, beta;
#endif
GlobalLU_t *Glu = pxgstrf_shared->Glu; /* modified */
/* krep = representative of current k-th supernode
* fsupc = first supernodal column
* nsupc = no of columns in supernode
* nsupr = no of rows in supernode (used as leading dimension)
* luptr = location of supernodal LU-block in storage
* kfnz = first nonz in the k-th supernodal segment
* no_zeros = no of leading zeros in a supernodal U-segment
*/
complex ukj, ukj1, ukj2;
register int lptr, kfnz, isub, irow, i, no_zeros;
register int luptr, luptr1, luptr2;
int fsupc, nsupc, nsupr, segsze;
int nrow; /* No of rows in the matrix of matrix-vector */
int jsupno, k, ksub, krep, krep_ind, ksupno;
int ufirst, nextlu;
int fst_col; /* First column within small LU update */
int d_fsupc; /* Distance between the first column of the current
panel and the first column of the current snode.*/
int *xsup, *supno;
int *lsub, *xlsub, *xlsub_end;
complex *lusup;
int *xlusup, *xlusup_end;
complex *tempv1;
int mem_error;
register float flopcnt;
complex zero = {0.0, 0.0};
complex one = {1.0, 0.0};
complex none = {-1.0, 0.0};
complex comp_temp, comp_temp1;
xsup = Glu->xsup;
supno = Glu->supno;
lsub = Glu->lsub;
xlsub = Glu->xlsub;
xlsub_end = Glu->xlsub_end;
lusup = Glu->lusup;
xlusup = Glu->xlusup;
xlusup_end = Glu->xlusup_end;
jsupno = supno[jcol];
/*
* For each nonz supernode segment of U[*,j] in topological order
*/
k = nseg - 1;
for (ksub = 0; ksub < nseg; ksub++) {
krep = segrep[k];
k--;
ksupno = supno[krep];
#if ( DEBUGlvel>=2 )
if (jcol==BADCOL)
printf("(%d) pcgstrf_column_bmod[1]: %d, nseg %d, krep %d, jsupno %d, ksupno %d\n",
pnum, jcol, nseg, krep, jsupno, ksupno);
#endif
if ( jsupno != ksupno ) { /* Outside the rectangular supernode */
fsupc = xsup[ksupno];
fst_col = SUPERLU_MAX ( fsupc, fpanelc );
/* Distance from the current supernode to the current panel;
d_fsupc=0 if fsupc >= fpanelc. */
d_fsupc = fst_col - fsupc;
luptr = xlusup[fst_col] + d_fsupc;
lptr = xlsub[fsupc] + d_fsupc;
kfnz = repfnz[krep];
kfnz = SUPERLU_MAX ( kfnz, fpanelc );
segsze = krep - kfnz + 1;
nsupc = krep - fst_col + 1;
nsupr = xlsub_end[fsupc] - xlsub[fsupc]; /* Leading dimension */
nrow = nsupr - d_fsupc - nsupc;
krep_ind = lptr + nsupc - 1;
flopcnt = segsze * (segsze - 1) + 2 * nrow * segsze;//sj
Gstat->procstat[pnum].fcops += flopcnt;
#if ( DEBUGlevel>=2 )
if (jcol==BADCOL)
printf("(%d) pcgstrf_column_bmod[2]: %d, krep %d, kfnz %d, segsze %d, d_fsupc %d,\
fsupc %d, nsupr %d, nsupc %d\n",
pnum, jcol, krep, kfnz, segsze, d_fsupc, fsupc, nsupr, nsupc);
#endif
/*
* Case 1: Update U-segment of size 1 -- col-col update
*/
if ( segsze == 1 ) {
ukj = dense[lsub[krep_ind]];
luptr += nsupr*(nsupc-1) + nsupc;
for (i = lptr + nsupc; i < xlsub_end[fsupc]; ++i) {
irow = lsub[i];
cc_mult(&comp_temp, &ukj, &lusup[luptr]);
c_sub(&dense[irow], &dense[irow], &comp_temp);
luptr++;
}
} else if ( segsze <= 3 ) {
ukj = dense[lsub[krep_ind]];
luptr += nsupr*(nsupc-1) + nsupc-1;
ukj1 = dense[lsub[krep_ind - 1]];
luptr1 = luptr - nsupr;
if ( segsze == 2 ) { /* Case 2: 2cols-col update */
cc_mult(&comp_temp, &ukj1, &lusup[luptr1]);
c_sub(&ukj, &ukj, &comp_temp);
dense[lsub[krep_ind]] = ukj;
for (i = lptr + nsupc; i < xlsub_end[fsupc]; ++i) {
irow = lsub[i];
luptr++;
luptr1++;
cc_mult(&comp_temp, &ukj, &lusup[luptr]);
cc_mult(&comp_temp1, &ukj1, &lusup[luptr1]);
c_add(&comp_temp, &comp_temp, &comp_temp1);
c_sub(&dense[irow], &dense[irow], &comp_temp);
}
} else { /* Case 3: 3cols-col update */
ukj2 = dense[lsub[krep_ind - 2]];
luptr2 = luptr1 - nsupr;
cc_mult(&comp_temp, &ukj2, &lusup[luptr2-1]);
c_sub(&ukj1, &ukj1, &comp_temp);
cc_mult(&comp_temp, &ukj1, &lusup[luptr1]);
cc_mult(&comp_temp1, &ukj2, &lusup[luptr2]);
c_add(&comp_temp, &comp_temp, &comp_temp1);
c_sub(&ukj, &ukj, &comp_temp);
dense[lsub[krep_ind]] = ukj;
dense[lsub[krep_ind-1]] = ukj1;
for (i = lptr + nsupc; i < xlsub_end[fsupc]; ++i) {
irow = lsub[i];
luptr++;
luptr1++;
luptr2++;
cc_mult(&comp_temp, &ukj, &lusup[luptr]);
cc_mult(&comp_temp1, &ukj1, &lusup[luptr1]);
c_add(&comp_temp, &comp_temp, &comp_temp1);
cc_mult(&comp_temp1, &ukj2, &lusup[luptr2]);
c_add(&comp_temp, &comp_temp, &comp_temp1);
c_sub(&dense[irow], &dense[irow], &comp_temp);
}
}
} else {
/*
* Case: sup-col update
* Perform a triangular solve and block update,
* then scatter the result of sup-col update to dense
*/
no_zeros = kfnz - fst_col;
/* Copy U[*,j] segment from dense[*] to tempv[*] */
isub = lptr + no_zeros;
for (i = 0; i < segsze; i++) {
irow = lsub[isub];
tempv[i] = dense[irow];
++isub;
}
/* Dense triangular solve -- start effective triangle */
luptr += nsupr * no_zeros + no_zeros;
#ifdef USE_VENDOR_BLAS
#if ( MACH==CRAY_PVP )
CTRSV( ftcs1, ftcs2, ftcs3, &segsze, &lusup[luptr],
&nsupr, tempv, &incx );
#else
ctrsv_( "L", "N", "U", &segsze, &lusup[luptr],
&nsupr, tempv, &incx );
#endif
luptr += segsze; /* Dense matrix-vector */
tempv1 = &tempv[segsze];
alpha = one;
beta = zero;
#if ( MACH==CRAY_PVP )
CGEMV( ftcs2, &nrow, &segsze, &alpha, &lusup[luptr],
&nsupr, tempv, &incx, &beta, tempv1, &incy );
#else
cgemv_( "N", &nrow, &segsze, &alpha, &lusup[luptr],
&nsupr, tempv, &incx, &beta, tempv1, &incy );
#endif
#else
clsolve ( nsupr, segsze, &lusup[luptr], tempv );
luptr += segsze; /* Dense matrix-vector */
tempv1 = &tempv[segsze];
cmatvec (nsupr, nrow , segsze, &lusup[luptr], tempv, tempv1);
#endif
/* Scatter tempv[] into SPA dense[*] */
isub = lptr + no_zeros;
for (i = 0; i < segsze; i++) {
irow = lsub[isub];
dense[irow] = tempv[i]; /* Scatter */
tempv[i] = zero;
isub++;
}
/* Scatter tempv1[] into SPA dense[*] */
for (i = 0; i < nrow; i++) {
irow = lsub[isub];
c_sub(&dense[irow], &dense[irow], &tempv1[i]);
tempv1[i] = zero;
++isub;
}
} /* else segsze >= 4 */
} /* if jsupno ... */
} /* for each segment... */
/* ------------------------------------------
Process the supernodal portion of L\U[*,j]
------------------------------------------ */
fsupc = SUPER_FSUPC (jsupno);
nsupr = xlsub_end[fsupc] - xlsub[fsupc];
if ( (mem_error = Glu_alloc(pnum, jcol, nsupr, LUSUP, &nextlu,
pxgstrf_shared)) )
return mem_error;
xlusup[jcol] = nextlu;
lusup = Glu->lusup;
/* Gather the nonzeros from SPA dense[*,j] into L\U[*,j] */
for (isub = xlsub[fsupc]; isub < xlsub_end[fsupc]; ++isub) {
irow = lsub[isub];
lusup[nextlu] = dense[irow];
dense[irow] = zero;
#ifdef DEBUG
if (jcol == -1)
printf("(%d) pcgstrf_column_bmod[lusup] jcol %d, irow %d, lusup %.10e\n",
pnum, jcol, irow, lusup[nextlu]);
#endif
++nextlu;
}
xlusup_end[jcol] = nextlu; /* close L\U[*,jcol] */
#if ( DEBUGlevel>=2 )
if (jcol == -1) {
nrow = xlusup_end[jcol] - xlusup[jcol];
print_double_vec("before sup-col update", nrow, &lsub[xlsub[fsupc]],
&lusup[xlusup[jcol]]);
}
#endif
/*
* For more updates within the panel (also within the current supernode),
* should start from the first column of the panel, or the first column
* of the supernode, whichever is bigger. There are 2 cases:
* (1) fsupc < fpanelc, then fst_col := fpanelc
* (2) fsupc >= fpanelc, then fst_col := fsupc
*/
fst_col = SUPERLU_MAX ( fsupc, fpanelc );
if ( fst_col < jcol ) {
/* distance between the current supernode and the current panel;
d_fsupc=0 if fsupc >= fpanelc. */
d_fsupc = fst_col - fsupc;
lptr = xlsub[fsupc] + d_fsupc;
luptr = xlusup[fst_col] + d_fsupc;
nsupr = xlsub_end[fsupc] - xlsub[fsupc]; /* Leading dimension */
nsupc = jcol - fst_col; /* Excluding jcol */
nrow = nsupr - d_fsupc - nsupc;
/* points to the beginning of jcol in supernode L\U[*,jsupno] */
ufirst = xlusup[jcol] + d_fsupc;
#if ( DEBUGlevel>=2 )
if (jcol==BADCOL)
printf("(%d) pcgstrf_column_bmod[3] jcol %d, fsupc %d, nsupr %d, nsupc %d, nrow %d\n",
pnum, jcol, fsupc, nsupr, nsupc, nrow);
#endif
flopcnt = nsupc * (nsupc - 1) + 2 * nrow * nsupc; //sj
Gstat->procstat[pnum].fcops += flopcnt;
/* ops[TRSV] += nsupc * (nsupc - 1);
ops[GEMV] += 2 * nrow * nsupc; */
#ifdef USE_VENDOR_BLAS
alpha = none; beta = one; /* y := beta*y + alpha*A*x */
#if ( MACH==CRAY_PVP )
CTRSV( ftcs1, ftcs2, ftcs3, &nsupc, &lusup[luptr],
&nsupr, &lusup[ufirst], &incx );
CGEMV( ftcs2, &nrow, &nsupc, &alpha, &lusup[luptr+nsupc], &nsupr,
&lusup[ufirst], &incx, &beta, &lusup[ufirst+nsupc], &incy );
#else
ctrsv_( "L", "N", "U", &nsupc, &lusup[luptr],
&nsupr, &lusup[ufirst], &incx );
cgemv_( "N", &nrow, &nsupc, &alpha, &lusup[luptr+nsupc], &nsupr,
&lusup[ufirst], &incx, &beta, &lusup[ufirst+nsupc], &incy );
#endif
#else
clsolve ( nsupr, nsupc, &lusup[luptr], &lusup[ufirst] );
cmatvec ( nsupr, nrow, nsupc, &lusup[luptr+nsupc],
&lusup[ufirst], tempv );
/* Copy updates from tempv[*] into lusup[*] */
isub = ufirst + nsupc;
for (i = 0; i < nrow; i++) {
c_sub(&lusup[isub], &lusup[isub], &tempv[i]);
tempv[i] = zero;
++isub;
}
#endif
} /* if fst_col < jcol ... */
return 0;
}
int cgst02(trans_t trans, int m, int n, int nrhs, SuperMatrix *A,
complex *x, int ldx, complex *b, int ldb, float *resid)
{
/*
Purpose
=======
CGST02 computes the residual for a solution of a system of linear
equations A*x = b or A'*x = b:
RESID = norm(B - A*X) / ( norm(A) * norm(X) * EPS ),
where EPS is the machine epsilon.
Arguments
=========
TRANS (input) trans_t
Specifies the form of the system of equations:
= NOTRANS: A *x = b
= TRANS : A'*x = b, where A' is the transpose of A
= CONJ : A'*x = b, where A' is the transpose of A
M (input) INTEGER
The number of rows of the matrix A. M >= 0.
N (input) INTEGER
The number of columns of the matrix A. N >= 0.
NRHS (input) INTEGER
The number of columns of B, the matrix of right hand sides.
NRHS >= 0.
A (input) SuperMatrix*, dimension (LDA,N)
The original M x N sparse matrix A.
X (input) COMPLEX PRECISION array, dimension (LDX,NRHS)
The computed solution vectors for the system of linear
equations.
LDX (input) INTEGER
The leading dimension of the array X. If TRANS = NOTRANS,
LDX >= max(1,N); if TRANS = TRANS or CONJ, LDX >= max(1,M).
B (input/output) COMPLEX PRECISION array, dimension (LDB,NRHS)
On entry, the right hand side vectors for the system of
linear equations.
On exit, B is overwritten with the difference B - A*X.
LDB (input) INTEGER
The leading dimension of the array B. IF TRANS = NOTRANS,
LDB >= max(1,M); if TRANS = TRANS or CONJ, LDB >= max(1,N).
RESID (output) FLOAT PRECISION
The maximum over the number of right hand sides of
norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
=====================================================================
*/
/* Table of constant values */
complex alpha = {-1., 0.0};
complex beta = {1., 0.0};
int c__1 = 1;
/* System generated locals */
float d__1, d__2;
/* Local variables */
int j;
int n1, n2;
float anorm, bnorm;
float xnorm;
float eps;
char transc[1];
/* Function prototypes */
extern int lsame_(char *, char *);
extern float clangs(char *, SuperMatrix *);
extern float scasum_(int *, complex *, int *);
/* Function Body */
if ( m <= 0 || n <= 0 || nrhs == 0) {
*resid = 0.;
return 0;
}
if ( (trans == TRANS) || (trans == CONJ) ) {
n1 = n;
n2 = m;
*transc = 'T';
} else {
n1 = m;
n2 = n;
*transc = 'N';
}
/* Exit with RESID = 1/EPS if ANORM = 0. */
eps = slamch_("Epsilon");
anorm = clangs("1", A);
if (anorm <= 0.) {
*resid = 1. / eps;
return 0;
}
/* Compute B - A*X (or B - A'*X ) and store in B. */
sp_cgemm(transc, "N", n1, nrhs, n2, alpha, A, x, ldx, beta, b, ldb);
/* Compute the maximum over the number of right hand sides of
norm(B - A*X) / ( norm(A) * norm(X) * EPS ) . */
*resid = 0.;
for (j = 0; j < nrhs; ++j) {
bnorm = scasum_(&n1, &b[j*ldb], &c__1);
xnorm = scasum_(&n2, &x[j*ldx], &c__1);
if (xnorm <= 0.) {
*resid = 1. / eps;
} else {
/* Computing MAX */
d__1 = *resid, d__2 = bnorm / anorm / xnorm / eps;
*resid = SUPERLU_MAX(d__1, d__2);
}
}
return 0;
} /* cgst02 */
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;
}
float
cPivotGrowth(int ncols, SuperMatrix *A, int *perm_c,
SuperMatrix *L, SuperMatrix *U)
{
/*
* Purpose
* =======
*
* Compute the reciprocal pivot growth factor of the leading ncols columns
* of the matrix, using the formula:
* min_j ( max_i(abs(A_ij)) / max_i(abs(U_ij)) )
*
* Arguments
* =========
*
* ncols (input) int
* The number of columns of matrices A, L and U.
*
* A (input) SuperMatrix*
* Original matrix A, permuted by columns, of dimension
* (A->nrow, A->ncol). The type of A can be:
* Stype = NC; Dtype = SLU_C; Mtype = GE.
*
* L (output) SuperMatrix*
* The factor L from the factorization Pr*A=L*U; use compressed row
* subscripts storage for supernodes, i.e., L has type:
* Stype = SC; Dtype = SLU_C; Mtype = TRLU.
*
* U (output) SuperMatrix*
* The factor U from the factorization Pr*A*Pc=L*U. Use column-wise
* storage scheme, i.e., U has types: Stype = NC;
* Dtype = SLU_C; Mtype = TRU.
*
*/
NCformat *Astore;
SCformat *Lstore;
NCformat *Ustore;
complex *Aval, *Lval, *Uval;
int fsupc, nsupr, luptr, nz_in_U;
int i, j, k, oldcol;
int *inv_perm_c;
float rpg, maxaj, maxuj;
extern double slamch_(char *);
float smlnum;
complex *luval;
complex temp_comp;
/* Get machine constants. */
smlnum = slamch_("S");
rpg = 1. / smlnum;
Astore = A->Store;
Lstore = L->Store;
Ustore = U->Store;
Aval = Astore->nzval;
Lval = Lstore->nzval;
Uval = Ustore->nzval;
inv_perm_c = (int *) SUPERLU_MALLOC(A->ncol*sizeof(int));
for (j = 0; j < A->ncol; ++j) inv_perm_c[perm_c[j]] = j;
for (k = 0; k <= Lstore->nsuper; ++k) {
fsupc = L_FST_SUPC(k);
nsupr = L_SUB_START(fsupc+1) - L_SUB_START(fsupc);
luptr = L_NZ_START(fsupc);
luval = &Lval[luptr];
nz_in_U = 1;
for (j = fsupc; j < L_FST_SUPC(k+1) && j < ncols; ++j) {
maxaj = 0.;
oldcol = inv_perm_c[j];
for (i = Astore->colptr[oldcol]; i < Astore->colptr[oldcol+1]; ++i)
maxaj = SUPERLU_MAX( maxaj, slu_c_abs1( &Aval[i]) );
maxuj = 0.;
for (i = Ustore->colptr[j]; i < Ustore->colptr[j+1]; i++)
maxuj = SUPERLU_MAX( maxuj, slu_c_abs1( &Uval[i]) );
/* Supernode */
for (i = 0; i < nz_in_U; ++i)
maxuj = SUPERLU_MAX( maxuj, slu_c_abs1( &luval[i]) );
++nz_in_U;
luval += nsupr;
if ( maxuj == 0. )
rpg = SUPERLU_MIN( rpg, 1.);
else
rpg = SUPERLU_MIN( rpg, maxaj / maxuj );
}
if ( j >= ncols ) break;
}
SUPERLU_FREE(inv_perm_c);
return (rpg);
}
void
dgsequ(SuperMatrix *A, double *r, double *c, double *rowcnd,
double *colcnd, double *amax, int *info)
{
/*
Purpose
=======
dgsequ() computes row and column scalings intended to equilibrate an
M-by-N sparse matrix A and reduce its condition number. R returns the row
scale factors and C the column scale factors, chosen to try to make
the largest element in each row and column of the matrix B with
elements B(i,j)=R(i)*A(i,j)*C(j) have absolute value 1.
R(i) and C(j) are restricted to be between SMLNUM = smallest safe
number and BIGNUM = largest safe number. Use of these scaling
factors is not guaranteed to reduce the condition number of A but
works well in practice.
See supermatrix.h for the definition of 'SuperMatrix' structure.
Arguments
=========
A (input) SuperMatrix*
The matrix of dimension (A->nrow, A->ncol) whose equilibration
factors are to be computed. The type of A can be:
Stype = SLU_NC; Dtype = SLU_D; Mtype = SLU_GE.
R (output) double*, size A->nrow
If INFO = 0 or INFO > M, R contains the row scale factors
for A.
C (output) double*, size A->ncol
If INFO = 0, C contains the column scale factors for A.
ROWCND (output) double*
If INFO = 0 or INFO > M, ROWCND contains the ratio of the
smallest R(i) to the largest R(i). If ROWCND >= 0.1 and
AMAX is neither too large nor too small, it is not worth
scaling by R.
COLCND (output) double*
If INFO = 0, COLCND contains the ratio of the smallest
C(i) to the largest C(i). If COLCND >= 0.1, it is not
worth scaling by C.
AMAX (output) double*
Absolute value of largest matrix element. If AMAX is very
close to overflow or very close to underflow, the matrix
should be scaled.
INFO (output) int*
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, and i is
<= M: the i-th row of A is exactly zero
> M: the (i-M)-th column of A is exactly zero
=====================================================================
*/
/* Local variables */
NCformat *Astore;
double *Aval;
int i, j, irow;
double rcmin, rcmax;
double bignum, smlnum;
extern double dlamch_(char *);
/* Test the input parameters. */
*info = 0;
if ( A->nrow < 0 || A->ncol < 0 ||
A->Stype != SLU_NC || A->Dtype != SLU_D || A->Mtype != SLU_GE )
*info = -1;
if (*info != 0) {
i = -(*info);
xerbla_("dgsequ", &i);
return;
}
/* Quick return if possible */
if ( A->nrow == 0 || A->ncol == 0 ) {
*rowcnd = 1.;
*colcnd = 1.;
*amax = 0.;
return;
}
Astore = A->Store;
Aval = Astore->nzval;
/* Get machine constants. */
smlnum = dlamch_("S");
bignum = 1. / smlnum;
/* Compute row scale factors. */
for (i = 0; i < A->nrow; ++i) r[i] = 0.;
/* Find the maximum element in each row. */
for (j = 0; j < A->ncol; ++j)
for (i = Astore->colptr[j]; i < Astore->colptr[j+1]; ++i) {
irow = Astore->rowind[i];
r[irow] = SUPERLU_MAX( r[irow], fabs(Aval[i]) );
}
/* Find the maximum and minimum scale factors. */
rcmin = bignum;
rcmax = 0.;
for (i = 0; i < A->nrow; ++i) {
rcmax = SUPERLU_MAX(rcmax, r[i]);
rcmin = SUPERLU_MIN(rcmin, r[i]);
}
*amax = rcmax;
if (rcmin == 0.) {
/* Find the first zero scale factor and return an error code. */
for (i = 0; i < A->nrow; ++i)
if (r[i] == 0.) {
*info = i + 1;
return;
}
} else {
/* Invert the scale factors. */
for (i = 0; i < A->nrow; ++i)
r[i] = 1. / SUPERLU_MIN( SUPERLU_MAX( r[i], smlnum ), bignum );
/* Compute ROWCND = min(R(I)) / max(R(I)) */
*rowcnd = SUPERLU_MAX( rcmin, smlnum ) / SUPERLU_MIN( rcmax, bignum );
}
/* Compute column scale factors */
for (j = 0; j < A->ncol; ++j) c[j] = 0.;
/* Find the maximum element in each column, assuming the row
scalings computed above. */
for (j = 0; j < A->ncol; ++j)
for (i = Astore->colptr[j]; i < Astore->colptr[j+1]; ++i) {
irow = Astore->rowind[i];
c[j] = SUPERLU_MAX( c[j], fabs(Aval[i]) * r[irow] );
}
/* Find the maximum and minimum scale factors. */
rcmin = bignum;
rcmax = 0.;
for (j = 0; j < A->ncol; ++j) {
rcmax = SUPERLU_MAX(rcmax, c[j]);
rcmin = SUPERLU_MIN(rcmin, c[j]);
}
if (rcmin == 0.) {
/* Find the first zero scale factor and return an error code. */
for (j = 0; j < A->ncol; ++j)
if ( c[j] == 0. ) {
*info = A->nrow + j + 1;
return;
}
} else {
/* Invert the scale factors. */
for (j = 0; j < A->ncol; ++j)
c[j] = 1. / SUPERLU_MIN( SUPERLU_MAX( c[j], smlnum ), bignum);
/* Compute COLCND = min(C(J)) / max(C(J)) */
*colcnd = SUPERLU_MAX( rcmin, smlnum ) / SUPERLU_MIN( rcmax, bignum );
}
return;
} /* dgsequ */
void
cpanel_bmod (
const int m, /* in - number of rows in the matrix */
const int w, /* in */
const int jcol, /* in */
const int nseg, /* in */
complex *dense, /* out, of size n by w */
complex *tempv, /* working array */
int *segrep, /* in */
int *repfnz, /* in, of size n by w */
GlobalLU_t *Glu, /* modified */
SuperLUStat_t *stat /* output */
)
{
#ifdef USE_VENDOR_BLAS
#ifdef _CRAY
_fcd ftcs1 = _cptofcd("L", strlen("L")),
ftcs2 = _cptofcd("N", strlen("N")),
ftcs3 = _cptofcd("U", strlen("U"));
#endif
int incx = 1, incy = 1;
complex alpha, beta;
#endif
register int k, ksub;
int fsupc, nsupc, nsupr, nrow;
int krep, krep_ind;
complex ukj, ukj1, ukj2;
int luptr, luptr1, luptr2;
int segsze;
int block_nrow; /* no of rows in a block row */
register int lptr; /* Points to the row subscripts of a supernode */
int kfnz, irow, no_zeros;
register int isub, isub1, i;
register int jj; /* Index through each column in the panel */
int *xsup, *supno;
int *lsub, *xlsub;
complex *lusup;
int *xlusup;
int *repfnz_col; /* repfnz[] for a column in the panel */
complex *dense_col; /* dense[] for a column in the panel */
complex *tempv1; /* Used in 1-D update */
complex *TriTmp, *MatvecTmp; /* used in 2-D update */
complex zero = {0.0, 0.0};
complex one = {1.0, 0.0};
complex comp_temp, comp_temp1;
register int ldaTmp;
register int r_ind, r_hi;
static int first = 1, maxsuper, rowblk, colblk;
flops_t *ops = stat->ops;
xsup = Glu->xsup;
supno = Glu->supno;
lsub = Glu->lsub;
xlsub = Glu->xlsub;
lusup = Glu->lusup;
xlusup = Glu->xlusup;
if ( first ) {
maxsuper = SUPERLU_MAX( sp_ienv(3), sp_ienv(7) );
rowblk = sp_ienv(4);
colblk = sp_ienv(5);
first = 0;
}
ldaTmp = maxsuper + rowblk;
/*
* For each nonz supernode segment of U[*,j] in topological order
*/
k = nseg - 1;
for (ksub = 0; ksub < nseg; ksub++) { /* for each updating supernode */
/* krep = representative of current k-th supernode
* fsupc = first supernodal column
* nsupc = no of columns in a supernode
* nsupr = no of rows in a supernode
*/
krep = segrep[k--];
fsupc = xsup[supno[krep]];
nsupc = krep - fsupc + 1;
nsupr = xlsub[fsupc+1] - xlsub[fsupc];
nrow = nsupr - nsupc;
lptr = xlsub[fsupc];
krep_ind = lptr + nsupc - 1;
repfnz_col = repfnz;
dense_col = dense;
if ( nsupc >= colblk && nrow > rowblk ) { /* 2-D block update */
TriTmp = tempv;
/* Sequence through each column in panel -- triangular solves */
for (jj = jcol; jj < jcol + w; jj++,
repfnz_col += m, dense_col += m, TriTmp += ldaTmp ) {
kfnz = repfnz_col[krep];
if ( kfnz == EMPTY ) continue; /* Skip any zero segment */
segsze = krep - kfnz + 1;
luptr = xlusup[fsupc];
ops[TRSV] += 4 * segsze * (segsze - 1);
ops[GEMV] += 8 * nrow * segsze;
/* Case 1: Update U-segment of size 1 -- col-col update */
if ( segsze == 1 ) {
ukj = dense_col[lsub[krep_ind]];
luptr += nsupr*(nsupc-1) + nsupc;
for (i = lptr + nsupc; i < xlsub[fsupc+1]; i++) {
irow = lsub[i];
cc_mult(&comp_temp, &ukj, &lusup[luptr]);
c_sub(&dense_col[irow], &dense_col[irow], &comp_temp);
++luptr;
}
} else if ( segsze <= 3 ) {
ukj = dense_col[lsub[krep_ind]];
ukj1 = dense_col[lsub[krep_ind - 1]];
luptr += nsupr*(nsupc-1) + nsupc-1;
luptr1 = luptr - nsupr;
if ( segsze == 2 ) {
cc_mult(&comp_temp, &ukj1, &lusup[luptr1]);
c_sub(&ukj, &ukj, &comp_temp);
dense_col[lsub[krep_ind]] = ukj;
for (i = lptr + nsupc; i < xlsub[fsupc+1]; ++i) {
irow = lsub[i];
luptr++; luptr1++;
cc_mult(&comp_temp, &ukj, &lusup[luptr]);
cc_mult(&comp_temp1, &ukj1, &lusup[luptr1]);
c_add(&comp_temp, &comp_temp, &comp_temp1);
c_sub(&dense_col[irow], &dense_col[irow], &comp_temp);
}
} else {
ukj2 = dense_col[lsub[krep_ind - 2]];
luptr2 = luptr1 - nsupr;
cc_mult(&comp_temp, &ukj2, &lusup[luptr2-1]);
c_sub(&ukj1, &ukj1, &comp_temp);
cc_mult(&comp_temp, &ukj1, &lusup[luptr1]);
cc_mult(&comp_temp1, &ukj2, &lusup[luptr2]);
c_add(&comp_temp, &comp_temp, &comp_temp1);
c_sub(&ukj, &ukj, &comp_temp);
dense_col[lsub[krep_ind]] = ukj;
dense_col[lsub[krep_ind-1]] = ukj1;
for (i = lptr + nsupc; i < xlsub[fsupc+1]; ++i) {
irow = lsub[i];
luptr++; luptr1++; luptr2++;
cc_mult(&comp_temp, &ukj, &lusup[luptr]);
cc_mult(&comp_temp1, &ukj1, &lusup[luptr1]);
c_add(&comp_temp, &comp_temp, &comp_temp1);
cc_mult(&comp_temp1, &ukj2, &lusup[luptr2]);
c_add(&comp_temp, &comp_temp, &comp_temp1);
c_sub(&dense_col[irow], &dense_col[irow], &comp_temp);
}
}
} else { /* segsze >= 4 */
/* Copy U[*,j] segment from dense[*] to TriTmp[*], which
holds the result of triangular solves. */
no_zeros = kfnz - fsupc;
isub = lptr + no_zeros;
for (i = 0; i < segsze; ++i) {
irow = lsub[isub];
TriTmp[i] = dense_col[irow]; /* Gather */
++isub;
}
/* start effective triangle */
luptr += nsupr * no_zeros + no_zeros;
#ifdef USE_VENDOR_BLAS
#ifdef _CRAY
CTRSV( ftcs1, ftcs2, ftcs3, &segsze, &lusup[luptr],
&nsupr, TriTmp, &incx );
#else
ctrsv_( "L", "N", "U", &segsze, &lusup[luptr],
&nsupr, TriTmp, &incx );
#endif
#else
clsolve ( nsupr, segsze, &lusup[luptr], TriTmp );
#endif
} /* else ... */
} /* for jj ... end tri-solves */
/* Block row updates; push all the way into dense[*] block */
for ( r_ind = 0; r_ind < nrow; r_ind += rowblk ) {
r_hi = SUPERLU_MIN(nrow, r_ind + rowblk);
block_nrow = SUPERLU_MIN(rowblk, r_hi - r_ind);
luptr = xlusup[fsupc] + nsupc + r_ind;
isub1 = lptr + nsupc + r_ind;
repfnz_col = repfnz;
TriTmp = tempv;
dense_col = dense;
/* Sequence through each column in panel -- matrix-vector */
for (jj = jcol; jj < jcol + w; jj++,
repfnz_col += m, dense_col += m, TriTmp += ldaTmp) {
kfnz = repfnz_col[krep];
if ( kfnz == EMPTY ) continue; /* Skip any zero segment */
segsze = krep - kfnz + 1;
if ( segsze <= 3 ) continue; /* skip unrolled cases */
/* Perform a block update, and scatter the result of
matrix-vector to dense[]. */
no_zeros = kfnz - fsupc;
luptr1 = luptr + nsupr * no_zeros;
MatvecTmp = &TriTmp[maxsuper];
#ifdef USE_VENDOR_BLAS
alpha = one;
beta = zero;
#ifdef _CRAY
CGEMV(ftcs2, &block_nrow, &segsze, &alpha, &lusup[luptr1],
&nsupr, TriTmp, &incx, &beta, MatvecTmp, &incy);
#else
cgemv_("N", &block_nrow, &segsze, &alpha, &lusup[luptr1],
&nsupr, TriTmp, &incx, &beta, MatvecTmp, &incy);
#endif
#else
cmatvec(nsupr, block_nrow, segsze, &lusup[luptr1],
TriTmp, MatvecTmp);
#endif
/* Scatter MatvecTmp[*] into SPA dense[*] temporarily
* such that MatvecTmp[*] can be re-used for the
* the next blok row update. dense[] will be copied into
* global store after the whole panel has been finished.
*/
isub = isub1;
for (i = 0; i < block_nrow; i++) {
irow = lsub[isub];
c_sub(&dense_col[irow], &dense_col[irow],
&MatvecTmp[i]);
MatvecTmp[i] = zero;
++isub;
}
} /* for jj ... */
} /* for each block row ... */
/* Scatter the triangular solves into SPA dense[*] */
repfnz_col = repfnz;
TriTmp = tempv;
dense_col = dense;
for (jj = jcol; jj < jcol + w; jj++,
repfnz_col += m, dense_col += m, TriTmp += ldaTmp) {
kfnz = repfnz_col[krep];
if ( kfnz == EMPTY ) continue; /* Skip any zero segment */
segsze = krep - kfnz + 1;
if ( segsze <= 3 ) continue; /* skip unrolled cases */
no_zeros = kfnz - fsupc;
isub = lptr + no_zeros;
for (i = 0; i < segsze; i++) {
irow = lsub[isub];
dense_col[irow] = TriTmp[i];
TriTmp[i] = zero;
++isub;
}
} /* for jj ... */
} else { /* 1-D block modification */
/* Sequence through each column in the panel */
for (jj = jcol; jj < jcol + w; jj++,
repfnz_col += m, dense_col += m) {
kfnz = repfnz_col[krep];
if ( kfnz == EMPTY ) continue; /* Skip any zero segment */
segsze = krep - kfnz + 1;
luptr = xlusup[fsupc];
ops[TRSV] += 4 * segsze * (segsze - 1);
ops[GEMV] += 8 * nrow * segsze;
/* Case 1: Update U-segment of size 1 -- col-col update */
if ( segsze == 1 ) {
ukj = dense_col[lsub[krep_ind]];
luptr += nsupr*(nsupc-1) + nsupc;
for (i = lptr + nsupc; i < xlsub[fsupc+1]; i++) {
irow = lsub[i];
cc_mult(&comp_temp, &ukj, &lusup[luptr]);
c_sub(&dense_col[irow], &dense_col[irow], &comp_temp);
++luptr;
}
} else if ( segsze <= 3 ) {
ukj = dense_col[lsub[krep_ind]];
luptr += nsupr*(nsupc-1) + nsupc-1;
ukj1 = dense_col[lsub[krep_ind - 1]];
luptr1 = luptr - nsupr;
if ( segsze == 2 ) {
cc_mult(&comp_temp, &ukj1, &lusup[luptr1]);
c_sub(&ukj, &ukj, &comp_temp);
dense_col[lsub[krep_ind]] = ukj;
for (i = lptr + nsupc; i < xlsub[fsupc+1]; ++i) {
irow = lsub[i];
++luptr; ++luptr1;
cc_mult(&comp_temp, &ukj, &lusup[luptr]);
cc_mult(&comp_temp1, &ukj1, &lusup[luptr1]);
c_add(&comp_temp, &comp_temp, &comp_temp1);
c_sub(&dense_col[irow], &dense_col[irow], &comp_temp);
}
} else {
ukj2 = dense_col[lsub[krep_ind - 2]];
luptr2 = luptr1 - nsupr;
cc_mult(&comp_temp, &ukj2, &lusup[luptr2-1]);
c_sub(&ukj1, &ukj1, &comp_temp);
cc_mult(&comp_temp, &ukj1, &lusup[luptr1]);
cc_mult(&comp_temp1, &ukj2, &lusup[luptr2]);
c_add(&comp_temp, &comp_temp, &comp_temp1);
c_sub(&ukj, &ukj, &comp_temp);
dense_col[lsub[krep_ind]] = ukj;
dense_col[lsub[krep_ind-1]] = ukj1;
for (i = lptr + nsupc; i < xlsub[fsupc+1]; ++i) {
irow = lsub[i];
++luptr; ++luptr1; ++luptr2;
cc_mult(&comp_temp, &ukj, &lusup[luptr]);
cc_mult(&comp_temp1, &ukj1, &lusup[luptr1]);
c_add(&comp_temp, &comp_temp, &comp_temp1);
cc_mult(&comp_temp1, &ukj2, &lusup[luptr2]);
c_add(&comp_temp, &comp_temp, &comp_temp1);
c_sub(&dense_col[irow], &dense_col[irow], &comp_temp);
}
}
} else { /* segsze >= 4 */
/*
* Perform a triangular solve and block update,
* then scatter the result of sup-col update to dense[].
*/
no_zeros = kfnz - fsupc;
/* Copy U[*,j] segment from dense[*] to tempv[*]:
* The result of triangular solve is in tempv[*];
* The result of matrix vector update is in dense_col[*]
*/
isub = lptr + no_zeros;
for (i = 0; i < segsze; ++i) {
irow = lsub[isub];
tempv[i] = dense_col[irow]; /* Gather */
++isub;
}
/* start effective triangle */
luptr += nsupr * no_zeros + no_zeros;
#ifdef USE_VENDOR_BLAS
#ifdef _CRAY
CTRSV( ftcs1, ftcs2, ftcs3, &segsze, &lusup[luptr],
&nsupr, tempv, &incx );
#else
ctrsv_( "L", "N", "U", &segsze, &lusup[luptr],
&nsupr, tempv, &incx );
#endif
luptr += segsze; /* Dense matrix-vector */
tempv1 = &tempv[segsze];
alpha = one;
beta = zero;
#ifdef _CRAY
CGEMV( ftcs2, &nrow, &segsze, &alpha, &lusup[luptr],
&nsupr, tempv, &incx, &beta, tempv1, &incy );
#else
cgemv_( "N", &nrow, &segsze, &alpha, &lusup[luptr],
&nsupr, tempv, &incx, &beta, tempv1, &incy );
#endif
#else
clsolve ( nsupr, segsze, &lusup[luptr], tempv );
luptr += segsze; /* Dense matrix-vector */
tempv1 = &tempv[segsze];
cmatvec (nsupr, nrow, segsze, &lusup[luptr], tempv, tempv1);
#endif
/* Scatter tempv[*] into SPA dense[*] temporarily, such
* that tempv[*] can be used for the triangular solve of
* the next column of the panel. They will be copied into
* ucol[*] after the whole panel has been finished.
*/
isub = lptr + no_zeros;
for (i = 0; i < segsze; i++) {
irow = lsub[isub];
dense_col[irow] = tempv[i];
tempv[i] = zero;
isub++;
}
/* Scatter the update from tempv1[*] into SPA dense[*] */
/* Start dense rectangular L */
for (i = 0; i < nrow; i++) {
irow = lsub[isub];
c_sub(&dense_col[irow], &dense_col[irow], &tempv1[i]);
tempv1[i] = zero;
++isub;
}
} /* else segsze>=4 ... */
} /* for each column in the panel... */
} /* else 1-D update ... */
} /* for each updating supernode ... */
}
void
psgstrf_panel_bmod(
const int pnum, /* process number */
const int m, /* number of rows in the matrix */
const int w, /* current panel width */
const int jcol, /* leading column of the current panel */
const int bcol, /* first column of the farthest busy snode*/
int *inv_perm_r,/* in; inverse of the row pivoting */
int *etree, /* in */
int *nseg, /* modified */
int *segrep, /* modified */
int *repfnz, /* modified, size n-by-w */
int *panel_lsub,/* modified */
int *w_lsub_end,/* modified */
int *spa_marker,/* modified; size n-by-w */
float *dense, /* modified, size n-by-w */
float *tempv, /* working array - zeros on input/output */
pxgstrf_shared_t *pxgstrf_shared /* modified */
)
{
/*
* -- SuperLU MT routine (version 2.0) --
* Lawrence Berkeley National Lab, Univ. of California Berkeley,
* and Xerox Palo Alto Research Center.
* September 10, 2007
*
* Purpose
* =======
*
* Performs numeric block updates (sup-panel) in topological order.
* It features combined 1D and 2D blocking of the source updating s-node.
* It consists of two steps:
* (1) accumulates updates from "done" s-nodes.
* (2) accumulates updates from "busy" s-nodes.
*
* Before entering this routine, the nonzeros of the original A in
* this panel were already copied into the SPA dense[n,w].
*
* Updated/Output arguments
* ========================
* L[*,j:j+w-1] and U[*,j:j+w-1] are returned collectively in the
* m-by-w vector dense[*,w]. The locations of nonzeros in L[*,j:j+w-1]
* are given by lsub[*] and U[*,j:j+w-1] by (nseg,segrep,repfnz).
*
*/
GlobalLU_t *Glu = pxgstrf_shared->Glu; /* modified */
Gstat_t *Gstat = pxgstrf_shared->Gstat; /* modified */
register int j, k, ksub;
register int fsupc, nsupc, nsupr, nrow;
register int kcol, krep, ksupno, dadsupno;
register int jj; /* index through each column in the panel */
int *xsup, *xsup_end, *supno;
int *lsub, *xlsub, *xlsub_end;
int *repfnz_col; /* repfnz[] for a column in the panel */
float *dense_col; /* dense[] for a column in the panel */
int *col_marker; /* each column of the spa_marker[*,w] */
int *col_lsub; /* each column of the panel_lsub[*,w] */
static int first = 1, rowblk, colblk;
#ifdef PROFILE
double t1, t2; /* temporary time */
#endif
#ifdef PREDICT_OPT
register float pmod, max_child_eft = 0, sum_pmod = 0, min_desc_eft = 0;
register float pmod_eft;
register int kid, ndesc = 0;
#endif
#if ( DEBUGlevel>=2 )
int dbg_addr = 0*m;
#endif
if ( first ) {
rowblk = sp_ienv(4);
colblk = sp_ienv(5);
first = 0;
}
xsup = Glu->xsup;
xsup_end = Glu->xsup_end;
supno = Glu->supno;
lsub = Glu->lsub;
xlsub = Glu->xlsub;
xlsub_end = Glu->xlsub_end;
#if ( DEBUGlevel>=2 )
/*if (jcol >= LOCOL && jcol <= HICOL)
check_panel_dfs_list(pnum, "begin", jcol, *nseg, segrep);*/
if (jcol == BADPAN)
printf("(%d) Enter psgstrf_panel_bmod() jcol %d,BADCOL %d,dense_col[%d] %.10f\n",
pnum, jcol, BADCOL, BADROW, dense[dbg_addr+BADROW]);
#endif
/* --------------------------------------------------------------------
For each non-busy supernode segment of U[*,jcol] in topological order,
perform sup-panel update.
-------------------------------------------------------------------- */
k = *nseg - 1;
for (ksub = 0; ksub < *nseg; ++ksub) {
/*
* krep = representative of current k-th supernode
* fsupc = first supernodal column
* nsupc = no of columns in a supernode
* nsupr = no of rows in a supernode
*/
krep = segrep[k--];
fsupc = xsup[supno[krep]];
nsupc = krep - fsupc + 1;
nsupr = xlsub_end[fsupc] - xlsub[fsupc];
nrow = nsupr - nsupc;
#ifdef PREDICT_OPT
pmod = Gstat->procstat[pnum].fcops;
#endif
if ( nsupc >= colblk && nrow >= rowblk ) {
/* 2-D block update */
#ifdef GEMV2
psgstrf_bmod2D_mv2(pnum, m, w, jcol, fsupc, krep, nsupc, nsupr,
nrow, repfnz, panel_lsub, w_lsub_end,
spa_marker, dense, tempv, Glu, Gstat);
#else
psgstrf_bmod2D(pnum, m, w, jcol, fsupc, krep, nsupc, nsupr, nrow,
repfnz, panel_lsub, w_lsub_end, spa_marker,
dense, tempv, Glu, Gstat);
#endif
} else {
/* 1-D block update */
#ifdef GEMV2
psgstrf_bmod1D_mv2(pnum, m, w, jcol, fsupc, krep, nsupc, nsupr,
nrow, repfnz, panel_lsub, w_lsub_end,
spa_marker, dense, tempv, Glu, Gstat);
#else
psgstrf_bmod1D(pnum, m, w, jcol, fsupc, krep, nsupc, nsupr, nrow,
repfnz, panel_lsub, w_lsub_end, spa_marker,
dense, tempv, Glu, Gstat);
#endif
}
#ifdef PREDICT_OPT
pmod = Gstat->procstat[pnum].fcops - pmod;
kid = (Glu->pan_status[krep].size > 0) ?
krep : (krep + Glu->pan_status[krep].size);
desc_eft[ndesc].eft = cp_panel[kid].est + cp_panel[kid].pdiv;
desc_eft[ndesc++].pmod = pmod;
#endif
#if ( DEBUGlevel>=2 )
if (jcol == BADPAN)
printf("(%d) non-busy update: krep %d, repfnz %d, dense_col[%d] %.10e\n",
pnum, krep, repfnz[dbg_addr+krep], BADROW, dense[dbg_addr+BADROW]);
#endif
} /* for each updating supernode ... */
#if ( DEBUGlevel>=2 )
if (jcol == BADPAN)
printf("(%d) After non-busy update: dense_col[%d] %.10e\n",
pnum, BADROW, dense[dbg_addr+BADROW]);
#endif
/* ---------------------------------------------------------------------
* Now wait for the "busy" s-nodes to become "done" -- this amounts to
* climbing up the e-tree along the path starting from "bcol".
* Several points are worth noting:
*
* (1) There are two possible relations between supernodes and panels
* along the path of the e-tree:
* o |s-node| < |panel|
* want to climb up the e-tree one column at a time in order
* to achieve more concurrency
* o |s-node| > |panel|
* want to climb up the e-tree one panel at a time; this
* processor is stalled anyway while waiting for the panel.
*
* (2) Need to accommodate new fills, append them in panel_lsub[*,w].
* o use an n-by-w marker array, as part of the SPA (not scalable!)
*
* (3) Symbolically, need to find out repfnz[S, w], for each (busy)
* supernode S.
* o use dense[inv_perm_r[kcol]], filter all zeros
* o detect the first nonzero in each segment
* (at this moment, the boundary of the busy supernode/segment
* S has already been identified)
*
* --------------------------------------------------------------------- */
kcol = bcol;
while ( kcol < jcol ) {
/* Pointers to each column of the w-wide arrays. */
repfnz_col = repfnz;
dense_col = dense;
col_marker = spa_marker;
col_lsub = panel_lsub;
/* Wait for the supernode, and collect wait-time statistics. */
if ( pxgstrf_shared->spin_locks[kcol] ) {
#ifdef PROFILE
TIC(t1);
#endif
await( &pxgstrf_shared->spin_locks[kcol] );
#ifdef PROFILE
TOC(t2, t1);
Gstat->panstat[jcol].pipewaits++;
Gstat->panstat[jcol].spintime += t2;
Gstat->procstat[pnum].spintime += t2;
#ifdef DOPRINT
PRINT_SPIN_TIME(1);
#endif
#endif
}
/* Find leading column "fsupc" in the supernode that
contains column "kcol" */
ksupno = supno[kcol];
fsupc = kcol;
#if ( DEBUGlevel>=2 )
/*if (jcol >= LOCOL && jcol <= HICOL) */
if ( jcol==BADCOL )
printf("(%d) psgstrf_panel_bmod[1] kcol %d, ksupno %d, fsupc %d\n",
pnum, kcol, ksupno, fsupc);
#endif
/* Wait for the whole supernode to become "done" --
climb up e-tree one column at a time */
do {
krep = SUPER_REP( ksupno );
kcol = etree[kcol];
if ( kcol >= jcol ) break;
if ( pxgstrf_shared->spin_locks[kcol] ) {
#ifdef PROFILE
TIC(t1);
#endif
await ( &pxgstrf_shared->spin_locks[kcol] );
#ifdef PROFILE
TOC(t2, t1);
Gstat->panstat[jcol].pipewaits++;
Gstat->panstat[jcol].spintime += t2;
Gstat->procstat[pnum].spintime += t2;
#ifdef DOPRINT
PRINT_SPIN_TIME(2);
#endif
#endif
}
dadsupno = supno[kcol];
#if ( DEBUGlevel>=2 )
/*if (jcol >= LOCOL && jcol <= HICOL)*/
if ( jcol==BADCOL )
printf("(%d) psgstrf_panel_bmod[2] krep %d, dad=kcol %d, dadsupno %d\n",
pnum, krep, kcol, dadsupno);
#endif
} while ( dadsupno == ksupno );
/* Append the new segment into segrep[*]. After column_bmod(),
copy_to_ucol() will use them. */
segrep[*nseg] = krep;
++(*nseg);
/* Determine repfnz[krep, w] for each column in the panel */
for (jj = jcol; jj < jcol + w; ++jj, dense_col += m,
repfnz_col += m, col_marker += m, col_lsub += m) {
/*
* Note: relaxed supernode may not form a path on the e-tree,
* but its column numbers are contiguous.
*/
#ifdef SCATTER_FOUND
for (kcol = fsupc; kcol <= krep; ++kcol) {
if ( col_marker[inv_perm_r[kcol]] == jj ) {
repfnz_col[krep] = kcol;
/* Append new fills in panel_lsub[*,jj]. */
j = w_lsub_end[jj - jcol];
/*#pragma ivdep*/
for (k = xlsub[krep]; k < xlsub_end[krep]; ++k) {
ksub = lsub[k];
if ( col_marker[ksub] != jj ) {
col_marker[ksub] = jj;
col_lsub[j++] = ksub;
}
}
w_lsub_end[jj - jcol] = j;
break; /* found the leading nonzero in the segment */
}
}
#else
for (kcol = fsupc; kcol <= krep; ++kcol) {
if ( dense_col[inv_perm_r[kcol]] != 0.0 ) {
repfnz_col[krep] = kcol;
break; /* Found the leading nonzero in the U-segment */
}
}
/* In this case, we always treat the L-subscripts of the
busy s-node [kcol : krep] as the new fills, even if the
corresponding U-segment may be all zero. */
/* Append new fills in panel_lsub[*,jj]. */
j = w_lsub_end[jj - jcol];
/*#pragma ivdep*/
for (k = xlsub[krep]; k < xlsub_end[krep]; ++k) {
ksub = lsub[k];
if ( col_marker[ksub] != jj ) {
col_marker[ksub] = jj;
col_lsub[j++] = ksub;
}
}
w_lsub_end[jj - jcol] = j;
#endif
#if ( DEBUGlevel>=2 )
if (jj == BADCOL) {
printf("(%d) psgstrf_panel_bmod[fills]: jj %d, repfnz_col[%d] %d, inv_pr[%d] %d\n",
pnum, jj, krep, repfnz_col[krep], fsupc, inv_perm_r[fsupc]);
printf("(%d) psgstrf_panel_bmod[fills] xlsub %d, xlsub_end %d, #lsub[%d] %d\n",
pnum,xlsub[krep],xlsub_end[krep],krep, xlsub_end[krep]-xlsub[krep]);
}
#endif
} /* for jj ... */
#ifdef PREDICT_OPT
pmod = Gstat->procstat[pnum].fcops;
#endif
/* Perform sup-panel updates - use combined 1D + 2D updates. */
nsupc = krep - fsupc + 1;
nsupr = xlsub_end[fsupc] - xlsub[fsupc];
nrow = nsupr - nsupc;
if ( nsupc >= colblk && nrow >= rowblk ) {
/* 2-D block update */
#ifdef GEMV2
psgstrf_bmod2D_mv2(pnum, m, w, jcol, fsupc, krep, nsupc, nsupr,
nrow, repfnz, panel_lsub, w_lsub_end,
spa_marker, dense, tempv, Glu, Gstat);
#else
psgstrf_bmod2D(pnum, m, w, jcol, fsupc, krep, nsupc, nsupr, nrow,
repfnz, panel_lsub, w_lsub_end, spa_marker,
dense, tempv, Glu, Gstat);
#endif
} else {
/* 1-D block update */
#ifdef GEMV2
psgstrf_bmod1D_mv2(pnum, m, w, jcol, fsupc, krep, nsupc, nsupr,
nrow, repfnz, panel_lsub, w_lsub_end,
spa_marker, dense, tempv, Glu, Gstat);
#else
psgstrf_bmod1D(pnum, m, w, jcol, fsupc, krep, nsupc, nsupr, nrow,
repfnz, panel_lsub, w_lsub_end, spa_marker,
dense, tempv, Glu, Gstat);
#endif
}
#ifdef PREDICT_OPT
pmod = Gstat->procstat[pnum].fcops - pmod;
kid = (pxgstrf_shared->pan_status[krep].size > 0) ?
krep : (krep + pxgstrf_shared->pan_status[krep].size);
desc_eft[ndesc].eft = cp_panel[kid].est + cp_panel[kid].pdiv;
desc_eft[ndesc++].pmod = pmod;
#endif
#if ( DEBUGlevel>=2 )
if (jcol == BADPAN)
printf("(%d) After busy update: dense_col[%d] %.10f\n",
pnum, BADROW, dense[dbg_addr+BADROW]);
#endif
/* Go to the parent of "krep" */
kcol = etree[krep];
} /* while kcol < jcol ... */
#if ( DEBUGlevel>=2 )
/*if (jcol >= LOCOL && jcol <= HICOL)*/
if ( jcol==BADCOL )
check_panel_dfs_list(pnum, "after-busy", jcol, *nseg, segrep);
#endif
#ifdef PREDICT_OPT
qsort(desc_eft, ndesc, sizeof(desc_eft_t), (int(*)())numcomp);
pmod_eft = 0;
for (j = 0; j < ndesc; ++j) {
pmod_eft = SUPERLU_MAX( pmod_eft, desc_eft[j].eft ) + desc_eft[j].pmod;
}
if ( ndesc == 0 ) {
/* No modifications from descendants */
pmod_eft = 0;
for (j = cp_firstkid[jcol]; j != EMPTY; j = cp_nextkid[j]) {
kid = (pxgstrf_shared->pan_status[j].size > 0) ?
j : (j + pxgstrf_shared->pan_status[j].size);
pmod_eft = SUPERLU_MAX( pmod_eft,
cp_panel[kid].est + cp_panel[kid].pdiv );
}
}
cp_panel[jcol].est = pmod_eft;
#endif
}
int dgst01(int m, int n, SuperMatrix *A, SuperMatrix *L,
SuperMatrix *U, int *perm_c, int *perm_r, double *resid)
{
/*
Purpose
=======
DGST01 reconstructs a matrix A from its L*U factorization and
computes the residual
norm(L*U - A) / ( N * norm(A) * EPS ),
where EPS is the machine epsilon.
Arguments
==========
M (input) INT
The number of rows of the matrix A. M >= 0.
N (input) INT
The number of columns of the matrix A. N >= 0.
A (input) SuperMatrix *, dimension (A->nrow, A->ncol)
The original M x N matrix A.
L (input) SuperMatrix *, dimension (L->nrow, L->ncol)
The factor matrix L.
U (input) SuperMatrix *, dimension (U->nrow, U->ncol)
The factor matrix U.
perm_c (input) INT array, dimension (N)
The column permutation from DGSTRF.
perm_r (input) INT array, dimension (M)
The pivot indices from DGSTRF.
RESID (output) DOUBLE*
norm(L*U - A) / ( N * norm(A) * EPS )
=====================================================================
*/
/* Local variables */
double zero = 0.0;
int i, j, k, arow, lptr,isub, urow, superno, fsupc, u_part;
double utemp, comp_temp;
double anorm, tnorm, cnorm;
double eps;
double *work;
SCformat *Lstore;
NCformat *Astore, *Ustore;
double *Aval, *Lval, *Uval;
int *colbeg, *colend;
/* Function prototypes */
extern double dlangs(char *, SuperMatrix *);
/* Quick exit if M = 0 or N = 0. */
if (m <= 0 || n <= 0) {
*resid = 0.f;
return 0;
}
work = (double *)doubleCalloc(m);
Astore = A->Store;
Aval = Astore->nzval;
Lstore = L->Store;
Lval = Lstore->nzval;
Ustore = U->Store;
Uval = Ustore->nzval;
colbeg = intMalloc(n);
colend = intMalloc(n);
for (i = 0; i < n; i++) {
colbeg[perm_c[i]] = Astore->colptr[i];
colend[perm_c[i]] = Astore->colptr[i+1];
}
/* Determine EPS and the norm of A. */
eps = dmach("Epsilon");
anorm = dlangs("1", A);
cnorm = 0.;
/* Compute the product L*U, one column at a time */
for (k = 0; k < n; ++k) {
/* The U part outside the rectangular supernode */
for (i = U_NZ_START(k); i < U_NZ_START(k+1); ++i) {
urow = U_SUB(i);
utemp = Uval[i];
superno = Lstore->col_to_sup[urow];
fsupc = L_FST_SUPC(superno);
u_part = urow - fsupc + 1;
lptr = L_SUB_START(fsupc) + u_part;
work[L_SUB(lptr-1)] -= utemp; /* L_ii = 1 */
for (j = L_NZ_START(urow) + u_part; j < L_NZ_START(urow+1); ++j) {
isub = L_SUB(lptr);
work[isub] -= Lval[j] * utemp;
++lptr;
}
}
/* The U part inside the rectangular supernode */
superno = Lstore->col_to_sup[k];
fsupc = L_FST_SUPC(superno);
urow = L_NZ_START(k);
for (i = fsupc; i <= k; ++i) {
utemp = Lval[urow++];
u_part = i - fsupc + 1;
lptr = L_SUB_START(fsupc) + u_part;
work[L_SUB(lptr-1)] -= utemp; /* L_ii = 1 */
for (j = L_NZ_START(i)+u_part; j < L_NZ_START(i+1); ++j) {
isub = L_SUB(lptr);
work[isub] -= Lval[j] * utemp;
++lptr;
}
}
/* Now compute A[k] - (L*U)[k] (Both matrices may be permuted.) */
for (i = colbeg[k]; i < colend[k]; ++i) {
arow = Astore->rowind[i];
work[perm_r[arow]] += Aval[i];
}
/* Now compute the 1-norm of the column vector work */
tnorm = 0.;
for (i = 0; i < m; ++i) {
tnorm += fabs(work[i]);
work[i] = zero;
}
cnorm = SUPERLU_MAX(tnorm, cnorm);
}
*resid = cnorm;
if (anorm <= 0.f) {
if (*resid != 0.f) {
*resid = 1.f / eps;
}
} else {
*resid = *resid / (float) n / anorm / eps;
}
SUPERLU_FREE(work);
SUPERLU_FREE(colbeg);
SUPERLU_FREE(colend);
return 0;
/* End of DGST01 */
} /* dgst01_ */
/*! \brief
*
* <pre>
* Purpose
* =======
*
* PDGSRFS improves the computed solution to a system of linear
* equations and provides error bounds and backward error estimates
* for the solution.
*
* Arguments
* =========
*
* n (input) int (global)
* The order of the system of linear equations.
*
* A (input) SuperMatrix*
* The original matrix A, or the scaled A if equilibration was done.
* A is also permuted into diag(R)*A*diag(C)*Pc'. The type of A can be:
* Stype = SLU_NR_loc; Dtype = SLU_D; Mtype = SLU_GE.
*
* anorm (input) double
* The norm of the original matrix A, or the scaled A if
* equilibration was done.
*
* LUstruct (input) LUstruct_t*
* The distributed data structures storing L and U factors.
* The L and U factors are obtained from pdgstrf for
* the possibly scaled and permuted matrix A.
* See superlu_ddefs.h for the definition of 'LUstruct_t'.
*
* ScalePermstruct (input) ScalePermstruct_t* (global)
* The data structure to store the scaling and permutation vectors
* describing the transformations performed to the matrix A.
*
* grid (input) gridinfo_t*
* The 2D process mesh. It contains the MPI communicator, the number
* of process rows (NPROW), the number of process columns (NPCOL),
* and my process rank. It is an input argument to all the
* parallel routines.
* Grid can be initialized by subroutine SUPERLU_GRIDINIT.
* See superlu_defs.h for the definition of 'gridinfo_t'.
*
* B (input) double* (local)
* The m_loc-by-NRHS right-hand side matrix of the possibly
* equilibrated system. That is, B may be overwritten by diag(R)*B.
*
* ldb (input) int (local)
* Leading dimension of matrix B.
*
* X (input/output) double* (local)
* On entry, the solution matrix Y, as computed by PDGSTRS, of the
* transformed system A1*Y = Pc*Pr*B. where
* A1 = Pc*Pr*diag(R)*A*diag(C)*Pc' and Y = Pc*diag(C)^(-1)*X.
* On exit, the improved solution matrix Y.
*
* In order to obtain the solution X to the original system,
* Y should be permutated by Pc^T, and premultiplied by diag(C)
* if DiagScale = COL or BOTH.
* This must be done after this routine is called.
*
* ldx (input) int (local)
* Leading dimension of matrix X.
*
* nrhs (input) int
* Number of right-hand sides.
*
* SOLVEstruct (output) SOLVEstruct_t* (global)
* Contains the information for the communication during the
* solution phase.
*
* berr (output) double*, dimension (nrhs)
* 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 about the refinement steps.
* 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
pdgsrfs(int_t n, SuperMatrix *A, double anorm, LUstruct_t *LUstruct,
ScalePermstruct_t *ScalePermstruct, gridinfo_t *grid,
double *B, int_t ldb, double *X, int_t ldx, int nrhs,
SOLVEstruct_t *SOLVEstruct,
double *berr, SuperLUStat_t *stat, int *info)
{
#define ITMAX 20
Glu_persist_t *Glu_persist = LUstruct->Glu_persist;
LocalLU_t *Llu = LUstruct->Llu;
double *ax, *R, *dx, *temp, *work, *B_col, *X_col;
int_t count, i, j, lwork, nz;
int iam;
double eps, lstres;
double s, safmin, safe1, safe2;
/* Data structures used by matrix-vector multiply routine. */
pdgsmv_comm_t *gsmv_comm = SOLVEstruct->gsmv_comm;
NRformat_loc *Astore;
int_t m_loc, fst_row;
/* Initialization. */
Astore = (NRformat_loc *) A->Store;
m_loc = Astore->m_loc;
fst_row = Astore->fst_row;
iam = grid->iam;
/* Test the input parameters. */
*info = 0;
if ( n < 0 ) *info = -1;
else if ( A->nrow != A->ncol || A->nrow < 0 || A->Stype != SLU_NR_loc
|| A->Dtype != SLU_D || A->Mtype != SLU_GE )
*info = -2;
else if ( ldb < SUPERLU_MAX(0, m_loc) ) *info = -10;
else if ( ldx < SUPERLU_MAX(0, m_loc) ) *info = -12;
else if ( nrhs < 0 ) *info = -13;
if (*info != 0) {
i = -(*info);
pxerbla("PDGSRFS", grid, i);
return;
}
/* Quick return if possible. */
if ( n == 0 || nrhs == 0 ) {
return;
}
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(iam, "Enter pdgsrfs()");
#endif
lwork = 2 * m_loc; /* For ax/R/dx and temp */
if ( !(work = doubleMalloc_dist(lwork)) )
ABORT("Malloc fails for work[]");
ax = R = dx = work;
temp = ax + m_loc;
/* NZ = maximum number of nonzero elements in each row of A, plus 1 */
nz = A->ncol + 1;
eps = dmach("Epsilon");
safmin = dmach("Safe minimum");
/* Set SAFE1 essentially to be the underflow threshold times the
number of additions in each row. */
safe1 = nz * safmin;
safe2 = safe1 / eps;
#if ( DEBUGlevel>=1 )
if ( !iam ) printf(".. eps = %e\tanorm = %e\tsafe1 = %e\tsafe2 = %e\n",
eps, anorm, safe1, safe2);
#endif
/* Do for each right-hand side ... */
for (j = 0; j < nrhs; ++j) {
count = 0;
lstres = 3.;
B_col = &B[j*ldb];
X_col = &X[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. */
/* Matrix-vector multiply. */
pdgsmv(0, A, grid, gsmv_comm, X_col, ax);
/* Compute residual, stored in R[]. */
for (i = 0; i < m_loc; ++i) R[i] = B_col[i] - ax[i];
/* Compute abs(op(A))*abs(X) + abs(B), stored in temp[]. */
pdgsmv(1, A, grid, gsmv_comm, X_col, temp);
for (i = 0; i < m_loc; ++i) temp[i] += fabs(B_col[i]);
s = 0.0;
for (i = 0; i < m_loc; ++i) {
if ( temp[i] > safe2 ) {
s = SUPERLU_MAX(s, fabs(R[i]) / temp[i]);
} else if ( temp[i] != 0.0 ) {
/* Adding SAFE1 to the numerator guards against
spuriously zero residuals (underflow). */
s = SUPERLU_MAX(s, (safe1 + fabs(R[i])) /temp[i]);
}
/* If temp[i] is exactly 0.0 (computed by PxGSMV), then
we know the true residual also must be exactly 0.0. */
}
MPI_Allreduce( &s, &berr[j], 1, MPI_DOUBLE, MPI_MAX, grid->comm );
#if ( PRNTlevel>= 1 )
if ( !iam )
printf("(%2d) .. Step " IFMT ": berr[j] = %e\n", iam, count, berr[j]);
#endif
if ( berr[j] > eps && berr[j] * 2 <= lstres && count < ITMAX ) {
/* Compute new dx. */
pdgstrs(n, LUstruct, ScalePermstruct, grid,
dx, m_loc, fst_row, m_loc, 1,
SOLVEstruct, stat, info);
/* Update solution. */
for (i = 0; i < m_loc; ++i) X_col[i] += dx[i];
lstres = berr[j];
++count;
} else {
break;
}
} /* end while */
stat->RefineSteps = count;
} /* for j ... */
/* Deallocate storage. */
SUPERLU_FREE(work);
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(iam, "Exit pdgsrfs()");
#endif
} /* PDGSRFS */
void
cgsrfs(trans_t trans, SuperMatrix *A, SuperMatrix *L, SuperMatrix *U,
int *perm_r, int *perm_c, equed_t equed, float *R, float *C,
SuperMatrix *B, SuperMatrix *X, float *ferr, float *berr,
Gstat_t *Gstat, int *info)
{
/*
* -- SuperLU MT routine (version 2.0) --
* Lawrence Berkeley National Lab, Univ. of California Berkeley,
* and Xerox Palo Alto Research Center.
* September 10, 2007
*
*
* Purpose
* =======
*
* cgsrfs improves the computed solution to a system of linear
* equations and provides error bounds and backward error estimates for
* the solution.
*
* 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**T * X = B (Transpose)
* = CONJ: A**H * X = B (Conjugate transpose = 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 = NC, Dtype = _D, Mtype = 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 = SCP, Dtype = _D, Mtype = TRLU.
*
* U (input) SuperMatrix*
* The factor U from the factorization Pr*A*Pc=L*U as computed by
* dgstrf(). Use column-wise storage scheme,
* i.e., U has types: Stype = NCP, Dtype = _D, Mtype = TRU.
*
* 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.
*
* 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.
*
* equed (input) equed_t
* Specifies the form of equilibration that was done.
* = NOEQUIL: No equilibration.
* = ROW: Row equilibration, i.e., A was premultiplied by diag(R).
* = COL: Column equilibration, i.e., A was postmultiplied by
* diag(C).
* = BOTH: Both row and column equilibration, i.e., A was replaced
* by diag(R)*A*diag(C).
*
* R (input) double*, dimension (A->nrow)
* The row scale factors for A.
* If equed = ROW or BOTH, A is premultiplied by diag(R).
* If equed = NOEQUIL or COL, R is not accessed.
*
* C (input) double*, dimension (A->ncol)
* The column scale factors for A.
* If equed = COL or BOTH, A is postmultiplied by diag(C).
* If equed = NOEQUIL or ROW, C is not accessed.
*
* B (input) SuperMatrix*
* B has types: Stype = DN, Dtype = _D, Mtype = GE.
* The right hand side matrix B.
*
* X (input/output) SuperMatrix*
* X has types: Stype = DN, Dtype = _D, Mtype = GE.
* On entry, the solution matrix X, as computed by dgstrs().
* On exit, the improved solution matrix X.
*
* FERR (output) double*, 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) double*, 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).
*
* 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;
complex ndone = {-1., 0.};
complex done = {1., 0.};
/* Local variables */
NCformat *Astore;
complex *Aval;
SuperMatrix Bjcol;
DNformat *Bstore, *Xstore, *Bjcol_store;
complex *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;
complex *work;
float *rwork;
int *iwork;
extern double slamch_(char *);
extern int clacon_(int *, complex *, complex *, float *, int *);
#ifdef _CRAY
extern int CCOPY(int *, complex *, int *, complex *, int *);
extern int CSAXPY(int *, complex *, complex *, int *, complex *, int *);
#else
extern int ccopy_(int *, complex *, int *, complex *, int *);
extern int caxpy_(int *, complex *, complex *, int *, complex *, 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_C || A->Mtype != SLU_GE )
*info = -2;
else if ( L->nrow != L->ncol || L->nrow < 0 ||
L->Stype != SLU_SCP || L->Dtype != SLU_C || L->Mtype != SLU_TRLU )
*info = -3;
else if ( U->nrow != U->ncol || U->nrow < 0 ||
U->Stype != SLU_NCP || U->Dtype != SLU_C || U->Mtype != SLU_TRU )
*info = -4;
else if ( ldb < SUPERLU_MAX(0, A->nrow) ||
B->Stype != SLU_DN || B->Dtype != SLU_C || B->Mtype != SLU_GE )
*info = -10;
else if ( ldx < SUPERLU_MAX(0, A->nrow) ||
X->Stype != SLU_DN || X->Dtype != SLU_C || X->Mtype != SLU_GE )
*info = -11;
if (*info != 0) {
i = -(*info);
xerbla_("cgsrfs", &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 = (equed == ROW) || (equed == BOTH);
colequ = (equed == COL) || (equed == BOTH);
/* Allocate working space */
work = complexMalloc(2*A->nrow);
rwork = (float *) SUPERLU_MALLOC( (size_t) A->nrow * sizeof(float) );
iwork = intMalloc(A->nrow);
if ( !work || !rwork || !iwork )
SUPERLU_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 ) SUPERLU_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
CCOPY(&A->nrow, Bptr, &ione, work, &ione);
#else
ccopy_(&A->nrow, Bptr, &ione, work, &ione);
#endif
sp_cgemv(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] = c_abs1( &Bptr[i] );
/* Compute abs(op(A))*abs(X) + abs(B). */
if (notran) {
for (k = 0; k < A->ncol; ++k) {
xk = c_abs1( &Xptr[k] );
for (i = Astore->colptr[k]; i < Astore->colptr[k+1]; ++i)
rwork[Astore->rowind[i]] += c_abs1(&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 += c_abs1(&Aval[i]) * c_abs1(&Xptr[irow]);
}
rwork[k] += s;
}
}
s = 0.;
for (i = 0; i < A->nrow; ++i) {
if (rwork[i] > safe2) {
s = SUPERLU_MAX( s, c_abs1(&work[i]) / rwork[i] );
} else if ( rwork[i] != 0.0 ) {
s = SUPERLU_MAX( s, (c_abs1(&work[i]) + safe1) / 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. */
cgstrs (trans, L, U, perm_r, perm_c, &Bjcol, Gstat, info);
#ifdef _CRAY
CAXPY(&A->nrow, &done, work, &ione,
&Xmat[j*ldx], &ione);
#else
caxpy_(&A->nrow, &done, work, &ione,
&Xmat[j*ldx], &ione);
#endif
lstres = berr[j];
++count;
} else {
break;
}
} /* end while */
/* 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 CLACON 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] = c_abs1( &Bptr[i] );
/* Compute abs(op(A))*abs(X) + abs(B). */
if ( notran ) {
for (k = 0; k < A->ncol; ++k) {
xk = c_abs1( &Xptr[k] );
for (i = Astore->colptr[k]; i < Astore->colptr[k+1]; ++i)
rwork[Astore->rowind[i]] += c_abs1(&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 = c_abs1( &Xptr[irow] );
s += c_abs1(&Aval[i]) * xk;
}
rwork[k] += s;
}
}
for (i = 0; i < A->nrow; ++i)
if (rwork[i] > safe2)
rwork[i] = c_abs(&work[i]) + (iwork[i]+1)*eps*rwork[i];
else
rwork[i] = c_abs(&work[i])+(iwork[i]+1)*eps*rwork[i]+safe1;
kase = 0;
do {
clacon_(&A->nrow, &work[A->nrow], work,
&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) {
cs_mult(&work[i], &work[i], C[i]);
}
else if ( !notran && rowequ )
for (i = 0; i < A->nrow; ++i) {
cs_mult(&work[i], &work[i], R[i]);
}
cgstrs (transt, L, U, perm_r, perm_c, &Bjcol, Gstat, info);
for (i = 0; i < A->nrow; ++i) {
cs_mult(&work[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) {
cs_mult(&work[i], &work[i], rwork[i]);
}
cgstrs (trans, L, U, perm_r, perm_c, &Bjcol, Gstat, info);
if ( notran && colequ )
for (i = 0; i < A->ncol; ++i) {
cs_mult(&work[i], &work[i], C[i]);
}
else if ( !notran && rowequ )
for (i = 0; i < A->ncol; ++i) {
cs_mult(&work[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] * c_abs1( &Xptr[i]) );
} else if ( !notran && rowequ ) {
for (i = 0; i < A->nrow; ++i)
lstres = SUPERLU_MAX( lstres, R[i] * c_abs1( &Xptr[i]) );
} else {
for (i = 0; i < A->nrow; ++i)
lstres = SUPERLU_MAX( lstres, c_abs1( &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;
} /* cgsrfs */
float clangs(char *norm, SuperMatrix *A)
{
/*
Purpose
=======
CLANGS returns the value of the one norm, or the Frobenius norm, or
the infinity norm, or the element of largest absolute value of a
real matrix A.
Description
===========
CLANGE returns the value
CLANGE = ( max(abs(A(i,j))), NORM = 'M' or 'm'
(
( norm1(A), NORM = '1', 'O' or 'o'
(
( normI(A), NORM = 'I' or 'i'
(
( normF(A), NORM = 'F', 'f', 'E' or 'e'
where norm1 denotes the one norm of a matrix (maximum column sum),
normI denotes the infinity norm of a matrix (maximum row sum) and
normF denotes the Frobenius norm of a matrix (square root of sum of
squares). Note that max(abs(A(i,j))) is not a matrix norm.
Arguments
=========
NORM (input) CHARACTER*1
Specifies the value to be returned in CLANGE as described above.
A (input) SuperMatrix*
The M by N sparse matrix A.
=====================================================================
*/
/* Local variables */
NCformat *Astore;
complex *Aval;
int i, j, irow;
float value, sum;
float *rwork;
Astore = A->Store;
Aval = Astore->nzval;
if ( SUPERLU_MIN(A->nrow, A->ncol) == 0) {
value = 0.;
} else if (lsame_(norm, "M")) {
/* Find max(abs(A(i,j))). */
value = 0.;
for (j = 0; j < A->ncol; ++j)
for (i = Astore->colptr[j]; i < Astore->colptr[j+1]; i++)
value = SUPERLU_MAX( value, slu_c_abs( &Aval[i]) );
} else if (lsame_(norm, "O") || *(unsigned char *)norm == '1') {
/* Find norm1(A). */
value = 0.;
for (j = 0; j < A->ncol; ++j) {
sum = 0.;
for (i = Astore->colptr[j]; i < Astore->colptr[j+1]; i++)
sum += slu_c_abs( &Aval[i] );
value = SUPERLU_MAX(value,sum);
}
} else if (lsame_(norm, "I")) {
/* Find normI(A). */
if ( !(rwork = (float *) SUPERLU_MALLOC(A->nrow * sizeof(float))) )
ABORT("SUPERLU_MALLOC fails for rwork.");
for (i = 0; i < A->nrow; ++i) rwork[i] = 0.;
for (j = 0; j < A->ncol; ++j)
for (i = Astore->colptr[j]; i < Astore->colptr[j+1]; i++) {
irow = Astore->rowind[i];
rwork[irow] += slu_c_abs( &Aval[i] );
}
value = 0.;
for (i = 0; i < A->nrow; ++i)
value = SUPERLU_MAX(value, rwork[i]);
SUPERLU_FREE (rwork);
} else if (lsame_(norm, "F") || lsame_(norm, "E")) {
/* Find normF(A). */
ABORT("Not implemented.");
} else
ABORT("Illegal norm specified.");
return (value);
} /* clangs */
