void
get_diag_procs(int_t n, Glu_persist_t *Glu_persist, gridinfo_t *grid,
int_t *num_diag_procs, int_t **diag_procs, int_t **diag_len)
{
int_t i, j, k, knsupc, nprow, npcol, nsupers, pkk;
int_t *xsup;
i = j = *num_diag_procs = pkk = 0;
nprow = grid->nprow;
npcol = grid->npcol;
nsupers = Glu_persist->supno[n-1] + 1;
xsup = Glu_persist->xsup;
do {
++(*num_diag_procs);
i = (++i) % nprow;
j = (++j) % npcol;
pkk = PNUM( i, j, grid );
} while ( pkk != 0 ); /* Until wrap back to process 0 */
if ( !(*diag_procs = intMalloc_dist(*num_diag_procs)) )
ABORT("Malloc fails for diag_procs[]");
if ( !(*diag_len = intCalloc_dist(*num_diag_procs)) )
ABORT("Calloc fails for diag_len[]");
for (i = j = k = 0; k < *num_diag_procs; ++k) {
pkk = PNUM( i, j, grid );
(*diag_procs)[k] = pkk;
i = (++i) % nprow;
j = (++j) % npcol;
}
for (k = 0; k < nsupers; ++k) {
knsupc = SuperSize( k );
i = k % *num_diag_procs;
(*diag_len)[i] += knsupc;
}
}
/*
* r[] is the residual vector distributed the same way as
* matrix-vector product.
*/
static void
redist_all_to_diag(int_t n, doublecomplex r[], Glu_persist_t *Glu_persist,
LocalLU_t *Llu, gridinfo_t *grid, int_t mv_sup_to_proc[],
doublecomplex work[])
{
int_t i, ii, k, lk, lr, nsupers;
int_t *ilsum, *xsup;
int iam, knsupc, psrc, pkk;
MPI_Status status;
iam = grid->iam;
nsupers = Glu_persist->supno[n-1] + 1;
xsup = Glu_persist->xsup;
ilsum = Llu->ilsum;
lr = 0;
for (k = 0; k < nsupers; ++k) {
pkk = PNUM( PROW( k, grid ), PCOL( k, grid ), grid );
psrc = mv_sup_to_proc[k];
knsupc = SuperSize( k );
lk = LBi( k, grid );
ii = ilsum[lk] + (lk+1)*XK_H;
if ( iam == psrc ) {
if ( iam != pkk ) { /* Send X component. */
MPI_Send( &r[lr], knsupc, SuperLU_MPI_DOUBLE_COMPLEX,
pkk, Xk, grid->comm );
} else { /* Local copy. */
for (i = 0; i < knsupc; ++i)
work[i + ii] = r[i + lr];
}
lr += knsupc;
} else {
if ( iam == pkk ) { /* Recv X component. */
MPI_Recv( &work[ii], knsupc, SuperLU_MPI_DOUBLE_COMPLEX,
psrc, Xk, grid->comm, &status );
}
}
}
} /* REDIST_ALL_TO_DIAG */
/*! \brief
*
* <pre>
* Purpose
* =======
* Perform local block modifications: lsum[i] -= L_i,k * X[k].
* </pre>
*/
void dlsum_fmod
/************************************************************************/
(
double *lsum, /* Sum of local modifications. */
double *x, /* X array (local) */
double *xk, /* X[k]. */
double *rtemp, /* Result of full matrix-vector multiply. */
int nrhs, /* Number of right-hand sides. */
int knsupc, /* Size of supernode k. */
int_t k, /* The k-th component of X. */
int_t *fmod, /* Modification count for L-solve. */
int_t nlb, /* Number of L blocks. */
int_t lptr, /* Starting position in lsub[*]. */
int_t luptr, /* Starting position in lusup[*]. */
int_t *xsup,
gridinfo_t *grid,
LocalLU_t *Llu,
MPI_Request send_req[],
SuperLUStat_t *stat
)
{
double alpha = 1.0, beta = 0.0;
double *lusup, *lusup1;
double *dest;
int iam, iknsupc, myrow, nbrow, nsupr, nsupr1, p, pi;
int_t i, ii, ik, il, ikcol, irow, j, lb, lk, rel;
int_t *lsub, *lsub1, nlb1, lptr1, luptr1;
int_t *ilsum = Llu->ilsum; /* Starting position of each supernode in lsum. */
int_t *frecv = Llu->frecv;
int_t **fsendx_plist = Llu->fsendx_plist;
MPI_Status status;
int test_flag;
iam = grid->iam;
myrow = MYROW( iam, grid );
lk = LBj( k, grid ); /* Local block number, column-wise. */
lsub = Llu->Lrowind_bc_ptr[lk];
lusup = Llu->Lnzval_bc_ptr[lk];
nsupr = lsub[1];
for (lb = 0; lb < nlb; ++lb) {
ik = lsub[lptr]; /* Global block number, row-wise. */
nbrow = lsub[lptr+1];
#ifdef _CRAY
SGEMM( ftcs2, ftcs2, &nbrow, &nrhs, &knsupc,
&alpha, &lusup[luptr], &nsupr, xk,
&knsupc, &beta, rtemp, &nbrow );
#else
dgemm_( "N", "N", &nbrow, &nrhs, &knsupc,
&alpha, &lusup[luptr], &nsupr, xk,
&knsupc, &beta, rtemp, &nbrow );
#endif
stat->ops[SOLVE] += 2 * nbrow * nrhs * knsupc + nbrow * nrhs;
lk = LBi( ik, grid ); /* Local block number, row-wise. */
iknsupc = SuperSize( ik );
il = LSUM_BLK( lk );
dest = &lsum[il];
lptr += LB_DESCRIPTOR;
rel = xsup[ik]; /* Global row index of block ik. */
for (i = 0; i < nbrow; ++i) {
irow = lsub[lptr++] - rel; /* Relative row. */
RHS_ITERATE(j)
dest[irow + j*iknsupc] -= rtemp[i + j*nbrow];
}
luptr += nbrow;
if ( (--fmod[lk])==0 ) { /* Local accumulation done. */
ikcol = PCOL( ik, grid );
p = PNUM( myrow, ikcol, grid );
if ( iam != p ) {
#ifdef ISEND_IRECV
MPI_Isend( &lsum[il - LSUM_H], iknsupc * nrhs + LSUM_H,
MPI_DOUBLE, p, LSUM, grid->comm,
&send_req[Llu->SolveMsgSent++] );
#else
#ifdef BSEND
MPI_Bsend( &lsum[il - LSUM_H], iknsupc * nrhs + LSUM_H,
MPI_DOUBLE, p, LSUM, grid->comm );
#else
MPI_Send( &lsum[il - LSUM_H], iknsupc * nrhs + LSUM_H,
MPI_DOUBLE, p, LSUM, grid->comm );
#endif
#endif
#if ( DEBUGlevel>=2 )
printf("(%2d) Sent LSUM[%2.0f], size %2d, to P %2d\n",
iam, lsum[il-LSUM_H], iknsupc*nrhs+LSUM_H, p);
#endif
} else { /* Diagonal process: X[i] += lsum[i]. */
ii = X_BLK( lk );
RHS_ITERATE(j)
for (i = 0; i < iknsupc; ++i)
x[i + ii + j*iknsupc] += lsum[i + il + j*iknsupc];
if ( frecv[lk]==0 ) { /* Becomes a leaf node. */
fmod[lk] = -1; /* Do not solve X[k] in the future. */
lk = LBj( ik, grid );/* Local block number, column-wise. */
lsub1 = Llu->Lrowind_bc_ptr[lk];
lusup1 = Llu->Lnzval_bc_ptr[lk];
nsupr1 = lsub1[1];
#ifdef _CRAY
STRSM(ftcs1, ftcs1, ftcs2, ftcs3, &iknsupc, &nrhs, &alpha,
lusup1, &nsupr1, &x[ii], &iknsupc);
#else
dtrsm_("L", "L", "N", "U", &iknsupc, &nrhs, &alpha,
lusup1, &nsupr1, &x[ii], &iknsupc);
#endif
stat->ops[SOLVE] += iknsupc * (iknsupc - 1) * nrhs;
#if ( DEBUGlevel>=2 )
printf("(%2d) Solve X[%2d]\n", iam, ik);
#endif
/*
* Send Xk to process column Pc[k].
*/
for (p = 0; p < grid->nprow; ++p) {
if ( fsendx_plist[lk][p] != EMPTY ) {
pi = PNUM( p, ikcol, grid );
#ifdef ISEND_IRECV
MPI_Isend( &x[ii - XK_H], iknsupc * nrhs + XK_H,
MPI_DOUBLE, pi, Xk, grid->comm,
&send_req[Llu->SolveMsgSent++] );
#else
#ifdef BSEND
MPI_Bsend( &x[ii - XK_H], iknsupc * nrhs + XK_H,
MPI_DOUBLE, pi, Xk, grid->comm );
#else
MPI_Send( &x[ii - XK_H], iknsupc * nrhs + XK_H,
MPI_DOUBLE, pi, Xk, grid->comm );
#endif
#endif
#if ( DEBUGlevel>=2 )
printf("(%2d) Sent X[%2.0f] to P %2d\n",
iam, x[ii-XK_H], pi);
#endif
}
}
/*
* Perform local block modifications.
*/
nlb1 = lsub1[0] - 1;
lptr1 = BC_HEADER + LB_DESCRIPTOR + iknsupc;
luptr1 = iknsupc; /* Skip diagonal block L(I,I). */
dlsum_fmod(lsum, x, &x[ii], rtemp, nrhs, iknsupc, ik,
fmod, nlb1, lptr1, luptr1, xsup,
grid, Llu, send_req, stat);
} /* if frecv[lk] == 0 */
} /* if iam == p */
} /* if fmod[lk] == 0 */
} /* for lb ... */
static void pdgstrs2
/************************************************************************/
#ifdef _CRAY
(
int_t m, int_t k, Glu_persist_t *Glu_persist, gridinfo_t *grid,
LocalLU_t *Llu, SuperLUStat_t *stat, _fcd ftcs1, _fcd ftcs2, _fcd ftcs3
)
#else
(
int_t m, int_t k, Glu_persist_t *Glu_persist, gridinfo_t *grid,
LocalLU_t *Llu, SuperLUStat_t *stat
)
#endif
/*
* Purpose
* =======
* Perform parallel triangular solves
* U(k,:) := A(k,:) \ L(k,k).
* Only the process row that owns block row *k* participates
* in the work.
*
* Arguments
* =========
*
* m (input) int (global)
* Number of rows in the matrix.
*
* k (input) int (global)
* The row number of the block row to be factorized.
*
* Glu_persist (input) Glu_persist_t*
* Global data structures (xsup, supno) replicated on all processes.
*
* grid (input) gridinfo_t*
* The 2D process mesh.
*
* Llu (input/output) LocalLU_t*
* Local data structures to store distributed L and U matrices.
*
* stat (output) SuperLUStat_t*
* Record the statistics about the factorization;
* See SuperLUStat_t structure defined in util.h.
*
*/
{
int iam, pkk;
int incx = 1;
int nsupr; /* number of rows in the block L(:,k) (LDA) */
int segsize;
int_t nsupc; /* number of columns in the block */
int_t luptr, iukp, rukp;
int_t b, gb, j, klst, knsupc, lk, nb;
int_t *xsup = Glu_persist->xsup;
int_t *usub;
double *lusup, *uval;
/* Quick return. */
lk = LBi( k, grid ); /* Local block number */
if ( !Llu->Unzval_br_ptr[lk] ) return;
/* Initialization. */
iam = grid->iam;
pkk = PNUM( PROW(k, grid), PCOL(k, grid), grid );
klst = FstBlockC( k+1 );
knsupc = SuperSize( k );
usub = Llu->Ufstnz_br_ptr[lk]; /* index[] of block row U(k,:) */
uval = Llu->Unzval_br_ptr[lk];
nb = usub[0];
iukp = BR_HEADER;
rukp = 0;
if ( iam == pkk ) {
lk = LBj( k, grid );
nsupr = Llu->Lrowind_bc_ptr[lk][1]; /* LDA of lusup[] */
lusup = Llu->Lnzval_bc_ptr[lk];
} else {
nsupr = Llu->Lsub_buf_2[k%2][1]; /* LDA of lusup[] */
lusup = Llu->Lval_buf_2[k%2];
}
/* Loop through all the row blocks. */
for (b = 0; b < nb; ++b) {
gb = usub[iukp];
nsupc = SuperSize( gb );
iukp += UB_DESCRIPTOR;
/* Loop through all the segments in the block. */
for (j = 0; j < nsupc; ++j) {
segsize = klst - usub[iukp++];
if ( segsize ) { /* Nonzero segment. */
luptr = (knsupc - segsize) * (nsupr + 1);
#ifdef _CRAY
STRSV(ftcs1, ftcs2, ftcs3, &segsize, &lusup[luptr], &nsupr,
&uval[rukp], &incx);
#elif defined (USE_VENDOR_BLAS)
dtrsv_("L", "N", "U", &segsize, &lusup[luptr], &nsupr,
&uval[rukp], &incx, 1, 1, 1);
#else
dtrsv_("L", "N", "U", &segsize, &lusup[luptr], &nsupr,
&uval[rukp], &incx);
#endif
stat->ops[FACT] += segsize * (segsize + 1);
rukp += segsize;
}
}
} /* for b ... */
} /* PDGSTRS2 */
static void pdgstrf2
/************************************************************************/
(
superlu_options_t *options,
int_t k, double thresh, Glu_persist_t *Glu_persist, gridinfo_t *grid,
LocalLU_t *Llu, MPI_Request *U_diag_blk_send_req,
SuperLUStat_t *stat, int* info
)
/*
* Purpose
* =======
*
* Panel factorization -- block column k
* Factor diagonal and subdiagonal blocks and test for exact singularity.
* Only the column processes that owns block column *k* participate
* in the work.
*
* Arguments
* =========
*
* k (input) int (global)
* The column number of the block column to be factorized.
*
* thresh (input) double (global)
* The threshold value = s_eps * anorm.
*
* Glu_persist (input) Glu_persist_t*
* Global data structures (xsup, supno) replicated on all processes.
*
* grid (input) gridinfo_t*
* The 2D process mesh.
*
* Llu (input/output) LocalLU_t*
* Local data structures to store distributed L and U matrices.
*
* U_diag_blk_send_req (input/output) MPI_Request*
* List of send requests to send down the diagonal block of U.
*
* stat (output) SuperLUStat_t*
* Record the statistics about the factorization.
* See SuperLUStat_t structure defined in util.h.
*
* info (output) int*
* = 0: successful exit
* < 0: if info = -i, the i-th argument had an illegal value
* > 0: if info = i, U(i,i) is exactly zero. The factorization has
* been completed, but the factor U is exactly singular,
* and division by zero will occur if it is used to solve a
* system of equations.
*
*/
{
int cols_left, iam, l, pkk, pr;
int incx = 1, incy = 1;
int nsupr; /* number of rows in the block (LDA) */
int luptr;
int_t i, krow, j, jfst, jlst, u_diag_cnt;
int_t nsupc; /* number of columns in the block */
int_t *xsup = Glu_persist->xsup;
int_t Pr;
MPI_Status status;
MPI_Comm comm = (grid->cscp).comm;
double *lusup, temp;
double *ujrow, *ublk_ptr; /* pointer to the U block */
double alpha = -1;
*info = 0;
/* Quick return. */
/* Initialization. */
iam = grid->iam;
Pr = grid->nprow;
krow = PROW( k, grid );
pkk = PNUM( PROW(k, grid), PCOL(k, grid), grid );
j = LBj( k, grid ); /* Local block number */
jfst = FstBlockC( k );
jlst = FstBlockC( k+1 );
lusup = Llu->Lnzval_bc_ptr[j];
nsupc = SuperSize( k );
if ( Llu->Lrowind_bc_ptr[j] ) nsupr = Llu->Lrowind_bc_ptr[j][1];
ublk_ptr = ujrow = Llu->ujrow;
luptr = 0; /* point to the diagonal entries. */
cols_left = nsupc; /* supernode size */
u_diag_cnt = 0;
if ( iam == pkk ) { /* diagonal process */
if ( U_diag_blk_send_req && U_diag_blk_send_req[krow] ) {
/* There are pending sends - wait for all Isend to complete */
for (pr = 0; pr < Pr; ++pr)
if (pr != krow)
MPI_Wait(U_diag_blk_send_req + pr, &status);
}
for (j = 0; j < jlst - jfst; ++j) { /* for each column in panel */
/* Diagonal pivot */
i = luptr;
if ( options->ReplaceTinyPivot == YES || lusup[i] == 0.0 ) {
if ( fabs(lusup[i]) < thresh ) {
#if ( PRNTlevel>=2 )
printf("(%d) .. col %d, tiny pivot %e ",
iam, jfst+j, lusup[i]);
#endif
/* Keep the new diagonal entry with the same sign. */
if ( lusup[i] < 0 ) lusup[i] = -thresh;
else lusup[i] = thresh;
#if ( PRNTlevel>=2 )
printf("replaced by %e\n", lusup[i]);
#endif
++(stat->TinyPivots);
}
}
for (l = 0; l < cols_left; ++l, i += nsupr, ++u_diag_cnt)
ublk_ptr[u_diag_cnt] = lusup[i]; /* copy one row of U */
if ( ujrow[0] == 0.0 ) { /* Test for singularity. */
*info = j+jfst+1;
} else { /* Scale the j-th column. */
temp = 1.0 / ujrow[0];
for (i = luptr+1; i < luptr-j+nsupr; ++i) lusup[i] *= temp;
stat->ops[FACT] += nsupr-j-1;
}
/* Rank-1 update of the trailing submatrix. */
if ( --cols_left ) {
l = nsupr - j - 1;
#ifdef _CRAY
SGER(&l, &cols_left, &alpha, &lusup[luptr+1], &incx,
&ujrow[1], &incy, &lusup[luptr+nsupr+1], &nsupr);
#else
dger_(&l, &cols_left, &alpha, &lusup[luptr+1], &incx,
&ujrow[1], &incy, &lusup[luptr+nsupr+1], &nsupr);
#endif
stat->ops[FACT] += 2 * l * cols_left;
}
ujrow = ublk_ptr + u_diag_cnt; /* move to next row of U */
luptr += nsupr + 1; /* move to next column */
} /* for column j ... */
if ( U_diag_blk_send_req && iam == pkk ) { /* Send the U block */
/** ALWAYS SEND TO ALL OTHERS - TO FIX **/
for (pr = 0; pr < Pr; ++pr)
if (pr != krow)
MPI_Isend(ublk_ptr, u_diag_cnt, MPI_DOUBLE, pr,
((k<<2)+2)%NTAGS, comm, U_diag_blk_send_req + pr);
U_diag_blk_send_req[krow] = 1; /* flag outstanding Isend */
}
} else { /* non-diagonal process */
/* Receive the diagonal block of U */
MPI_Recv(ublk_ptr, (nsupc*(nsupc+1))>>1, MPI_DOUBLE,
krow, ((k<<2)+2)%NTAGS, comm, &status);
for (j = 0; j < jlst - jfst; ++j) { /* for each column in panel */
u_diag_cnt += cols_left;
if ( !lusup ) { /* empty block column */
--cols_left;
if ( ujrow[0] == 0.0 ) *info = j+jfst+1;
continue;
}
/* Test for singularity. */
if ( ujrow[0] == 0.0 ) {
*info = j+jfst+1;
} else {
/* Scale the j-th column. */
temp = 1.0 / ujrow[0];
for (i = luptr; i < luptr+nsupr; ++i) lusup[i] *= temp;
stat->ops[FACT] += nsupr;
}
/* Rank-1 update of the trailing submatrix. */
if ( --cols_left ) {
#ifdef _CRAY
SGER(&nsupr, &cols_left, &alpha, &lusup[luptr], &incx,
&ujrow[1], &incy, &lusup[luptr+nsupr], &nsupr);
#else
dger_(&nsupr, &cols_left, &alpha, &lusup[luptr], &incx,
&ujrow[1], &incy, &lusup[luptr+nsupr], &nsupr);
#endif
stat->ops[FACT] += 2 * nsupr * cols_left;
}
ujrow = ublk_ptr + u_diag_cnt; /* move to next row of U */
luptr += nsupr; /* move to next column */
} /* for column j ... */
} /* end if pkk ... */
} /* PDGSTRF2 */
static void pdgstrf2
/************************************************************************/
(
superlu_options_t *options,
int_t k, double thresh, Glu_persist_t *Glu_persist, gridinfo_t *grid,
LocalLU_t *Llu, SuperLUStat_t *stat, int* info
)
/*
* Purpose
* =======
* Factor diagonal and subdiagonal blocks and test for exact singularity.
* Only the process column that owns block column *k* participates
* in the work.
*
* Arguments
* =========
*
* k (input) int (global)
* The column number of the block column to be factorized.
*
* thresh (input) double (global)
* The threshold value = s_eps * anorm.
*
* Glu_persist (input) Glu_persist_t*
* Global data structures (xsup, supno) replicated on all processes.
*
* grid (input) gridinfo_t*
* The 2D process mesh.
*
* Llu (input/output) LocalLU_t*
* Local data structures to store distributed L and U matrices.
*
* stat (output) SuperLUStat_t*
* Record the statistics about the factorization.
* See SuperLUStat_t structure defined in util.h.
*
* info (output) int*
* = 0: successful exit
* < 0: if info = -i, the i-th argument had an illegal value
* > 0: if info = i, U(i,i) is exactly zero. The factorization has
* been completed, but the factor U is exactly singular,
* and division by zero will occur if it is used to solve a
* system of equations.
*
*/
{
int c, iam, l, pkk;
int incx = 1, incy = 1;
int nsupr; /* number of rows in the block (LDA) */
int luptr;
int_t i, krow, j, jfst, jlst;
int_t nsupc; /* number of columns in the block */
int_t *xsup = Glu_persist->xsup;
double *lusup, temp;
double *ujrow;
double alpha = -1;
*info = 0;
/* Quick return. */
/* Initialization. */
iam = grid->iam;
krow = PROW( k, grid );
pkk = PNUM( PROW(k, grid), PCOL(k, grid), grid );
j = LBj( k, grid ); /* Local block number */
jfst = FstBlockC( k );
jlst = FstBlockC( k+1 );
lusup = Llu->Lnzval_bc_ptr[j];
nsupc = SuperSize( k );
if ( Llu->Lrowind_bc_ptr[j] ) nsupr = Llu->Lrowind_bc_ptr[j][1];
ujrow = Llu->ujrow;
luptr = 0; /* Point to the diagonal entries. */
c = nsupc;
for (j = 0; j < jlst - jfst; ++j) {
/* Broadcast the j-th row (nsupc - j) elements to
the process column. */
if ( iam == pkk ) { /* Diagonal process. */
i = luptr;
if ( options->ReplaceTinyPivot == YES || lusup[i] == 0.0 ) {
if ( fabs(lusup[i]) < thresh ) { /* Diagonal */
#if ( PRNTlevel>=2 )
printf("(%d) .. col %d, tiny pivot %e ",
iam, jfst+j, lusup[i]);
#endif
/* Keep the replaced diagonal with the same sign. */
if ( lusup[i] < 0 ) lusup[i] = -thresh;
else lusup[i] = thresh;
#if ( PRNTlevel>=2 )
printf("replaced by %e\n", lusup[i]);
#endif
++(stat->TinyPivots);
}
}
for (l = 0; l < c; ++l, i += nsupr) ujrow[l] = lusup[i];
}
#if 0
dbcast_col(ujrow, c, pkk, UjROW, grid, &c);
#else
MPI_Bcast(ujrow, c, MPI_DOUBLE, krow, (grid->cscp).comm);
/*bcast_tree(ujrow, c, MPI_DOUBLE, krow, (24*k+j)%NTAGS,
grid, COMM_COLUMN, &c);*/
#endif
#if ( DEBUGlevel>=2 )
if ( k == 3329 && j == 2 ) {
if ( iam == pkk ) {
printf("..(%d) k %d, j %d: Send ujrow[0] %e\n",iam,k,j,ujrow[0]);
} else {
printf("..(%d) k %d, j %d: Recv ujrow[0] %e\n",iam,k,j,ujrow[0]);
}
}
#endif
if ( !lusup ) { /* Empty block column. */
--c;
if ( ujrow[0] == 0.0 ) *info = j+jfst+1;
continue;
}
/* Test for singularity. */
if ( ujrow[0] == 0.0 ) {
*info = j+jfst+1;
} else {
/* Scale the j-th column of the matrix. */
temp = 1.0 / ujrow[0];
if ( iam == pkk ) {
for (i = luptr+1; i < luptr-j+nsupr; ++i) lusup[i] *= temp;
stat->ops[FACT] += nsupr-j-1;
} else {
for (i = luptr; i < luptr+nsupr; ++i) lusup[i] *= temp;
stat->ops[FACT] += nsupr;
}
}
/* Rank-1 update of the trailing submatrix. */
if ( --c ) {
if ( iam == pkk ) {
l = nsupr - j - 1;
#ifdef _CRAY
SGER(&l, &c, &alpha, &lusup[luptr+1], &incx,
&ujrow[1], &incy, &lusup[luptr+nsupr+1], &nsupr);
#elif defined (USE_VENDOR_BLAS)
dger_(&l, &c, &alpha, &lusup[luptr+1], &incx,
&ujrow[1], &incy, &lusup[luptr+nsupr+1], &nsupr);
#else
hypre_F90_NAME_BLAS(dger,DGER)(&l, &c, &alpha,
&lusup[luptr+1], &incx,
&ujrow[1], &incy, &lusup[luptr+nsupr+1], &nsupr);
#endif
stat->ops[FACT] += 2 * l * c;
} else {
#ifdef _CRAY
SGER(&nsupr, &c, &alpha, &lusup[luptr], &incx,
&ujrow[1], &incy, &lusup[luptr+nsupr], &nsupr);
#elif defined (USE_VENDOR_BLAS)
dger_(&nsupr, &c, &alpha, &lusup[luptr], &incx,
&ujrow[1], &incy, &lusup[luptr+nsupr], &nsupr);
#else
hypre_F90_NAME_BLAS(dger,DGER)(&nsupr, &c, &alpha,
&lusup[luptr], &incx,
&ujrow[1], &incy, &lusup[luptr+nsupr], &nsupr);
#endif
stat->ops[FACT] += 2 * nsupr * c;
}
}
/* Move to the next column. */
if ( iam == pkk ) luptr += nsupr + 1;
else luptr += nsupr;
} /* for j ... */
} /* PDGSTRF2 */
void
pzgstrs(int_t n, LUstruct_t *LUstruct,
ScalePermstruct_t *ScalePermstruct,
gridinfo_t *grid, doublecomplex *B,
int_t m_loc, int_t fst_row, int_t ldb, int nrhs,
SOLVEstruct_t *SOLVEstruct,
SuperLUStat_t *stat, int *info)
{
/*
* Purpose
* =======
*
* PZGSTRS solves a system of distributed linear equations
* A*X = B with a general N-by-N matrix A using the LU factorization
* computed by PZGSTRF.
* If the equilibration, and row and column permutations were performed,
* the LU factorization was performed for A1 where
* A1 = Pc*Pr*diag(R)*A*diag(C)*Pc^T = L*U
* and the linear system solved is
* A1 * Y = Pc*Pr*B1, where B was overwritten by B1 = diag(R)*B, and
* the permutation to B1 by Pc*Pr is applied internally in this routine.
*
* Arguments
* =========
*
* n (input) int (global)
* The order of the system of linear equations.
*
* LUstruct (input) LUstruct_t*
* The distributed data structures storing L and U factors.
* The L and U factors are obtained from PZGSTRF for
* the possibly scaled and permuted matrix A.
* See superlu_zdefs.h for the definition of 'LUstruct_t'.
* A may be scaled and permuted into A1, so that
* A1 = Pc*Pr*diag(R)*A*diag(C)*Pc^T = L*U
*
* 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/output) doublecomplex*
* On entry, the distributed right-hand side matrix of the possibly
* equilibrated system. That is, B may be overwritten by diag(R)*B.
* On exit, the distributed solution matrix Y of the possibly
* equilibrated system if info = 0, where Y = Pc*diag(C)^(-1)*X,
* and X is the solution of the original system.
*
* m_loc (input) int (local)
* The local row dimension of matrix B.
*
* fst_row (input) int (global)
* The row number of B's first row in the global matrix.
*
* ldb (input) int (local)
* The leading dimension of matrix B.
*
* nrhs (input) int (global)
* Number of right-hand sides.
*
* SOLVEstruct (output) SOLVEstruct_t* (global)
* Contains the information for the communication during the
* solution phase.
*
* stat (output) SuperLUStat_t*
* Record the statistics about the triangular solves.
* 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
*
*/
Glu_persist_t *Glu_persist = LUstruct->Glu_persist;
LocalLU_t *Llu = LUstruct->Llu;
doublecomplex alpha = {1.0, 0.0};
doublecomplex zero = {0.0, 0.0};
doublecomplex *lsum; /* Local running sum of the updates to B-components */
doublecomplex *x; /* X component at step k. */
/* NOTE: x and lsum are of same size. */
doublecomplex *lusup, *dest;
doublecomplex *recvbuf, *tempv;
doublecomplex *rtemp; /* Result of full matrix-vector multiply. */
int_t **Ufstnz_br_ptr = Llu->Ufstnz_br_ptr;
int_t *Urbs, *Urbs1; /* Number of row blocks in each block column of U. */
Ucb_indptr_t **Ucb_indptr;/* Vertical linked list pointing to Uindex[] */
int_t **Ucb_valptr; /* Vertical linked list pointing to Unzval[] */
int_t iam, kcol, krow, mycol, myrow;
int_t i, ii, il, j, jj, k, lb, ljb, lk, lptr, luptr;
int_t nb, nlb, nub, nsupers;
int_t *xsup, *supno, *lsub, *usub;
int_t *ilsum; /* Starting position of each supernode in lsum (LOCAL)*/
int_t Pc, Pr;
int knsupc, nsupr;
int ldalsum; /* Number of lsum entries locally owned. */
int maxrecvsz, p, pi;
int_t **Lrowind_bc_ptr;
doublecomplex **Lnzval_bc_ptr;
MPI_Status status;
#ifdef ISEND_IRECV
MPI_Request *send_req, recv_req;
#endif
pxgstrs_comm_t *gstrs_comm = SOLVEstruct->gstrs_comm;
/*-- Counts used for L-solve --*/
int_t *fmod; /* Modification count for L-solve --
Count the number of local block products to
be summed into lsum[lk]. */
int_t **fsendx_plist = Llu->fsendx_plist;
int_t nfrecvx = Llu->nfrecvx; /* Number of X components to be recv'd. */
int_t *frecv; /* Count of lsum[lk] contributions to be received
from processes in this row.
It is only valid on the diagonal processes. */
int_t nfrecvmod = 0; /* Count of total modifications to be recv'd. */
int_t nleaf = 0, nroot = 0;
/*-- Counts used for U-solve --*/
int_t *bmod; /* Modification count for U-solve. */
int_t **bsendx_plist = Llu->bsendx_plist;
int_t nbrecvx = Llu->nbrecvx; /* Number of X components to be recv'd. */
int_t *brecv; /* Count of modifications to be recv'd from
processes in this row. */
int_t nbrecvmod = 0; /* Count of total modifications to be recv'd. */
double t;
#if ( DEBUGlevel>=2 )
int_t Ublocks = 0;
#endif
t = SuperLU_timer_();
/* Test input parameters. */
*info = 0;
if ( n < 0 ) *info = -1;
else if ( nrhs < 0 ) *info = -9;
if ( *info ) {
pxerbla("PZGSTRS", grid, -*info);
return;
}
/*
* Initialization.
*/
iam = grid->iam;
Pc = grid->npcol;
Pr = grid->nprow;
myrow = MYROW( iam, grid );
mycol = MYCOL( iam, grid );
xsup = Glu_persist->xsup;
supno = Glu_persist->supno;
nsupers = supno[n-1] + 1;
Lrowind_bc_ptr = Llu->Lrowind_bc_ptr;
Lnzval_bc_ptr = Llu->Lnzval_bc_ptr;
nlb = CEILING( nsupers, Pr ); /* Number of local block rows. */
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(iam, "Enter pzgstrs()");
#endif
stat->ops[SOLVE] = 0.0;
Llu->SolveMsgSent = 0;
/* Save the count to be altered so it can be used by
subsequent call to PDGSTRS. */
if ( !(fmod = intMalloc_dist(nlb)) )
ABORT("Calloc fails for fmod[].");
for (i = 0; i < nlb; ++i) fmod[i] = Llu->fmod[i];
if ( !(frecv = intMalloc_dist(nlb)) )
ABORT("Malloc fails for frecv[].");
Llu->frecv = frecv;
#ifdef ISEND_IRECV
k = SUPERLU_MAX( Llu->nfsendx, Llu->nbsendx ) + nlb;
if ( !(send_req = (MPI_Request*) SUPERLU_MALLOC(k*sizeof(MPI_Request))) )
ABORT("Malloc fails for send_req[].");
#endif
#ifdef _CRAY
ftcs1 = _cptofcd("L", strlen("L"));
ftcs2 = _cptofcd("N", strlen("N"));
ftcs3 = _cptofcd("U", strlen("U"));
#endif
/* Obtain ilsum[] and ldalsum for process column 0. */
ilsum = Llu->ilsum;
ldalsum = Llu->ldalsum;
/* Allocate working storage. */
knsupc = sp_ienv_dist(3);
maxrecvsz = knsupc * nrhs + SUPERLU_MAX( XK_H, LSUM_H );
if ( !(lsum = doublecomplexCalloc_dist(((size_t)ldalsum)*nrhs + nlb*LSUM_H)) )
ABORT("Calloc fails for lsum[].");
if ( !(x = doublecomplexMalloc_dist(ldalsum * nrhs + nlb * XK_H)) )
ABORT("Malloc fails for x[].");
if ( !(recvbuf = doublecomplexMalloc_dist(maxrecvsz)) )
ABORT("Malloc fails for recvbuf[].");
if ( !(rtemp = doublecomplexCalloc_dist(maxrecvsz)) )
ABORT("Malloc fails for rtemp[].");
/*---------------------------------------------------
* Forward solve Ly = b.
*---------------------------------------------------*/
/* Redistribute B into X on the diagonal processes. */
pzReDistribute_B_to_X(B, m_loc, nrhs, ldb, fst_row, ilsum, x,
ScalePermstruct, Glu_persist, grid, SOLVEstruct);
/* Set up the headers in lsum[]. */
ii = 0;
for (k = 0; k < nsupers; ++k) {
knsupc = SuperSize( k );
krow = PROW( k, grid );
if ( myrow == krow ) {
lk = LBi( k, grid ); /* Local block number. */
il = LSUM_BLK( lk );
lsum[il - LSUM_H].r = k;/* Block number prepended in the header.*/
lsum[il - LSUM_H].i = 0;
}
ii += knsupc;
}
/*
* Compute frecv[] and nfrecvmod counts on the diagonal processes.
*/
{
superlu_scope_t *scp = &grid->rscp;
for (k = 0; k < nsupers; ++k) {
krow = PROW( k, grid );
if ( myrow == krow ) {
lk = LBi( k, grid ); /* Local block number. */
kcol = PCOL( k, grid ); /* Root process in this row scope. */
if ( mycol != kcol && fmod[lk] )
i = 1; /* Contribution from non-diagonal process. */
else i = 0;
MPI_Reduce( &i, &frecv[lk], 1, mpi_int_t,
MPI_SUM, kcol, scp->comm );
if ( mycol == kcol ) { /* Diagonal process. */
nfrecvmod += frecv[lk];
if ( !frecv[lk] && !fmod[lk] ) ++nleaf;
#if ( DEBUGlevel>=2 )
printf("(%2d) frecv[%4d] %2d\n", iam, k, frecv[lk]);
assert( frecv[lk] < Pc );
#endif
}
}
}
}
/* ---------------------------------------------------------
Solve the leaf nodes first by all the diagonal processes.
--------------------------------------------------------- */
#if ( DEBUGlevel>=2 )
printf("(%2d) nleaf %4d\n", iam, nleaf);
#endif
for (k = 0; k < nsupers && nleaf; ++k) {
krow = PROW( k, grid );
kcol = PCOL( k, grid );
if ( myrow == krow && mycol == kcol ) { /* Diagonal process */
knsupc = SuperSize( k );
lk = LBi( k, grid );
if ( frecv[lk]==0 && fmod[lk]==0 ) {
fmod[lk] = -1; /* Do not solve X[k] in the future. */
ii = X_BLK( lk );
lk = LBj( k, grid ); /* Local block number, column-wise. */
lsub = Lrowind_bc_ptr[lk];
lusup = Lnzval_bc_ptr[lk];
nsupr = lsub[1];
#ifdef _CRAY
CTRSM(ftcs1, ftcs1, ftcs2, ftcs3, &knsupc, &nrhs, &alpha,
lusup, &nsupr, &x[ii], &knsupc);
#elif defined (USE_VENDOR_BLAS)
ztrsm_("L", "L", "N", "U", &knsupc, &nrhs, &alpha,
lusup, &nsupr, &x[ii], &knsupc, 1, 1, 1, 1);
#else
ztrsm_("L", "L", "N", "U", &knsupc, &nrhs, &alpha,
lusup, &nsupr, &x[ii], &knsupc);
#endif
stat->ops[SOLVE] += 4 * knsupc * (knsupc - 1) * nrhs
+ 10 * knsupc * nrhs; /* complex division */
--nleaf;
#if ( DEBUGlevel>=2 )
printf("(%2d) Solve X[%2d]\n", iam, k);
#endif
/*
* Send Xk to process column Pc[k].
*/
for (p = 0; p < Pr; ++p) {
if ( fsendx_plist[lk][p] != EMPTY ) {
pi = PNUM( p, kcol, grid );
#ifdef ISEND_IRECV
MPI_Isend( &x[ii - XK_H], knsupc * nrhs + XK_H,
SuperLU_MPI_DOUBLE_COMPLEX, pi, Xk, grid->comm,
&send_req[Llu->SolveMsgSent++]);
#else
MPI_Send( &x[ii - XK_H], knsupc * nrhs + XK_H,
SuperLU_MPI_DOUBLE_COMPLEX, pi, Xk, grid->comm );
#endif
#if ( DEBUGlevel>=2 )
printf("(%2d) Sent X[%2.0f] to P %2d\n",
iam, x[ii-XK_H], pi);
#endif
}
}
/*
* Perform local block modifications: lsum[i] -= L_i,k * X[k]
*/
nb = lsub[0] - 1;
lptr = BC_HEADER + LB_DESCRIPTOR + knsupc;
luptr = knsupc; /* Skip diagonal block L(k,k). */
zlsum_fmod(lsum, x, &x[ii], rtemp, nrhs, knsupc, k,
fmod, nb, lptr, luptr, xsup, grid, Llu,
send_req, stat);
}
} /* if diagonal process ... */
} /* for k ... */
/* -----------------------------------------------------------
Compute the internal nodes asynchronously by all processes.
----------------------------------------------------------- */
#if ( DEBUGlevel>=2 )
printf("(%2d) nfrecvx %4d, nfrecvmod %4d, nleaf %4d\n",
iam, nfrecvx, nfrecvmod, nleaf);
#endif
while ( nfrecvx || nfrecvmod ) { /* While not finished. */
/* Receive a message. */
#ifdef ISEND_IRECV
/* -MPI- FATAL: Remote protocol queue full */
MPI_Irecv( recvbuf, maxrecvsz, SuperLU_MPI_DOUBLE_COMPLEX,
MPI_ANY_SOURCE, MPI_ANY_TAG, grid->comm, &recv_req );
MPI_Wait( &recv_req, &status );
#else
MPI_Recv( recvbuf, maxrecvsz, SuperLU_MPI_DOUBLE_COMPLEX,
MPI_ANY_SOURCE, MPI_ANY_TAG, grid->comm, &status );
#endif
k = (*recvbuf).r;
#if ( DEBUGlevel>=2 )
printf("(%2d) Recv'd block %d, tag %2d\n", iam, k, status.MPI_TAG);
#endif
switch ( status.MPI_TAG ) {
case Xk:
--nfrecvx;
lk = LBj( k, grid ); /* Local block number, column-wise. */
lsub = Lrowind_bc_ptr[lk];
lusup = Lnzval_bc_ptr[lk];
if ( lsub ) {
nb = lsub[0];
lptr = BC_HEADER;
luptr = 0;
knsupc = SuperSize( k );
/*
* Perform local block modifications: lsum[i] -= L_i,k * X[k]
*/
zlsum_fmod(lsum, x, &recvbuf[XK_H], rtemp, nrhs, knsupc, k,
fmod, nb, lptr, luptr, xsup, grid, Llu,
send_req, stat);
} /* if lsub */
break;
case LSUM: /* Receiver must be a diagonal process */
--nfrecvmod;
lk = LBi( k, grid ); /* Local block number, row-wise. */
ii = X_BLK( lk );
knsupc = SuperSize( k );
tempv = &recvbuf[LSUM_H];
RHS_ITERATE(j) {
for (i = 0; i < knsupc; ++i)
z_add(&x[i + ii + j*knsupc],
&x[i + ii + j*knsupc],
&tempv[i + j*knsupc]);
}
if ( (--frecv[lk])==0 && fmod[lk]==0 ) {
fmod[lk] = -1; /* Do not solve X[k] in the future. */
lk = LBj( k, grid ); /* Local block number, column-wise. */
lsub = Lrowind_bc_ptr[lk];
lusup = Lnzval_bc_ptr[lk];
nsupr = lsub[1];
#ifdef _CRAY
CTRSM(ftcs1, ftcs1, ftcs2, ftcs3, &knsupc, &nrhs, &alpha,
lusup, &nsupr, &x[ii], &knsupc);
#elif defined (USE_VENDOR_BLAS)
ztrsm_("L", "L", "N", "U", &knsupc, &nrhs, &alpha,
lusup, &nsupr, &x[ii], &knsupc, 1, 1, 1, 1);
#else
ztrsm_("L", "L", "N", "U", &knsupc, &nrhs, &alpha,
lusup, &nsupr, &x[ii], &knsupc);
#endif
stat->ops[SOLVE] += 4 * knsupc * (knsupc - 1) * nrhs
+ 10 * knsupc * nrhs; /* complex division */
#if ( DEBUGlevel>=2 )
printf("(%2d) Solve X[%2d]\n", iam, k);
#endif
/*
* Send Xk to process column Pc[k].
*/
kcol = PCOL( k, grid );
for (p = 0; p < Pr; ++p) {
if ( fsendx_plist[lk][p] != EMPTY ) {
pi = PNUM( p, kcol, grid );
#ifdef ISEND_IRECV
MPI_Isend( &x[ii-XK_H], knsupc * nrhs + XK_H,
SuperLU_MPI_DOUBLE_COMPLEX, pi, Xk, grid->comm,
&send_req[Llu->SolveMsgSent++]);
#else
MPI_Send( &x[ii - XK_H], knsupc * nrhs + XK_H,
SuperLU_MPI_DOUBLE_COMPLEX, pi, Xk, grid->comm );
#endif
#if ( DEBUGlevel>=2 )
printf("(%2d) Sent X[%2.0f] to P %2d\n",
iam, x[ii-XK_H], pi);
#endif
}
}
/*
* Perform local block modifications.
*/
nb = lsub[0] - 1;
lptr = BC_HEADER + LB_DESCRIPTOR + knsupc;
luptr = knsupc; /* Skip diagonal block L(k,k). */
zlsum_fmod(lsum, x, &x[ii], rtemp, nrhs, knsupc, k,
fmod, nb, lptr, luptr, xsup, grid, Llu,
send_req, stat);
} /* if */
break;
#if ( DEBUGlevel>=2 )
default:
printf("(%2d) Recv'd wrong message tag %4d\n", status.MPI_TAG);
break;
#endif
} /* switch */
} /* while not finished ... */
#if ( PRNTlevel>=2 )
t = SuperLU_timer_() - t;
if ( !iam ) printf(".. L-solve time\t%8.2f\n", t);
t = SuperLU_timer_();
#endif
#if ( DEBUGlevel==2 )
{
printf("(%d) .. After L-solve: y =\n", iam);
for (i = 0, k = 0; k < nsupers; ++k) {
krow = PROW( k, grid );
kcol = PCOL( k, grid );
if ( myrow == krow && mycol == kcol ) { /* Diagonal process */
knsupc = SuperSize( k );
lk = LBi( k, grid );
ii = X_BLK( lk );
for (j = 0; j < knsupc; ++j)
printf("\t(%d)\t%4d\t%.10f\n", iam, xsup[k]+j, x[ii+j]);
fflush(stdout);
}
MPI_Barrier( grid->comm );
}
}
#endif
SUPERLU_FREE(fmod);
SUPERLU_FREE(frecv);
SUPERLU_FREE(rtemp);
#ifdef ISEND_IRECV
for (i = 0; i < Llu->SolveMsgSent; ++i) MPI_Request_free(&send_req[i]);
Llu->SolveMsgSent = 0;
#endif
/*---------------------------------------------------
* Back solve Ux = y.
*
* The Y components from the forward solve is already
* on the diagonal processes.
*---------------------------------------------------*/
/* Save the count to be altered so it can be used by
subsequent call to PZGSTRS. */
if ( !(bmod = intMalloc_dist(nlb)) )
ABORT("Calloc fails for bmod[].");
for (i = 0; i < nlb; ++i) bmod[i] = Llu->bmod[i];
if ( !(brecv = intMalloc_dist(nlb)) )
ABORT("Malloc fails for brecv[].");
Llu->brecv = brecv;
/*
* Compute brecv[] and nbrecvmod counts on the diagonal processes.
*/
{
superlu_scope_t *scp = &grid->rscp;
for (k = 0; k < nsupers; ++k) {
krow = PROW( k, grid );
if ( myrow == krow ) {
lk = LBi( k, grid ); /* Local block number. */
kcol = PCOL( k, grid ); /* Root process in this row scope. */
if ( mycol != kcol && bmod[lk] )
i = 1; /* Contribution from non-diagonal process. */
else i = 0;
MPI_Reduce( &i, &brecv[lk], 1, mpi_int_t,
MPI_SUM, kcol, scp->comm );
if ( mycol == kcol ) { /* Diagonal process. */
nbrecvmod += brecv[lk];
if ( !brecv[lk] && !bmod[lk] ) ++nroot;
#if ( DEBUGlevel>=2 )
printf("(%2d) brecv[%4d] %2d\n", iam, k, brecv[lk]);
assert( brecv[lk] < Pc );
#endif
}
}
}
}
/* Re-initialize lsum to zero. Each block header is already in place. */
for (k = 0; k < nsupers; ++k) {
krow = PROW( k, grid );
if ( myrow == krow ) {
knsupc = SuperSize( k );
lk = LBi( k, grid );
il = LSUM_BLK( lk );
dest = &lsum[il];
RHS_ITERATE(j) {
for (i = 0; i < knsupc; ++i) dest[i + j*knsupc] = zero;
}
}
}
int_t
pzReDistribute_B_to_X(doublecomplex *B, int_t m_loc, int nrhs, int_t ldb,
int_t fst_row, int_t *ilsum, doublecomplex *x,
ScalePermstruct_t *ScalePermstruct,
Glu_persist_t *Glu_persist,
gridinfo_t *grid, SOLVEstruct_t *SOLVEstruct)
{
/*
* Purpose
* =======
* Re-distribute B on the diagonal processes of the 2D process mesh.
*
* Note
* ====
* This routine can only be called after the routine pxgstrs_init(),
* in which the structures of the send and receive buffers are set up.
*
* Arguments
* =========
*
* B (input) doublecomplex*
* The distributed right-hand side matrix of the possibly
* equilibrated system.
*
* m_loc (input) int (local)
* The local row dimension of matrix B.
*
* nrhs (input) int (global)
* Number of right-hand sides.
*
* ldb (input) int (local)
* Leading dimension of matrix B.
*
* fst_row (input) int (global)
* The row number of B's first row in the global matrix.
*
* ilsum (input) int* (global)
* Starting position of each supernode in a full array.
*
* x (output) doublecomplex*
* The solution vector. It is valid only on the diagonal processes.
*
* ScalePermstruct (input) ScalePermstruct_t*
* The data structure to store the scaling and permutation vectors
* describing the transformations performed to the original matrix A.
*
* grid (input) gridinfo_t*
* The 2D process mesh.
*
* SOLVEstruct (input) SOLVEstruct_t*
* Contains the information for the communication during the
* solution phase.
*
* Return value
* ============
*
*/
int *SendCnt, *SendCnt_nrhs, *RecvCnt, *RecvCnt_nrhs;
int *sdispls, *sdispls_nrhs, *rdispls, *rdispls_nrhs;
int *ptr_to_ibuf, *ptr_to_dbuf;
int_t *perm_r, *perm_c; /* row and column permutation vectors */
int_t *send_ibuf, *recv_ibuf;
doublecomplex *send_dbuf, *recv_dbuf;
int_t *xsup, *supno;
int_t i, ii, irow, gbi, j, jj, k, knsupc, l, lk;
int p, procs;
pxgstrs_comm_t *gstrs_comm = SOLVEstruct->gstrs_comm;
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(grid->iam, "Enter pzReDistribute_B_to_X()");
#endif
/* ------------------------------------------------------------
INITIALIZATION.
------------------------------------------------------------*/
perm_r = ScalePermstruct->perm_r;
perm_c = ScalePermstruct->perm_c;
procs = grid->nprow * grid->npcol;
xsup = Glu_persist->xsup;
supno = Glu_persist->supno;
SendCnt = gstrs_comm->B_to_X_SendCnt;
SendCnt_nrhs = gstrs_comm->B_to_X_SendCnt + procs;
RecvCnt = gstrs_comm->B_to_X_SendCnt + 2*procs;
RecvCnt_nrhs = gstrs_comm->B_to_X_SendCnt + 3*procs;
sdispls = gstrs_comm->B_to_X_SendCnt + 4*procs;
sdispls_nrhs = gstrs_comm->B_to_X_SendCnt + 5*procs;
rdispls = gstrs_comm->B_to_X_SendCnt + 6*procs;
rdispls_nrhs = gstrs_comm->B_to_X_SendCnt + 7*procs;
ptr_to_ibuf = gstrs_comm->ptr_to_ibuf;
ptr_to_dbuf = gstrs_comm->ptr_to_dbuf;
/* ------------------------------------------------------------
NOW COMMUNICATE THE ACTUAL DATA.
------------------------------------------------------------*/
k = sdispls[procs-1] + SendCnt[procs-1]; /* Total number of sends */
l = rdispls[procs-1] + RecvCnt[procs-1]; /* Total number of receives */
if ( !(send_ibuf = intMalloc_dist(k + l)) )
ABORT("Malloc fails for send_ibuf[].");
recv_ibuf = send_ibuf + k;
if ( !(send_dbuf = doublecomplexMalloc_dist((k + l)* (size_t)nrhs)) )
ABORT("Malloc fails for send_dbuf[].");
recv_dbuf = send_dbuf + k * nrhs;
for (p = 0; p < procs; ++p) {
ptr_to_ibuf[p] = sdispls[p];
ptr_to_dbuf[p] = sdispls[p] * nrhs;
}
/* Copy the row indices and values to the send buffer. */
for (i = 0, l = fst_row; i < m_loc; ++i, ++l) {
irow = perm_c[perm_r[l]]; /* Row number in Pc*Pr*B */
gbi = BlockNum( irow );
p = PNUM( PROW(gbi,grid), PCOL(gbi,grid), grid ); /* Diagonal process */
k = ptr_to_ibuf[p];
send_ibuf[k] = irow;
k = ptr_to_dbuf[p];
RHS_ITERATE(j) { /* RHS is stored in row major in the buffer. */
send_dbuf[k++] = B[i + j*ldb];
}
++ptr_to_ibuf[p];
ptr_to_dbuf[p] += nrhs;
}
/* Communicate the (permuted) row indices. */
MPI_Alltoallv(send_ibuf, SendCnt, sdispls, mpi_int_t,
recv_ibuf, RecvCnt, rdispls, mpi_int_t, grid->comm);
/* Communicate the numerical values. */
MPI_Alltoallv(send_dbuf, SendCnt_nrhs, sdispls_nrhs, SuperLU_MPI_DOUBLE_COMPLEX,
recv_dbuf, RecvCnt_nrhs, rdispls_nrhs, SuperLU_MPI_DOUBLE_COMPLEX,
grid->comm);
/* ------------------------------------------------------------
Copy buffer into X on the diagonal processes.
------------------------------------------------------------*/
ii = 0;
for (p = 0; p < procs; ++p) {
jj = rdispls_nrhs[p];
for (i = 0; i < RecvCnt[p]; ++i) {
/* Only the diagonal processes do this; the off-diagonal processes
have 0 RecvCnt. */
irow = recv_ibuf[ii]; /* The permuted row index. */
k = BlockNum( irow );
knsupc = SuperSize( k );
lk = LBi( k, grid ); /* Local block number. */
l = X_BLK( lk );
x[l - XK_H].r = k; /* Block number prepended in the header. */
x[l - XK_H].i = 0;
irow = irow - FstBlockC(k); /* Relative row number in X-block */
RHS_ITERATE(j) {
x[l + irow + j*knsupc] = recv_dbuf[jj++];
}
++ii;
}
}
SUPERLU_FREE(send_ibuf);
SUPERLU_FREE(send_dbuf);
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(grid->iam, "Exit pzReDistribute_B_to_X()");
#endif
return 0;
} /* pzReDistribute_B_to_X */
int_t
pzReDistribute_B_to_X(doublecomplex *B, int_t m_loc, int nrhs, int_t ldb,
int_t fst_row, int_t *ilsum, doublecomplex *x,
ScalePermstruct_t *ScalePermstruct,
Glu_persist_t *Glu_persist,
gridinfo_t *grid, SOLVEstruct_t *SOLVEstruct)
{
int *SendCnt, *SendCnt_nrhs, *RecvCnt, *RecvCnt_nrhs;
int *sdispls, *sdispls_nrhs, *rdispls, *rdispls_nrhs;
int *ptr_to_ibuf, *ptr_to_dbuf;
int_t *perm_r, *perm_c; /* row and column permutation vectors */
int_t *send_ibuf, *recv_ibuf;
doublecomplex *send_dbuf, *recv_dbuf;
int_t *xsup, *supno;
int_t i, ii, irow, gbi, j, jj, k, knsupc, l, lk;
int p, procs;
pxgstrs_comm_t *gstrs_comm = SOLVEstruct->gstrs_comm;
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(grid->iam, "Enter pzReDistribute_B_to_X()");
#endif
/* ------------------------------------------------------------
INITIALIZATION.
------------------------------------------------------------*/
perm_r = ScalePermstruct->perm_r;
perm_c = ScalePermstruct->perm_c;
procs = grid->nprow * grid->npcol;
xsup = Glu_persist->xsup;
supno = Glu_persist->supno;
SendCnt = gstrs_comm->B_to_X_SendCnt;
SendCnt_nrhs = gstrs_comm->B_to_X_SendCnt + procs;
RecvCnt = gstrs_comm->B_to_X_SendCnt + 2*procs;
RecvCnt_nrhs = gstrs_comm->B_to_X_SendCnt + 3*procs;
sdispls = gstrs_comm->B_to_X_SendCnt + 4*procs;
sdispls_nrhs = gstrs_comm->B_to_X_SendCnt + 5*procs;
rdispls = gstrs_comm->B_to_X_SendCnt + 6*procs;
rdispls_nrhs = gstrs_comm->B_to_X_SendCnt + 7*procs;
ptr_to_ibuf = gstrs_comm->ptr_to_ibuf;
ptr_to_dbuf = gstrs_comm->ptr_to_dbuf;
/* ------------------------------------------------------------
NOW COMMUNICATE THE ACTUAL DATA.
------------------------------------------------------------*/
k = sdispls[procs-1] + SendCnt[procs-1]; /* Total number of sends */
l = rdispls[procs-1] + RecvCnt[procs-1]; /* Total number of receives */
if ( !(send_ibuf = intMalloc_dist(k + l)) )
ABORT("Malloc fails for send_ibuf[].");
recv_ibuf = send_ibuf + k;
if ( !(send_dbuf = doublecomplexMalloc_dist((k + l)* (size_t)nrhs)) )
ABORT("Malloc fails for send_dbuf[].");
recv_dbuf = send_dbuf + k * nrhs;
for (p = 0; p < procs; ++p) {
ptr_to_ibuf[p] = sdispls[p];
ptr_to_dbuf[p] = sdispls[p] * nrhs;
}
/* Copy the row indices and values to the send buffer. */
for (i = 0, l = fst_row; i < m_loc; ++i, ++l) {
irow = perm_c[perm_r[l]]; /* Row number in Pc*Pr*B */
gbi = BlockNum( irow );
p = PNUM( PROW(gbi,grid), PCOL(gbi,grid), grid ); /* Diagonal process */
k = ptr_to_ibuf[p];
send_ibuf[k] = irow;
k = ptr_to_dbuf[p];
RHS_ITERATE(j) { /* RHS is stored in row major in the buffer. */
send_dbuf[k++] = B[i + j*ldb];
}
++ptr_to_ibuf[p];
ptr_to_dbuf[p] += nrhs;
}
/* Communicate the (permuted) row indices. */
MPI_Alltoallv(send_ibuf, SendCnt, sdispls, mpi_int_t,
recv_ibuf, RecvCnt, rdispls, mpi_int_t, grid->comm);
/* Communicate the numerical values. */
MPI_Alltoallv(send_dbuf, SendCnt_nrhs, sdispls_nrhs, SuperLU_MPI_DOUBLE_COMPLEX,
recv_dbuf, RecvCnt_nrhs, rdispls_nrhs, SuperLU_MPI_DOUBLE_COMPLEX,
grid->comm);
/* ------------------------------------------------------------
Copy buffer into X on the diagonal processes.
------------------------------------------------------------*/
ii = 0;
for (p = 0; p < procs; ++p) {
jj = rdispls_nrhs[p];
for (i = 0; i < RecvCnt[p]; ++i) {
/* Only the diagonal processes do this; the off-diagonal processes
have 0 RecvCnt. */
irow = recv_ibuf[ii]; /* The permuted row index. */
k = BlockNum( irow );
knsupc = SuperSize( k );
lk = LBi( k, grid ); /* Local block number. */
l = X_BLK( lk );
x[l - XK_H].r = k; /* Block number prepended in the header. */
x[l - XK_H].i = 0;
irow = irow - FstBlockC(k); /* Relative row number in X-block */
RHS_ITERATE(j) {
x[l + irow + j*knsupc] = recv_dbuf[jj++];
}
++ii;
}
}
SUPERLU_FREE(send_ibuf);
SUPERLU_FREE(send_dbuf);
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(grid->iam, "Exit pzReDistribute_B_to_X()");
#endif
return 0;
} /* pzReDistribute_B_to_X */
/*! \brief
*
* <pre>
* Purpose
* =======
* Perform parallel triangular solves
* U(k,:) := A(k,:) \ L(k,k).
* Only the process column that owns block column *k* participates
* in the work.
*
* Arguments
* =========
*
* m (input) int (global)
* Number of rows in the matrix.
*
* k (input) int (global)
* The row number of the block row to be factorized.
*
* Glu_persist (input) Glu_persist_t*
* Global data structures (xsup, supno) replicated on all processes.
*
* grid (input) gridinfo_t*
* The 2D process mesh.
*
* Llu (input/output) LocalLU_t*
* Local data structures to store distributed L and U matrices.
*
* stat (output) SuperLUStat_t*
* Record the statistics about the factorization;
* See SuperLUStat_t structure defined in util.h.
* </pre>
*/
static void pdgstrs2
/************************************************************************/
#ifdef _CRAY
(
int_t m, int_t k, Glu_persist_t *Glu_persist, gridinfo_t *grid,
LocalLU_t *Llu, SuperLUStat_t *stat, _fcd ftcs1, _fcd ftcs2, _fcd ftcs3
)
#else
(
int_t m, int_t k, Glu_persist_t *Glu_persist, gridinfo_t *grid,
LocalLU_t *Llu, SuperLUStat_t *stat
)
#endif
{
int iam, pkk;
int incx = 1;
int nsupr; /* number of rows in the block L(:,k) (LDA) */
int segsize;
int_t nsupc; /* number of columns in the block */
int_t luptr, iukp, rukp;
int_t b, gb, j, klst, knsupc, lk, nb;
int_t *xsup = Glu_persist->xsup;
int_t *usub;
double *lusup, *uval;
/* Quick return. */
lk = LBi( k, grid ); /* Local block number */
if ( !Llu->Unzval_br_ptr[lk] ) return;
/* Initialization. */
iam = grid->iam;
pkk = PNUM( PROW(k, grid), PCOL(k, grid), grid );
klst = FstBlockC( k+1 );
knsupc = SuperSize( k );
usub = Llu->Ufstnz_br_ptr[lk]; /* index[] of block row U(k,:) */
uval = Llu->Unzval_br_ptr[lk];
nb = usub[0];
iukp = BR_HEADER;
rukp = 0;
if ( iam == pkk ) {
lk = LBj( k, grid );
nsupr = Llu->Lrowind_bc_ptr[lk][1]; /* LDA of lusup[] */
lusup = Llu->Lnzval_bc_ptr[lk];
} else {
nsupr = Llu->Lsub_buf_2[k%2][1]; /* LDA of lusup[] */
lusup = Llu->Lval_buf_2[k%2];
}
/* Loop through all the row blocks. */
for (b = 0; b < nb; ++b) {
gb = usub[iukp];
nsupc = SuperSize( gb );
iukp += UB_DESCRIPTOR;
/* Loop through all the segments in the block. */
for (j = 0; j < nsupc; ++j) {
segsize = klst - usub[iukp++];
if ( segsize ) { /* Nonzero segment. */
luptr = (knsupc - segsize) * (nsupr + 1);
#ifdef _CRAY
STRSV(ftcs1, ftcs2, ftcs3, &segsize, &lusup[luptr], &nsupr,
&uval[rukp], &incx);
#else
dtrsv_("L", "N", "U", &segsize, &lusup[luptr], &nsupr,
&uval[rukp], &incx);
#endif
stat->ops[FACT] += segsize * (segsize + 1);
rukp += segsize;
}
}
} /* for b ... */
} /* PDGSTRS2 */
/*! \brief
*
* <pre>
* Purpose
* =======
* Factor diagonal and subdiagonal blocks and test for exact singularity.
* Only the process column that owns block column *k* participates
* in the work.
*
* Arguments
* =========
*
* k (input) int (global)
* The column number of the block column to be factorized.
*
* thresh (input) double (global)
* The threshold value = s_eps * anorm.
*
* Glu_persist (input) Glu_persist_t*
* Global data structures (xsup, supno) replicated on all processes.
*
* grid (input) gridinfo_t*
* The 2D process mesh.
*
* Llu (input/output) LocalLU_t*
* Local data structures to store distributed L and U matrices.
*
* stat (output) SuperLUStat_t*
* Record the statistics about the factorization.
* See SuperLUStat_t structure defined in util.h.
*
* info (output) int*
* = 0: successful exit
* < 0: if info = -i, the i-th argument had an illegal value
* > 0: if info = i, U(i,i) is exactly zero. The factorization has
* been completed, but the factor U is exactly singular,
* and division by zero will occur if it is used to solve a
* system of equations.
* </pre>
*/
static void pdgstrf2
/************************************************************************/
(
superlu_options_t *options,
int_t k, double thresh, Glu_persist_t *Glu_persist, gridinfo_t *grid,
LocalLU_t *Llu, SuperLUStat_t *stat, int* info
)
{
int c, iam, l, pkk;
int incx = 1, incy = 1;
int nsupr; /* number of rows in the block (LDA) */
int luptr;
int_t i, krow, j, jfst, jlst;
int_t nsupc; /* number of columns in the block */
int_t *xsup = Glu_persist->xsup;
double *lusup, temp;
double *ujrow;
double alpha = -1;
*info = 0;
/* Quick return. */
/* Initialization. */
iam = grid->iam;
krow = PROW( k, grid );
pkk = PNUM( PROW(k, grid), PCOL(k, grid), grid );
j = LBj( k, grid ); /* Local block number */
jfst = FstBlockC( k );
jlst = FstBlockC( k+1 );
lusup = Llu->Lnzval_bc_ptr[j];
nsupc = SuperSize( k );
if ( Llu->Lrowind_bc_ptr[j] ) nsupr = Llu->Lrowind_bc_ptr[j][1];
ujrow = Llu->ujrow;
luptr = 0; /* Point to the diagonal entries. */
c = nsupc;
for (j = 0; j < jlst - jfst; ++j) {
/* Broadcast the j-th row (nsupc - j) elements to
the process column. */
if ( iam == pkk ) { /* Diagonal process. */
i = luptr;
if ( options->ReplaceTinyPivot == YES || lusup[i] == 0.0 ) {
if ( fabs(lusup[i]) < thresh ) { /* Diagonal */
#if ( PRNTlevel>=2 )
printf("(%d) .. col %d, tiny pivot %e ",
iam, jfst+j, lusup[i]);
#endif
/* Keep the replaced diagonal with the same sign. */
if ( lusup[i] < 0 ) lusup[i] = -thresh;
else lusup[i] = thresh;
#if ( PRNTlevel>=2 )
printf("replaced by %e\n", lusup[i]);
#endif
++(stat->TinyPivots);
}
}
for (l = 0; l < c; ++l, i += nsupr) ujrow[l] = lusup[i];
}
#if 0
dbcast_col(ujrow, c, pkk, UjROW, grid, &c);
#else
MPI_Bcast(ujrow, c, MPI_DOUBLE, krow, (grid->cscp).comm);
/*bcast_tree(ujrow, c, MPI_DOUBLE, krow, (24*k+j)%NTAGS,
grid, COMM_COLUMN, &c);*/
#endif
#if ( DEBUGlevel>=2 )
if ( k == 3329 && j == 2 ) {
if ( iam == pkk ) {
printf("..(%d) k %d, j %d: Send ujrow[0] %e\n",iam,k,j,ujrow[0]);
} else {
printf("..(%d) k %d, j %d: Recv ujrow[0] %e\n",iam,k,j,ujrow[0]);
}
}
#endif
if ( !lusup ) { /* Empty block column. */
--c;
if ( ujrow[0] == 0.0 ) *info = j+jfst+1;
continue;
}
/* Test for singularity. */
if ( ujrow[0] == 0.0 ) {
*info = j+jfst+1;
} else {
/* Scale the j-th column of the matrix. */
temp = 1.0 / ujrow[0];
if ( iam == pkk ) {
for (i = luptr+1; i < luptr-j+nsupr; ++i) lusup[i] *= temp;
stat->ops[FACT] += nsupr-j-1;
} else {
for (i = luptr; i < luptr+nsupr; ++i) lusup[i] *= temp;
stat->ops[FACT] += nsupr;
}
}
/* Rank-1 update of the trailing submatrix. */
if ( --c ) {
if ( iam == pkk ) {
l = nsupr - j - 1;
#ifdef _CRAY
SGER(&l, &c, &alpha, &lusup[luptr+1], &incx,
&ujrow[1], &incy, &lusup[luptr+nsupr+1], &nsupr);
#else
dger_(&l, &c, &alpha, &lusup[luptr+1], &incx,
&ujrow[1], &incy, &lusup[luptr+nsupr+1], &nsupr);
#endif
stat->ops[FACT] += 2 * l * c;
} else {
#ifdef _CRAY
SGER(&nsupr, &c, &alpha, &lusup[luptr], &incx,
&ujrow[1], &incy, &lusup[luptr+nsupr], &nsupr);
#else
dger_(&nsupr, &c, &alpha, &lusup[luptr], &incx,
&ujrow[1], &incy, &lusup[luptr+nsupr], &nsupr);
#endif
stat->ops[FACT] += 2 * nsupr * c;
}
}
/* Move to the next column. */
if ( iam == pkk ) luptr += nsupr + 1;
else luptr += nsupr;
} /* for j ... */
} /* PDGSTRF2 */
void
pzgstrs(int_t n, LUstruct_t *LUstruct,
ScalePermstruct_t *ScalePermstruct,
gridinfo_t *grid, doublecomplex *B,
int_t m_loc, int_t fst_row, int_t ldb, int nrhs,
SOLVEstruct_t *SOLVEstruct,
SuperLUStat_t *stat, int *info)
{
Glu_persist_t *Glu_persist = LUstruct->Glu_persist;
LocalLU_t *Llu = LUstruct->Llu;
doublecomplex alpha = {1.0, 0.0};
doublecomplex zero = {0.0, 0.0};
doublecomplex *lsum; /* Local running sum of the updates to B-components */
doublecomplex *x; /* X component at step k. */
/* NOTE: x and lsum are of same size. */
doublecomplex *lusup, *dest;
doublecomplex *recvbuf, *tempv;
doublecomplex *rtemp; /* Result of full matrix-vector multiply. */
int_t **Ufstnz_br_ptr = Llu->Ufstnz_br_ptr;
int_t *Urbs, *Urbs1; /* Number of row blocks in each block column of U. */
Ucb_indptr_t **Ucb_indptr;/* Vertical linked list pointing to Uindex[] */
int_t **Ucb_valptr; /* Vertical linked list pointing to Unzval[] */
int_t iam, kcol, krow, mycol, myrow;
int_t i, ii, il, j, jj, k, lb, ljb, lk, lptr, luptr;
int_t nb, nlb, nub, nsupers;
int_t *xsup, *supno, *lsub, *usub;
int_t *ilsum; /* Starting position of each supernode in lsum (LOCAL)*/
int_t Pc, Pr;
int knsupc, nsupr;
int ldalsum; /* Number of lsum entries locally owned. */
int maxrecvsz, p, pi;
int_t **Lrowind_bc_ptr;
doublecomplex **Lnzval_bc_ptr;
MPI_Status status;
MPI_Request *send_req, recv_req;
pxgstrs_comm_t *gstrs_comm = SOLVEstruct->gstrs_comm;
/*-- Counts used for L-solve --*/
int_t *fmod; /* Modification count for L-solve --
Count the number of local block products to
be summed into lsum[lk]. */
int_t **fsendx_plist = Llu->fsendx_plist;
int_t nfrecvx = Llu->nfrecvx; /* Number of X components to be recv'd. */
int_t *frecv; /* Count of lsum[lk] contributions to be received
from processes in this row.
It is only valid on the diagonal processes. */
int_t nfrecvmod = 0; /* Count of total modifications to be recv'd. */
int_t nleaf = 0, nroot = 0;
/*-- Counts used for U-solve --*/
int_t *bmod; /* Modification count for U-solve. */
int_t **bsendx_plist = Llu->bsendx_plist;
int_t nbrecvx = Llu->nbrecvx; /* Number of X components to be recv'd. */
int_t *brecv; /* Count of modifications to be recv'd from
processes in this row. */
int_t nbrecvmod = 0; /* Count of total modifications to be recv'd. */
double t;
#if ( DEBUGlevel>=2 )
int_t Ublocks = 0;
#endif
int_t *mod_bit = Llu->mod_bit; /* flag contribution from each row block */
t = SuperLU_timer_();
/* Test input parameters. */
*info = 0;
if ( n < 0 ) *info = -1;
else if ( nrhs < 0 ) *info = -9;
if ( *info ) {
pxerbla("PZGSTRS", grid, -*info);
return;
}
/*
* Initialization.
*/
iam = grid->iam;
Pc = grid->npcol;
Pr = grid->nprow;
myrow = MYROW( iam, grid );
mycol = MYCOL( iam, grid );
xsup = Glu_persist->xsup;
supno = Glu_persist->supno;
nsupers = supno[n-1] + 1;
Lrowind_bc_ptr = Llu->Lrowind_bc_ptr;
Lnzval_bc_ptr = Llu->Lnzval_bc_ptr;
nlb = CEILING( nsupers, Pr ); /* Number of local block rows. */
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(iam, "Enter pzgstrs()");
#endif
stat->ops[SOLVE] = 0.0;
Llu->SolveMsgSent = 0;
/* Save the count to be altered so it can be used by
subsequent call to PDGSTRS. */
if ( !(fmod = intMalloc_dist(nlb)) )
ABORT("Calloc fails for fmod[].");
for (i = 0; i < nlb; ++i) fmod[i] = Llu->fmod[i];
if ( !(frecv = intMalloc_dist(nlb)) )
ABORT("Malloc fails for frecv[].");
Llu->frecv = frecv;
k = SUPERLU_MAX( Llu->nfsendx, Llu->nbsendx ) + nlb;
if ( !(send_req = (MPI_Request*) SUPERLU_MALLOC(k*sizeof(MPI_Request))) )
ABORT("Malloc fails for send_req[].");
#ifdef _CRAY
ftcs1 = _cptofcd("L", strlen("L"));
ftcs2 = _cptofcd("N", strlen("N"));
ftcs3 = _cptofcd("U", strlen("U"));
#endif
/* Obtain ilsum[] and ldalsum for process column 0. */
ilsum = Llu->ilsum;
ldalsum = Llu->ldalsum;
/* Allocate working storage. */
knsupc = sp_ienv_dist(3);
maxrecvsz = knsupc * nrhs + SUPERLU_MAX( XK_H, LSUM_H );
if ( !(lsum = doublecomplexCalloc_dist(((size_t)ldalsum)*nrhs + nlb*LSUM_H)) )
ABORT("Calloc fails for lsum[].");
if ( !(x = doublecomplexMalloc_dist(ldalsum * nrhs + nlb * XK_H)) )
ABORT("Malloc fails for x[].");
if ( !(recvbuf = doublecomplexMalloc_dist(maxrecvsz)) )
ABORT("Malloc fails for recvbuf[].");
if ( !(rtemp = doublecomplexCalloc_dist(maxrecvsz)) )
ABORT("Malloc fails for rtemp[].");
/*---------------------------------------------------
* Forward solve Ly = b.
*---------------------------------------------------*/
/* Redistribute B into X on the diagonal processes. */
pzReDistribute_B_to_X(B, m_loc, nrhs, ldb, fst_row, ilsum, x,
ScalePermstruct, Glu_persist, grid, SOLVEstruct);
/* Set up the headers in lsum[]. */
ii = 0;
for (k = 0; k < nsupers; ++k) {
knsupc = SuperSize( k );
krow = PROW( k, grid );
if ( myrow == krow ) {
lk = LBi( k, grid ); /* Local block number. */
il = LSUM_BLK( lk );
lsum[il - LSUM_H].r = k;/* Block number prepended in the header.*/
lsum[il - LSUM_H].i = 0;
}
ii += knsupc;
}
/*
* Compute frecv[] and nfrecvmod counts on the diagonal processes.
*/
{
superlu_scope_t *scp = &grid->rscp;
#if 1
for (k = 0; k < nlb; ++k) mod_bit[k] = 0;
for (k = 0; k < nsupers; ++k) {
krow = PROW( k, grid );
if ( myrow == krow ) {
lk = LBi( k, grid ); /* local block number */
kcol = PCOL( k, grid );
if ( mycol != kcol && fmod[lk] )
mod_bit[lk] = 1; /* contribution from off-diagonal */
}
}
/*PrintInt10("mod_bit", nlb, mod_bit);*/
#if ( PROFlevel>=2 )
t_reduce_tmp = SuperLU_timer_();
#endif
/* Every process receives the count, but it is only useful on the
diagonal processes. */
MPI_Allreduce( mod_bit, frecv, nlb, mpi_int_t, MPI_SUM, scp->comm );
#if ( PROFlevel>=2 )
t_reduce += SuperLU_timer_() - t_reduce_tmp;
#endif
for (k = 0; k < nsupers; ++k) {
krow = PROW( k, grid );
if ( myrow == krow ) {
lk = LBi( k, grid ); /* local block number */
kcol = PCOL( k, grid );
if ( mycol == kcol ) { /* diagonal process */
nfrecvmod += frecv[lk];
if ( !frecv[lk] && !fmod[lk] ) ++nleaf;
}
}
}
#else /* old */
for (k = 0; k < nsupers; ++k) {
krow = PROW( k, grid );
if ( myrow == krow ) {
lk = LBi( k, grid ); /* Local block number. */
kcol = PCOL( k, grid ); /* Root process in this row scope. */
if ( mycol != kcol && fmod[lk] )
i = 1; /* Contribution from non-diagonal process. */
else i = 0;
MPI_Reduce( &i, &frecv[lk], 1, mpi_int_t,
MPI_SUM, kcol, scp->comm );
if ( mycol == kcol ) { /* Diagonal process. */
nfrecvmod += frecv[lk];
if ( !frecv[lk] && !fmod[lk] ) ++nleaf;
#if ( DEBUGlevel>=2 )
printf("(%2d) frecv[%4d] %2d\n", iam, k, frecv[lk]);
assert( frecv[lk] < Pc );
#endif
}
}
}
#endif
}
/* ---------------------------------------------------------
Solve the leaf nodes first by all the diagonal processes.
--------------------------------------------------------- */
#if ( DEBUGlevel>=2 )
printf("(%2d) nleaf %4d\n", iam, nleaf);
#endif
for (k = 0; k < nsupers && nleaf; ++k) {
krow = PROW( k, grid );
kcol = PCOL( k, grid );
if ( myrow == krow && mycol == kcol ) { /* Diagonal process */
knsupc = SuperSize( k );
lk = LBi( k, grid );
if ( frecv[lk]==0 && fmod[lk]==0 ) {
fmod[lk] = -1; /* Do not solve X[k] in the future. */
ii = X_BLK( lk );
lk = LBj( k, grid ); /* Local block number, column-wise. */
lsub = Lrowind_bc_ptr[lk];
lusup = Lnzval_bc_ptr[lk];
nsupr = lsub[1];
#ifdef _CRAY
CTRSM(ftcs1, ftcs1, ftcs2, ftcs3, &knsupc, &nrhs, &alpha,
lusup, &nsupr, &x[ii], &knsupc);
#elif defined (USE_VENDOR_BLAS)
ztrsm_("L", "L", "N", "U", &knsupc, &nrhs, &alpha,
lusup, &nsupr, &x[ii], &knsupc, 1, 1, 1, 1);
#else
ztrsm_("L", "L", "N", "U", &knsupc, &nrhs, &alpha,
lusup, &nsupr, &x[ii], &knsupc);
#endif
stat->ops[SOLVE] += 4 * knsupc * (knsupc - 1) * nrhs
+ 10 * knsupc * nrhs; /* complex division */
--nleaf;
#if ( DEBUGlevel>=2 )
printf("(%2d) Solve X[%2d]\n", iam, k);
#endif
/*
* Send Xk to process column Pc[k].
*/
for (p = 0; p < Pr; ++p) {
if ( fsendx_plist[lk][p] != EMPTY ) {
pi = PNUM( p, kcol, grid );
MPI_Isend( &x[ii - XK_H], knsupc * nrhs + XK_H,
SuperLU_MPI_DOUBLE_COMPLEX, pi, Xk, grid->comm,
&send_req[Llu->SolveMsgSent++]);
#if 0
MPI_Send( &x[ii - XK_H], knsupc * nrhs + XK_H,
SuperLU_MPI_DOUBLE_COMPLEX, pi, Xk, grid->comm );
#endif
#if ( DEBUGlevel>=2 )
printf("(%2d) Sent X[%2.0f] to P %2d\n",
iam, x[ii-XK_H], pi);
#endif
}
}
/*
* Perform local block modifications: lsum[i] -= L_i,k * X[k]
*/
nb = lsub[0] - 1;
lptr = BC_HEADER + LB_DESCRIPTOR + knsupc;
luptr = knsupc; /* Skip diagonal block L(k,k). */
zlsum_fmod(lsum, x, &x[ii], rtemp, nrhs, knsupc, k,
fmod, nb, lptr, luptr, xsup, grid, Llu,
send_req, stat);
}
} /* if diagonal process ... */
} /* for k ... */
/* -----------------------------------------------------------
Compute the internal nodes asynchronously by all processes.
----------------------------------------------------------- */
#if ( DEBUGlevel>=2 )
printf("(%2d) nfrecvx %4d, nfrecvmod %4d, nleaf %4d\n",
iam, nfrecvx, nfrecvmod, nleaf);
#endif
while ( nfrecvx || nfrecvmod ) { /* While not finished. */
/* Receive a message. */
MPI_Recv( recvbuf, maxrecvsz, SuperLU_MPI_DOUBLE_COMPLEX,
MPI_ANY_SOURCE, MPI_ANY_TAG, grid->comm, &status );
k = (*recvbuf).r;
#if ( DEBUGlevel>=2 )
printf("(%2d) Recv'd block %d, tag %2d\n", iam, k, status.MPI_TAG);
#endif
switch ( status.MPI_TAG ) {
case Xk:
--nfrecvx;
lk = LBj( k, grid ); /* Local block number, column-wise. */
lsub = Lrowind_bc_ptr[lk];
lusup = Lnzval_bc_ptr[lk];
if ( lsub ) {
nb = lsub[0];
lptr = BC_HEADER;
luptr = 0;
knsupc = SuperSize( k );
/*
* Perform local block modifications: lsum[i] -= L_i,k * X[k]
*/
zlsum_fmod(lsum, x, &recvbuf[XK_H], rtemp, nrhs, knsupc, k,
fmod, nb, lptr, luptr, xsup, grid, Llu,
send_req, stat);
} /* if lsub */
break;
case LSUM: /* Receiver must be a diagonal process */
--nfrecvmod;
lk = LBi( k, grid ); /* Local block number, row-wise. */
ii = X_BLK( lk );
knsupc = SuperSize( k );
tempv = &recvbuf[LSUM_H];
RHS_ITERATE(j) {
for (i = 0; i < knsupc; ++i)
z_add(&x[i + ii + j*knsupc],
&x[i + ii + j*knsupc],
&tempv[i + j*knsupc]);
}
if ( (--frecv[lk])==0 && fmod[lk]==0 ) {
fmod[lk] = -1; /* Do not solve X[k] in the future. */
lk = LBj( k, grid ); /* Local block number, column-wise. */
lsub = Lrowind_bc_ptr[lk];
lusup = Lnzval_bc_ptr[lk];
nsupr = lsub[1];
#ifdef _CRAY
CTRSM(ftcs1, ftcs1, ftcs2, ftcs3, &knsupc, &nrhs, &alpha,
lusup, &nsupr, &x[ii], &knsupc);
#elif defined (USE_VENDOR_BLAS)
ztrsm_("L", "L", "N", "U", &knsupc, &nrhs, &alpha,
lusup, &nsupr, &x[ii], &knsupc, 1, 1, 1, 1);
#else
ztrsm_("L", "L", "N", "U", &knsupc, &nrhs, &alpha,
lusup, &nsupr, &x[ii], &knsupc);
#endif
stat->ops[SOLVE] += 4 * knsupc * (knsupc - 1) * nrhs
+ 10 * knsupc * nrhs; /* complex division */
#if ( DEBUGlevel>=2 )
printf("(%2d) Solve X[%2d]\n", iam, k);
#endif
/*
* Send Xk to process column Pc[k].
*/
kcol = PCOL( k, grid );
for (p = 0; p < Pr; ++p) {
if ( fsendx_plist[lk][p] != EMPTY ) {
pi = PNUM( p, kcol, grid );
MPI_Isend( &x[ii-XK_H], knsupc * nrhs + XK_H,
SuperLU_MPI_DOUBLE_COMPLEX, pi, Xk, grid->comm,
&send_req[Llu->SolveMsgSent++]);
#if 0
MPI_Send( &x[ii - XK_H], knsupc * nrhs + XK_H,
SuperLU_MPI_DOUBLE_COMPLEX, pi, Xk, grid->comm );
#endif
#if ( DEBUGlevel>=2 )
printf("(%2d) Sent X[%2.0f] to P %2d\n",
iam, x[ii-XK_H], pi);
#endif
}
}
/*
* Perform local block modifications.
*/
nb = lsub[0] - 1;
lptr = BC_HEADER + LB_DESCRIPTOR + knsupc;
luptr = knsupc; /* Skip diagonal block L(k,k). */
zlsum_fmod(lsum, x, &x[ii], rtemp, nrhs, knsupc, k,
fmod, nb, lptr, luptr, xsup, grid, Llu,
send_req, stat);
} /* if */
break;
#if ( DEBUGlevel>=2 )
default:
printf("(%2d) Recv'd wrong message tag %4d\n", status.MPI_TAG);
break;
#endif
} /* switch */
} /* while not finished ... */
#if ( PRNTlevel>=2 )
t = SuperLU_timer_() - t;
if ( !iam ) printf(".. L-solve time\t%8.2f\n", t);
t = SuperLU_timer_();
#endif
#if ( DEBUGlevel==2 )
{
printf("(%d) .. After L-solve: y =\n", iam);
for (i = 0, k = 0; k < nsupers; ++k) {
krow = PROW( k, grid );
kcol = PCOL( k, grid );
if ( myrow == krow && mycol == kcol ) { /* Diagonal process */
knsupc = SuperSize( k );
lk = LBi( k, grid );
ii = X_BLK( lk );
for (j = 0; j < knsupc; ++j)
printf("\t(%d)\t%4d\t%.10f\n", iam, xsup[k]+j, x[ii+j]);
fflush(stdout);
}
MPI_Barrier( grid->comm );
}
}
#endif
SUPERLU_FREE(fmod);
SUPERLU_FREE(frecv);
SUPERLU_FREE(rtemp);
/*for (i = 0; i < Llu->SolveMsgSent; ++i) MPI_Request_free(&send_req[i]);*/
for (i = 0; i < Llu->SolveMsgSent; ++i) MPI_Wait(&send_req[i], &status);
Llu->SolveMsgSent = 0;
MPI_Barrier( grid->comm );
/*---------------------------------------------------
* Back solve Ux = y.
*
* The Y components from the forward solve is already
* on the diagonal processes.
*---------------------------------------------------*/
/* Save the count to be altered so it can be used by
subsequent call to PZGSTRS. */
if ( !(bmod = intMalloc_dist(nlb)) )
ABORT("Calloc fails for bmod[].");
for (i = 0; i < nlb; ++i) bmod[i] = Llu->bmod[i];
if ( !(brecv = intMalloc_dist(nlb)) )
ABORT("Malloc fails for brecv[].");
Llu->brecv = brecv;
/*
* Compute brecv[] and nbrecvmod counts on the diagonal processes.
*/
{
superlu_scope_t *scp = &grid->rscp;
#if 1
for (k = 0; k < nlb; ++k) mod_bit[k] = 0;
for (k = 0; k < nsupers; ++k) {
krow = PROW( k, grid );
if ( myrow == krow ) {
lk = LBi( k, grid ); /* local block number */
kcol = PCOL( k, grid ); /* root process in this row scope */
if ( mycol != kcol && bmod[lk] )
mod_bit[lk] = 1; /* Contribution from off-diagonal */
}
}
/* Every process receives the count, but it is only useful on the
diagonal processes. */
MPI_Allreduce( mod_bit, brecv, nlb, mpi_int_t, MPI_SUM, scp->comm );
for (k = 0; k < nsupers; ++k) {
krow = PROW( k, grid );
if ( myrow == krow ) {
lk = LBi( k, grid ); /* local block number */
kcol = PCOL( k, grid ); /* root process in this row scope. */
if ( mycol == kcol ) { /* diagonal process */
nbrecvmod += brecv[lk];
if ( !brecv[lk] && !bmod[lk] ) ++nroot;
#if ( DEBUGlevel>=2 )
printf("(%2d) brecv[%4d] %2d\n", iam, k, brecv[lk]);
assert( brecv[lk] < Pc );
#endif
}
}
}
#else /* old */
for (k = 0; k < nsupers; ++k) {
krow = PROW( k, grid );
if ( myrow == krow ) {
lk = LBi( k, grid ); /* Local block number. */
kcol = PCOL( k, grid ); /* Root process in this row scope. */
if ( mycol != kcol && bmod[lk] )
i = 1; /* Contribution from non-diagonal process. */
else i = 0;
MPI_Reduce( &i, &brecv[lk], 1, mpi_int_t,
MPI_SUM, kcol, scp->comm );
if ( mycol == kcol ) { /* Diagonal process. */
nbrecvmod += brecv[lk];
if ( !brecv[lk] && !bmod[lk] ) ++nroot;
#if ( DEBUGlevel>=2 )
printf("(%2d) brecv[%4d] %2d\n", iam, k, brecv[lk]);
assert( brecv[lk] < Pc );
#endif
}
}
}
#endif
}
/* Re-initialize lsum to zero. Each block header is already in place. */
for (k = 0; k < nsupers; ++k) {
krow = PROW( k, grid );
if ( myrow == krow ) {
knsupc = SuperSize( k );
lk = LBi( k, grid );
il = LSUM_BLK( lk );
dest = &lsum[il];
RHS_ITERATE(j) {
for (i = 0; i < knsupc; ++i) dest[i + j*knsupc] = zero;
}
}
}
int_t
dReDistribute_A(SuperMatrix *A, ScalePermstruct_t *ScalePermstruct,
Glu_freeable_t *Glu_freeable, int_t *xsup, int_t *supno,
gridinfo_t *grid, int_t *colptr[], int_t *rowind[],
double *a[])
{
/*
* -- Distributed SuperLU routine (version 2.0) --
* Lawrence Berkeley National Lab, Univ. of California Berkeley.
* March 15, 2003
*
* Purpose
* =======
* Re-distribute A on the 2D process mesh.
*
* Arguments
* =========
*
* A (input) SuperMatrix*
* The distributed input matrix A of dimension (A->nrow, A->ncol).
* A may be overwritten by diag(R)*A*diag(C)*Pc^T.
* The type of A can be: Stype = NR; Dtype = SLU_D; Mtype = GE.
*
* ScalePermstruct (input) ScalePermstruct_t*
* The data structure to store the scaling and permutation vectors
* describing the transformations performed to the original matrix A.
*
* Glu_freeable (input) *Glu_freeable_t
* The global structure describing the graph of L and U.
*
* grid (input) gridinfo_t*
* The 2D process mesh.
*
* colptr (output) int*
*
* rowind (output) int*
*
* a (output) double*
*
* Return value
* ============
*
*/
NRformat_loc *Astore;
int_t *perm_r; /* row permutation vector */
int_t *perm_c; /* column permutation vector */
int_t i, irow, fst_row, j, jcol, k, gbi, gbj, n, m_loc, jsize;
int_t nnz_loc; /* number of local nonzeros */
int_t nnz_remote; /* number of remote nonzeros to be sent */
int_t SendCnt; /* number of remote nonzeros to be sent */
int_t RecvCnt; /* number of remote nonzeros to be sent */
int_t *nnzToSend, *nnzToRecv, maxnnzToRecv;
int_t *ia, *ja, **ia_send, *index, *itemp;
int_t *ptr_to_send;
double *aij, **aij_send, *nzval, *dtemp;
double *nzval_a;
int iam, it, p, procs;
MPI_Request *send_req;
MPI_Status status;
/* ------------------------------------------------------------
INITIALIZATION.
------------------------------------------------------------*/
iam = grid->iam;
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(iam, "Enter dReDistribute_A()");
#endif
perm_r = ScalePermstruct->perm_r;
perm_c = ScalePermstruct->perm_c;
procs = grid->nprow * grid->npcol;
Astore = (NRformat_loc *) A->Store;
n = A->ncol;
m_loc = Astore->m_loc;
fst_row = Astore->fst_row;
nnzToRecv = intCalloc_dist(2*procs);
nnzToSend = nnzToRecv + procs;
/* ------------------------------------------------------------
COUNT THE NUMBER OF NONZEROS TO BE SENT TO EACH PROCESS,
THEN ALLOCATE SPACE.
THIS ACCOUNTS FOR THE FIRST PASS OF A.
------------------------------------------------------------*/
for (i = 0; i < m_loc; ++i) {
for (j = Astore->rowptr[i]; j < Astore->rowptr[i+1]; ++j) {
irow = perm_c[perm_r[i+fst_row]]; /* Row number in Pc*Pr*A */
jcol = Astore->colind[j];
gbi = BlockNum( irow );
gbj = BlockNum( jcol );
p = PNUM( PROW(gbi,grid), PCOL(gbj,grid), grid );
++nnzToSend[p];
}
}
/* All-to-all communication */
MPI_Alltoall( nnzToSend, 1, mpi_int_t, nnzToRecv, 1, mpi_int_t,
grid->comm);
maxnnzToRecv = 0;
nnz_loc = SendCnt = RecvCnt = 0;
for (p = 0; p < procs; ++p) {
if ( p != iam ) {
SendCnt += nnzToSend[p];
RecvCnt += nnzToRecv[p];
maxnnzToRecv = SUPERLU_MAX( nnzToRecv[p], maxnnzToRecv );
} else {
nnz_loc += nnzToRecv[p];
/*assert(nnzToSend[p] == nnzToRecv[p]);*/
}
}
k = nnz_loc + RecvCnt; /* Total nonzeros ended up in my process. */
/* Allocate space for storing the triplets after redistribution. */
if ( !(ia = intMalloc_dist(2*k)) )
ABORT("Malloc fails for ia[].");
ja = ia + k;
if ( !(aij = doubleMalloc_dist(k)) )
ABORT("Malloc fails for aij[].");
/* Allocate temporary storage for sending/receiving the A triplets. */
if ( procs > 1 ) {
if ( !(send_req = (MPI_Request *)
SUPERLU_MALLOC(2*procs *sizeof(MPI_Request))) )
ABORT("Malloc fails for send_req[].");
if ( !(ia_send = (int_t **) SUPERLU_MALLOC(procs*sizeof(int_t*))) )
ABORT("Malloc fails for ia_send[].");
if ( !(aij_send = (double **)SUPERLU_MALLOC(procs*sizeof(double*))) )
ABORT("Malloc fails for aij_send[].");
if ( !(index = intMalloc_dist(2*SendCnt)) )
ABORT("Malloc fails for index[].");
if ( !(nzval = doubleMalloc_dist(SendCnt)) )
ABORT("Malloc fails for nzval[].");
if ( !(ptr_to_send = intCalloc_dist(procs)) )
ABORT("Malloc fails for ptr_to_send[].");
if ( !(itemp = intMalloc_dist(2*maxnnzToRecv)) )
ABORT("Malloc fails for itemp[].");
if ( !(dtemp = doubleMalloc_dist(maxnnzToRecv)) )
ABORT("Malloc fails for dtemp[].");
for (i = 0, j = 0, p = 0; p < procs; ++p) {
if ( p != iam ) {
ia_send[p] = &index[i];
i += 2 * nnzToSend[p]; /* ia/ja indices alternate */
aij_send[p] = &nzval[j];
j += nnzToSend[p];
}
}
} /* if procs > 1 */
if ( !(*colptr = intCalloc_dist(n+1)) )
ABORT("Malloc fails for *colptr[].");
/* ------------------------------------------------------------
LOAD THE ENTRIES OF A INTO THE (IA,JA,AIJ) STRUCTURES TO SEND.
THIS ACCOUNTS FOR THE SECOND PASS OF A.
------------------------------------------------------------*/
nnz_loc = 0; /* Reset the local nonzero count. */
nzval_a = Astore->nzval;
for (i = 0; i < m_loc; ++i) {
for (j = Astore->rowptr[i]; j < Astore->rowptr[i+1]; ++j) {
irow = perm_c[perm_r[i+fst_row]]; /* Row number in Pc*Pr*A */
jcol = Astore->colind[j];
gbi = BlockNum( irow );
gbj = BlockNum( jcol );
p = PNUM( PROW(gbi,grid), PCOL(gbj,grid), grid );
if ( p != iam ) { /* remote */
k = ptr_to_send[p];
ia_send[p][k] = irow;
ia_send[p][k + nnzToSend[p]] = jcol;
aij_send[p][k] = nzval_a[j];
++ptr_to_send[p];
} else { /* local */
ia[nnz_loc] = irow;
ja[nnz_loc] = jcol;
aij[nnz_loc] = nzval_a[j];
++nnz_loc;
++(*colptr)[jcol]; /* Count nonzeros in each column */
}
}
}
/* ------------------------------------------------------------
PERFORM REDISTRIBUTION. THIS INVOLVES ALL-TO-ALL COMMUNICATION.
NOTE: Can possibly use MPI_Alltoallv.
------------------------------------------------------------*/
for (p = 0; p < procs; ++p) {
if ( p != iam ) {
it = 2*nnzToSend[p];
MPI_Isend( ia_send[p], it, mpi_int_t,
p, iam, grid->comm, &send_req[p] );
it = nnzToSend[p];
MPI_Isend( aij_send[p], it, MPI_DOUBLE,
p, iam+procs, grid->comm, &send_req[procs+p] );
}
}
for (p = 0; p < procs; ++p) {
if ( p != iam ) {
it = 2*nnzToRecv[p];
MPI_Recv( itemp, it, mpi_int_t, p, p, grid->comm, &status );
it = nnzToRecv[p];
MPI_Recv( dtemp, it, MPI_DOUBLE, p, p+procs,
grid->comm, &status );
for (i = 0; i < nnzToRecv[p]; ++i) {
ia[nnz_loc] = itemp[i];
jcol = itemp[i + nnzToRecv[p]];
/*assert(jcol<n);*/
ja[nnz_loc] = jcol;
aij[nnz_loc] = dtemp[i];
++nnz_loc;
++(*colptr)[jcol]; /* Count nonzeros in each column */
}
}
}
for (p = 0; p < procs; ++p) {
if ( p != iam ) {
MPI_Wait( &send_req[p], &status);
MPI_Wait( &send_req[procs+p], &status);
}
}
/* ------------------------------------------------------------
DEALLOCATE TEMPORARY STORAGE
------------------------------------------------------------*/
SUPERLU_FREE(nnzToRecv);
if ( procs > 1 ) {
SUPERLU_FREE(send_req);
SUPERLU_FREE(ia_send);
SUPERLU_FREE(aij_send);
SUPERLU_FREE(index);
SUPERLU_FREE(nzval);
SUPERLU_FREE(ptr_to_send);
SUPERLU_FREE(itemp);
SUPERLU_FREE(dtemp);
}
/* ------------------------------------------------------------
CONVERT THE TRIPLET FORMAT INTO THE CCS FORMAT.
------------------------------------------------------------*/
if ( !(*rowind = intMalloc_dist(nnz_loc)) )
ABORT("Malloc fails for *rowind[].");
if ( !(*a = doubleMalloc_dist(nnz_loc)) )
ABORT("Malloc fails for *a[].");
/* Initialize the array of column pointers */
k = 0;
jsize = (*colptr)[0];
(*colptr)[0] = 0;
for (j = 1; j < n; ++j) {
k += jsize;
jsize = (*colptr)[j];
(*colptr)[j] = k;
}
/* Copy the triplets into the column oriented storage */
for (i = 0; i < nnz_loc; ++i) {
j = ja[i];
k = (*colptr)[j];
(*rowind)[k] = ia[i];
(*a)[k] = aij[i];
++(*colptr)[j];
}
/* Reset the column pointers to the beginning of each column */
for (j = n; j > 0; --j) (*colptr)[j] = (*colptr)[j-1];
(*colptr)[0] = 0;
SUPERLU_FREE(ia);
SUPERLU_FREE(aij);
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(iam, "Exit dReDistribute_A()");
#endif
} /* dReDistribute_A */
/*! \brief
*
* <pre>
* Purpose
* =======
* Set up the communication pattern for the triangular solution.
*
* Arguments
* =========
*
* n (input) int (global)
* The dimension of the linear system.
*
* m_loc (input) int (local)
* The local row dimension of the distributed input matrix.
*
* nrhs (input) int (global)
* Number of right-hand sides.
*
* fst_row (input) int (global)
* The row number of matrix B's first row in the global matrix.
*
* perm_r (input) int* (global)
* The row permutation vector.
*
* perm_c (input) int* (global)
* The column permutation vector.
*
* grid (input) gridinfo_t*
* The 2D process mesh.
* </pre>
*/
int_t
pxgstrs_init(int_t n, int_t m_loc, int_t nrhs, int_t fst_row,
int_t perm_r[], int_t perm_c[], gridinfo_t *grid,
Glu_persist_t *Glu_persist, SOLVEstruct_t *SOLVEstruct)
{
int *SendCnt, *SendCnt_nrhs, *RecvCnt, *RecvCnt_nrhs;
int *sdispls, *sdispls_nrhs, *rdispls, *rdispls_nrhs;
int *itemp, *ptr_to_ibuf, *ptr_to_dbuf;
int_t *row_to_proc;
int_t i, gbi, k, l, num_diag_procs, *diag_procs;
int_t irow, lk, q, knsupc, nsupers, *xsup, *supno;
int iam, p, pkk, procs;
pxgstrs_comm_t *gstrs_comm;
procs = grid->nprow * grid->npcol;
iam = grid->iam;
gstrs_comm = SOLVEstruct->gstrs_comm;
xsup = Glu_persist->xsup;
supno = Glu_persist->supno;
nsupers = Glu_persist->supno[n-1] + 1;
row_to_proc = SOLVEstruct->row_to_proc;
/* ------------------------------------------------------------
SET UP COMMUNICATION PATTERN FOR ReDistribute_B_to_X.
------------------------------------------------------------*/
if ( !(itemp = SUPERLU_MALLOC(8*procs * sizeof(int))) )
ABORT("Malloc fails for B_to_X_itemp[].");
SendCnt = itemp;
SendCnt_nrhs = itemp + procs;
RecvCnt = itemp + 2*procs;
RecvCnt_nrhs = itemp + 3*procs;
sdispls = itemp + 4*procs;
sdispls_nrhs = itemp + 5*procs;
rdispls = itemp + 6*procs;
rdispls_nrhs = itemp + 7*procs;
/* Count the number of elements to be sent to each diagonal process.*/
for (p = 0; p < procs; ++p) SendCnt[p] = 0;
for (i = 0, l = fst_row; i < m_loc; ++i, ++l) {
irow = perm_c[perm_r[l]]; /* Row number in Pc*Pr*B */
gbi = BlockNum( irow );
p = PNUM( PROW(gbi,grid), PCOL(gbi,grid), grid ); /* Diagonal process */
++SendCnt[p];
}
/* Set up the displacements for alltoall. */
MPI_Alltoall(SendCnt, 1, MPI_INT, RecvCnt, 1, MPI_INT, grid->comm);
sdispls[0] = rdispls[0] = 0;
for (p = 1; p < procs; ++p) {
sdispls[p] = sdispls[p-1] + SendCnt[p-1];
rdispls[p] = rdispls[p-1] + RecvCnt[p-1];
}
for (p = 0; p < procs; ++p) {
SendCnt_nrhs[p] = SendCnt[p] * nrhs;
sdispls_nrhs[p] = sdispls[p] * nrhs;
RecvCnt_nrhs[p] = RecvCnt[p] * nrhs;
rdispls_nrhs[p] = rdispls[p] * nrhs;
}
/* This is saved for repeated solves, and is freed in pxgstrs_finalize().*/
gstrs_comm->B_to_X_SendCnt = SendCnt;
/* ------------------------------------------------------------
SET UP COMMUNICATION PATTERN FOR ReDistribute_X_to_B.
------------------------------------------------------------*/
/* This is freed in pxgstrs_finalize(). */
if ( !(itemp = SUPERLU_MALLOC(8*procs * sizeof(int))) )
ABORT("Malloc fails for X_to_B_itemp[].");
SendCnt = itemp;
SendCnt_nrhs = itemp + procs;
RecvCnt = itemp + 2*procs;
RecvCnt_nrhs = itemp + 3*procs;
sdispls = itemp + 4*procs;
sdispls_nrhs = itemp + 5*procs;
rdispls = itemp + 6*procs;
rdispls_nrhs = itemp + 7*procs;
/* Count the number of X entries to be sent to each process.*/
for (p = 0; p < procs; ++p) SendCnt[p] = 0;
num_diag_procs = SOLVEstruct->num_diag_procs;
diag_procs = SOLVEstruct->diag_procs;
for (p = 0; p < num_diag_procs; ++p) { /* for all diagonal processes */
pkk = diag_procs[p];
if ( iam == pkk ) {
for (k = p; k < nsupers; k += num_diag_procs) {
knsupc = SuperSize( k );
lk = LBi( k, grid ); /* Local block number */
irow = FstBlockC( k );
for (i = 0; i < knsupc; ++i) {
#if 0
q = row_to_proc[inv_perm_c[irow]];
#else
q = row_to_proc[irow];
#endif
++SendCnt[q];
++irow;
}
}
}
}
MPI_Alltoall(SendCnt, 1, MPI_INT, RecvCnt, 1, MPI_INT, grid->comm);
sdispls[0] = rdispls[0] = 0;
sdispls_nrhs[0] = rdispls_nrhs[0] = 0;
SendCnt_nrhs[0] = SendCnt[0] * nrhs;
RecvCnt_nrhs[0] = RecvCnt[0] * nrhs;
for (p = 1; p < procs; ++p) {
sdispls[p] = sdispls[p-1] + SendCnt[p-1];
rdispls[p] = rdispls[p-1] + RecvCnt[p-1];
sdispls_nrhs[p] = sdispls[p] * nrhs;
rdispls_nrhs[p] = rdispls[p] * nrhs;
SendCnt_nrhs[p] = SendCnt[p] * nrhs;
RecvCnt_nrhs[p] = RecvCnt[p] * nrhs;
}
/* This is saved for repeated solves, and is freed in pxgstrs_finalize().*/
gstrs_comm->X_to_B_SendCnt = SendCnt;
if ( !(ptr_to_ibuf = SUPERLU_MALLOC(2*procs * sizeof(int))) )
ABORT("Malloc fails for ptr_to_ibuf[].");
gstrs_comm->ptr_to_ibuf = ptr_to_ibuf;
gstrs_comm->ptr_to_dbuf = ptr_to_ibuf + procs;
} /* PXGSTRS_INIT */
/*! \brief
*
* <pre>
* Purpose
* =======
* Panel factorization -- block column k
*
* Factor diagonal and subdiagonal blocks and test for exact singularity.
* Only the column processes that own block column *k* participate
* in the work.
*
* Arguments
* =========
*
* k (input) int (global)
* The column number of the block column to be factorized.
*
* thresh (input) double (global)
* The threshold value = s_eps * anorm.
*
* Glu_persist (input) Glu_persist_t*
* Global data structures (xsup, supno) replicated on all processes.
*
* grid (input) gridinfo_t*
* The 2D process mesh.
*
* Llu (input/output) LocalLU_t*
* Local data structures to store distributed L and U matrices.
*
* U_diag_blk_send_req (input/output) MPI_Request*
* List of send requests to send down the diagonal block of U.
*
* stat (output) SuperLUStat_t*
* Record the statistics about the factorization.
* See SuperLUStat_t structure defined in util.h.
*
* info (output) int*
* = 0: successful exit
* < 0: if info = -i, the i-th argument had an illegal value
* > 0: if info = i, U(i,i) is exactly zero. The factorization has
* been completed, but the factor U is exactly singular,
* and division by zero will occur if it is used to solve a
* system of equations.
* </pre>
*/
static void pdgstrf2
(
superlu_options_t *options,
int_t k, double thresh, Glu_persist_t *Glu_persist, gridinfo_t *grid,
LocalLU_t *Llu, MPI_Request *U_diag_blk_send_req,
SuperLUStat_t *stat, int* info
)
{
int cols_left, iam, l, pkk, pr;
int incx = 1, incy = 1;
int nsupr; /* number of rows in the block (LDA) */
int luptr;
int_t i, krow, j, jfst, jlst, u_diag_cnt;
int_t nsupc; /* number of columns in the block */
int_t *xsup = Glu_persist->xsup;
double *lusup, temp;
double *ujrow, *ublk_ptr; /* pointer to the U block */
double alpha = -1, zero = 0.0;
int_t Pr;
MPI_Status status;
MPI_Comm comm = (grid->cscp).comm;
/* Quick return. */
*info = 0;
/* Initialization. */
iam = grid->iam;
Pr = grid->nprow;
krow = PROW( k, grid );
pkk = PNUM( PROW(k, grid), PCOL(k, grid), grid );
j = LBj( k, grid ); /* Local block number */
jfst = FstBlockC( k );
jlst = FstBlockC( k+1 );
lusup = Llu->Lnzval_bc_ptr[j];
nsupc = SuperSize( k );
if ( Llu->Lrowind_bc_ptr[j] ) nsupr = Llu->Lrowind_bc_ptr[j][1];
ublk_ptr = ujrow = Llu->ujrow;
luptr = 0; /* Point to the diagonal entries. */
cols_left = nsupc; /* supernode size */
u_diag_cnt = 0;
if ( iam == pkk ) { /* diagonal process */
if ( U_diag_blk_send_req && U_diag_blk_send_req[krow] ) {
/* There are pending sends - wait for all Isend to complete */
for (pr = 0; pr < Pr; ++pr)
if (pr != krow)
MPI_Wait(U_diag_blk_send_req + pr, &status);
}
for (j = 0; j < jlst - jfst; ++j) { /* for each column in panel */
/* Diagonal pivot */
i = luptr;
if ( options->ReplaceTinyPivot == YES || lusup[i] == 0.0 ) {
if ( fabs(lusup[i]) < thresh ) { /* Diagonal */
#if ( PRNTlevel>=2 )
printf("(%d) .. col %d, tiny pivot %e ",
iam, jfst+j, lusup[i]);
#endif
/* Keep the new diagonal entry with the same sign. */
if ( lusup[i] < 0 ) lusup[i] = -thresh;
else lusup[i] = thresh;
#if ( PRNTlevel>=2 )
printf("replaced by %e\n", lusup[i]);
#endif
++(stat->TinyPivots);
}
}
for (l = 0; l < cols_left; ++l, i += nsupr, ++u_diag_cnt)
ublk_ptr[u_diag_cnt] = lusup[i]; /* copy one row of U */
if ( ujrow[0] == zero ) { /* Test for singularity. */
*info = j+jfst+1;
} else { /* Scale the j-th column. */
temp = 1.0 / ujrow[0];
for (i = luptr+1; i < luptr-j+nsupr; ++i) lusup[i] *= temp;
stat->ops[FACT] += nsupr-j-1;
}
/* Rank-1 update of the trailing submatrix. */
if ( --cols_left ) {
l = nsupr - j - 1;
#ifdef _CRAY
SGER(&l, &cols_left, &alpha, &lusup[luptr+1], &incx,
&ujrow[1], &incy, &lusup[luptr+nsupr+1], &nsupr);
#else
dger_(&l, &cols_left, &alpha, &lusup[luptr+1], &incx,
&ujrow[1], &incy, &lusup[luptr+nsupr+1], &nsupr);
#endif
stat->ops[FACT] += 2 * l * cols_left;
}
ujrow = ublk_ptr + u_diag_cnt; /* move to next row of U */
luptr += nsupr + 1; /* move to next column */
} /* for column j ... */
if ( U_diag_blk_send_req && iam == pkk ) { /* Send the U block */
/** ALWAYS SEND TO ALL OTHERS - TO FIX **/
for (pr = 0; pr < Pr; ++pr)
if (pr != krow)
MPI_Isend(ublk_ptr, u_diag_cnt, MPI_DOUBLE, pr,
((k<<2)+2)%NTAGS, comm, U_diag_blk_send_req + pr);
U_diag_blk_send_req[krow] = 1; /* flag outstanding Isend */
}
} else { /* non-diagonal process */
/* Receive the diagonal block of U */
MPI_Recv(ublk_ptr, (nsupc*(nsupc+1))>>1, MPI_DOUBLE,
krow, ((k<<2)+2)%NTAGS, comm, &status);
for (j = 0; j < jlst - jfst; ++j) { /* for each column in panel */
u_diag_cnt += cols_left;
if ( !lusup ) { /* empty block column */
--cols_left;
if ( ujrow[0] == zero ) *info = j+jfst+1;
continue;
}
/* Test for singularity. */
if ( ujrow[0] == zero ) {
*info = j+jfst+1;
} else {
/* Scale the j-th column. */
temp = 1.0 / ujrow[0];
for (i = luptr; i < luptr+nsupr; ++i) lusup[i] *= temp;
stat->ops[FACT] += nsupr;
}
/* Rank-1 update of the trailing submatrix. */
if ( --cols_left ) {
#ifdef _CRAY
SGER(&nsupr, &cols_left, &alpha, &lusup[luptr], &incx,
&ujrow[1], &incy, &lusup[luptr+nsupr], &nsupr);
#else
dger_(&nsupr, &cols_left, &alpha, &lusup[luptr], &incx,
&ujrow[1], &incy, &lusup[luptr+nsupr], &nsupr);
#endif
stat->ops[FACT] += 2 * nsupr * cols_left;
}
ujrow = ublk_ptr + u_diag_cnt; /* move to next row of U */
luptr += nsupr; /* move to next column */
} /* for column j ... */
} /* end if pkk ... */
} /* PDGSTRF2 */
void pdgstrs1(int_t n, LUstruct_t *LUstruct, gridinfo_t *grid,
double *x, int nrhs, SuperLUStat_t *stat, int *info)
{
/*
* Purpose
* =======
*
* PDGSTRS1 solves a system of distributed linear equations
*
* op( sub(A) ) * X = sub( B )
*
* with a general N-by-N distributed matrix sub( A ) using the LU
* factorization computed by PDGSTRF.
*
* Arguments
* =========
*
* n (input) int (global)
* The order of the system of linear equations.
*
* LUstruct (input) LUstruct_t*
* The distributed data structures to store L and U factors,
* and the permutation vectors.
* See superlu_ddefs.h for the definition of 'LUstruct_t' structure.
*
* grid (input) gridinfo_t*
* The 2D process mesh.
*
* x (input/output) double*
* On entry, the right hand side matrix.
* On exit, the solution matrix if info = 0;
*
* NOTE: the right-hand side matrix is already distributed on
* the diagonal processes.
*
* nrhs (input) int (global)
* Number of right-hand sides.
*
* stat (output) SuperLUStat_t*
* Record the statistics about the triangular solves;
* See SuperLUStat_t structure defined in util.h.
*
* info (output) int*
* = 0: successful exit
* < 0: if info = -i, the i-th argument had an illegal value
*
*/
Glu_persist_t *Glu_persist = LUstruct->Glu_persist;
LocalLU_t *Llu = LUstruct->Llu;
double alpha = 1.0;
double *lsum; /* Local running sum of the updates to B-components */
double *lusup, *dest;
double *recvbuf, *tempv;
double *rtemp; /* Result of full matrix-vector multiply. */
int_t **Ufstnz_br_ptr = Llu->Ufstnz_br_ptr;
int_t *Urbs, *Urbs1; /* Number of row blocks in each block column of U. */
Ucb_indptr_t **Ucb_indptr;/* Vertical linked list pointing to Uindex[] */
int_t **Ucb_valptr; /* Vertical linked list pointing to Unzval[] */
int_t iam, kcol, krow, mycol, myrow;
int_t i, ii, il, j, k, lb, ljb, lk, lptr, luptr;
int_t nb, nlb, nub, nsupers;
int_t *xsup, *lsub, *usub;
int_t *ilsum; /* Starting position of each supernode in lsum (LOCAL)*/
int_t Pc, Pr;
int knsupc, nsupr;
int ldalsum; /* Number of lsum entries locally owned. */
int maxrecvsz, p, pi;
int_t **Lrowind_bc_ptr;
double **Lnzval_bc_ptr;
MPI_Status status;
#ifdef ISEND_IRECV
MPI_Request *send_req, recv_req;
#endif
/*-- Counts used for L-solve --*/
int_t *fmod; /* Modification count for L-solve. */
int_t **fsendx_plist = Llu->fsendx_plist;
int_t nfrecvx = Llu->nfrecvx; /* Number of X components to be recv'd. */
int_t *frecv; /* Count of modifications to be recv'd from
processes in this row. */
int_t nfrecvmod = 0; /* Count of total modifications to be recv'd. */
int_t nleaf = 0, nroot = 0;
/*-- Counts used for U-solve --*/
int_t *bmod; /* Modification count for L-solve. */
int_t **bsendx_plist = Llu->bsendx_plist;
int_t nbrecvx = Llu->nbrecvx; /* Number of X components to be recv'd. */
int_t *brecv; /* Count of modifications to be recv'd from
processes in this row. */
int_t nbrecvmod = 0; /* Count of total modifications to be recv'd. */
double t;
#if ( DEBUGlevel>=2 )
int_t Ublocks = 0;
#endif
t = SuperLU_timer_();
/* Test input parameters. */
*info = 0;
if ( n < 0 ) *info = -1;
else if ( nrhs < 0 ) *info = -8;
if ( *info ) {
pxerbla("PDGSTRS1", grid, -*info);
return;
}
/*
* Initialization.
*/
iam = grid->iam;
Pc = grid->npcol;
Pr = grid->nprow;
myrow = MYROW( iam, grid );
mycol = MYCOL( iam, grid );
nsupers = Glu_persist->supno[n-1] + 1;
xsup = Glu_persist->xsup;
Lrowind_bc_ptr = Llu->Lrowind_bc_ptr;
Lnzval_bc_ptr = Llu->Lnzval_bc_ptr;
nlb = CEILING( nsupers, Pr ); /* Number of local block rows. */
Llu->SolveMsgSent = 0;
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(iam, "Enter pdgstrs1()");
#endif
/* Save the count to be altered so it can be used by
subsequent call to PDGSTRS1. */
if ( !(fmod = intMalloc_dist(nlb)) )
ABORT("Calloc fails for fmod[].");
for (i = 0; i < nlb; ++i) fmod[i] = Llu->fmod[i];
if ( !(frecv = intMalloc_dist(nlb)) )
ABORT("Malloc fails for frecv[].");
Llu->frecv = frecv;
#ifdef ISEND_IRECV
k = SUPERLU_MAX( Llu->nfsendx, Llu->nbsendx ) + nlb;
if ( !(send_req = (MPI_Request*) SUPERLU_MALLOC(k*sizeof(MPI_Request))) )
ABORT("Malloc fails for send_req[].");
#endif
#ifdef _CRAY
ftcs1 = _cptofcd("L", strlen("L"));
ftcs2 = _cptofcd("N", strlen("N"));
ftcs3 = _cptofcd("U", strlen("U"));
#endif
/* Compute ilsum[] and ldalsum for process column 0. */
ilsum = Llu->ilsum;
ldalsum = Llu->ldalsum;
/* Allocate working storage. */
knsupc = sp_ienv_dist(3);
if ( !(lsum = doubleCalloc_dist(((size_t)ldalsum) * nrhs
+ nlb * LSUM_H)) )
ABORT("Calloc fails for lsum[].");
maxrecvsz = knsupc * nrhs + SUPERLU_MAX(XK_H, LSUM_H);
if ( !(recvbuf = doubleMalloc_dist(maxrecvsz)) )
ABORT("Malloc fails for recvbuf[].");
if ( !(rtemp = doubleCalloc_dist(maxrecvsz)) )
ABORT("Malloc fails for rtemp[].");
/*---------------------------------------------------
* Forward solve Ly = b.
*---------------------------------------------------*/
/*
* Prepended the block number in the header for lsum[].
*/
for (k = 0; k < nsupers; ++k) {
knsupc = SuperSize( k );
krow = PROW( k, grid );
if ( myrow == krow ) {
lk = LBi( k, grid ); /* Local block number. */
il = LSUM_BLK( lk );
lsum[il - LSUM_H] = k;
}
}
/*
* Compute frecv[] and nfrecvmod counts on the diagonal processes.
*/
{
superlu_scope_t *scp = &grid->rscp;
for (k = 0; k < nsupers; ++k) {
krow = PROW( k, grid );
if ( myrow == krow ) {
lk = LBi( k, grid ); /* Local block number. */
kcol = PCOL( k, grid ); /* Root process in this row scope. */
if ( mycol != kcol && fmod[lk] )
i = 1; /* Contribution from non-diagonal process. */
else i = 0;
MPI_Reduce( &i, &frecv[lk], 1, mpi_int_t,
MPI_SUM, kcol, scp->comm );
if ( mycol == kcol ) { /* Diagonal process. */
nfrecvmod += frecv[lk];
if ( !frecv[lk] && !fmod[lk] ) ++nleaf;
#if ( DEBUGlevel>=2 )
printf("(%2d) frecv[%4d] %2d\n", iam, k, frecv[lk]);
assert( frecv[lk] < Pc );
#endif
}
}
}
}
/* ---------------------------------------------------------
Solve the leaf nodes first by all the diagonal processes.
--------------------------------------------------------- */
#if ( DEBUGlevel>=2 )
printf("(%2d) nleaf %4d\n", iam, nleaf);
#endif
for (k = 0; k < nsupers && nleaf; ++k) {
krow = PROW( k, grid );
kcol = PCOL( k, grid );
if ( myrow == krow && mycol == kcol ) { /* Diagonal process */
knsupc = SuperSize( k );
lk = LBi( k, grid );
if ( !frecv[lk] && !fmod[lk] ) {
fmod[lk] = -1; /* Do not solve X[k] in the future. */
ii = X_BLK( lk );
lk = LBj( k, grid ); /* Local block number, column-wise. */
lsub = Lrowind_bc_ptr[lk];
lusup = Lnzval_bc_ptr[lk];
nsupr = lsub[1];
#ifdef _CRAY
STRSM(ftcs1, ftcs1, ftcs2, ftcs3, &knsupc, &nrhs, &alpha,
lusup, &nsupr, &x[ii], &knsupc);
#elif defined (USE_VENDOR_BLAS)
dtrsm_("L", "L", "N", "U", &knsupc, &nrhs, &alpha,
lusup, &nsupr, &x[ii], &knsupc, 1, 1, 1, 1);
#else
dtrsm_("L", "L", "N", "U", &knsupc, &nrhs, &alpha,
lusup, &nsupr, &x[ii], &knsupc);
#endif
/*stat->ops[SOLVE] += knsupc * (knsupc - 1) * nrhs;*/
--nleaf;
#if ( DEBUGlevel>=2 )
printf("(%2d) Solve X[%2d]\n", iam, k);
#endif
/*
* Send Xk to process column Pc[k].
*/
for (p = 0; p < Pr; ++p)
if ( fsendx_plist[lk][p] != EMPTY ) {
pi = PNUM( p, kcol, grid );
#ifdef ISEND_IRECV
MPI_Isend( &x[ii - XK_H], knsupc * nrhs + XK_H,
MPI_DOUBLE, pi, Xk, grid->comm,
&send_req[Llu->SolveMsgSent++]);
#else
MPI_Send( &x[ii - XK_H], knsupc * nrhs + XK_H,
MPI_DOUBLE,
pi, Xk, grid->comm );
#endif
#if ( DEBUGlevel>=2 )
printf("(%2d) Sent X[%2.0f] to P %2d\n",
iam, x[ii-XK_H], pi);
#endif
}
/*
* Perform local block modifications: lsum[i] -= L_i,k * X[k]
*/
nb = lsub[0] - 1;
lptr = BC_HEADER + LB_DESCRIPTOR + knsupc;
luptr = knsupc; /* Skip diagonal block L(k,k). */
dlsum_fmod(lsum, x, &x[ii], rtemp, nrhs, knsupc, k,
fmod, nb, lptr, luptr, xsup, grid, Llu,
send_req, stat);
}
} /* if diagonal process ... */
} /* for k ... */
/*
* Compute the internal nodes asynchronously by all processes.
*/
#if ( DEBUGlevel>=2 )
printf("(%2d) nfrecvx %4d, nfrecvmod %4d, nleaf %4d\n",
iam, nfrecvx, nfrecvmod, nleaf);
#endif
while ( nfrecvx || nfrecvmod ) { /* While not finished. */
/* Receive a message. */
#ifdef ISEND_IRECV
/* -MPI- FATAL: Remote protocol queue full */
MPI_Irecv( recvbuf, maxrecvsz, MPI_DOUBLE, MPI_ANY_SOURCE,
MPI_ANY_TAG, grid->comm, &recv_req );
MPI_Wait( &recv_req, &status );
#else
MPI_Recv( recvbuf, maxrecvsz, MPI_DOUBLE, MPI_ANY_SOURCE,
MPI_ANY_TAG, grid->comm, &status );
#endif
k = *recvbuf;
#if ( DEBUGlevel>=2 )
printf("(%2d) Recv'd block %d, tag %2d\n", iam, k, status.MPI_TAG);
#endif
switch ( status.MPI_TAG ) {
case Xk:
--nfrecvx;
lk = LBj( k, grid ); /* Local block number, column-wise. */
lsub = Lrowind_bc_ptr[lk];
lusup = Lnzval_bc_ptr[lk];
if ( lsub ) {
nb = lsub[0];
lptr = BC_HEADER;
luptr = 0;
knsupc = SuperSize( k );
/*
* Perform local block modifications: lsum[i] -= L_i,k * X[k]
*/
dlsum_fmod(lsum, x, &recvbuf[XK_H], rtemp, nrhs, knsupc, k,
fmod, nb, lptr, luptr, xsup, grid, Llu,
send_req, stat);
} /* if lsub */
break;
case LSUM:
--nfrecvmod;
lk = LBi( k, grid ); /* Local block number, row-wise. */
ii = X_BLK( lk );
knsupc = SuperSize( k );
tempv = &recvbuf[LSUM_H];
RHS_ITERATE(j)
for (i = 0; i < knsupc; ++i)
x[i + ii + j*knsupc] += tempv[i + j*knsupc];
if ( (--frecv[lk])==0 && fmod[lk]==0 ) {
fmod[lk] = -1; /* Do not solve X[k] in the future. */
lk = LBj( k, grid ); /* Local block number, column-wise. */
lsub = Lrowind_bc_ptr[lk];
lusup = Lnzval_bc_ptr[lk];
nsupr = lsub[1];
#ifdef _CRAY
STRSM(ftcs1, ftcs1, ftcs2, ftcs3, &knsupc, &nrhs, &alpha,
lusup, &nsupr, &x[ii], &knsupc);
#elif defined (USE_VENDOR_BLAS)
dtrsm_("L", "L", "N", "U", &knsupc, &nrhs, &alpha,
lusup, &nsupr, &x[ii], &knsupc, 1, 1, 1, 1);
#else
dtrsm_("L", "L", "N", "U", &knsupc, &nrhs, &alpha,
lusup, &nsupr, &x[ii], &knsupc);
#endif
/*stat->ops[SOLVE] += knsupc * (knsupc - 1) * nrhs;*/
#if ( DEBUGlevel>=2 )
printf("(%2d) Solve X[%2d]\n", iam, k);
#endif
/*
* Send Xk to process column Pc[k].
*/
kcol = PCOL( k, grid );
for (p = 0; p < Pr; ++p)
if ( fsendx_plist[lk][p] != EMPTY ) {
pi = PNUM( p, kcol, grid );
#ifdef ISEND_IRECV
MPI_Isend( &x[ii - XK_H], knsupc * nrhs + XK_H,
MPI_DOUBLE, pi, Xk, grid->comm,
&send_req[Llu->SolveMsgSent++] );
#else
MPI_Send( &x[ii - XK_H], knsupc * nrhs + XK_H,
MPI_DOUBLE, pi, Xk, grid->comm );
#endif
#if ( DEBUGlevel>=2 )
printf("(%2d) Sent X[%2.0f] to P %2d\n",
iam, x[ii-XK_H], pi);
#endif
}
/*
* Perform local block modifications.
*/
nb = lsub[0] - 1;
lptr = BC_HEADER + LB_DESCRIPTOR + knsupc;
luptr = knsupc; /* Skip diagonal block L(k,k). */
dlsum_fmod(lsum, x, &x[ii], rtemp, nrhs, knsupc, k,
fmod, nb, lptr, luptr, xsup, grid, Llu,
send_req, stat);
} /* if */
break;
#if ( DEBUGlevel>=2 )
default:
printf("(%2d) Recv'd wrong message tag %4d\n", status.MPI_TAG);
break;
#endif
} /* switch */
} /* while not finished ... */
#if ( PRNTlevel>=2 )
t = SuperLU_timer_() - t;
if ( !iam ) printf(".. L-solve time\t%8.2f\n", t);
t = SuperLU_timer_();
#endif
#if ( DEBUGlevel>=2 )
if ( !iam ) printf("\n.. After L-solve: y =\n");
for (i = 0, k = 0; k < nsupers; ++k) {
krow = PROW( k, grid );
kcol = PCOL( k, grid );
if ( myrow == krow && mycol == kcol ) { /* Diagonal process */
knsupc = SuperSize( k );
lk = LBi( k, grid );
ii = X_BLK( lk );
for (j = 0; j < knsupc; ++j)
printf("\t(%d)\t%4d\t%.10f\n", iam, xsup[k]+j, x[ii+j]);
}
MPI_Barrier( grid->comm );
}
#endif
SUPERLU_FREE(fmod);
SUPERLU_FREE(frecv);
SUPERLU_FREE(rtemp);
#ifdef ISEND_IRECV
for (i = 0; i < Llu->SolveMsgSent; ++i) MPI_Request_free(&send_req[i]);
Llu->SolveMsgSent = 0;
#endif
/*---------------------------------------------------
* Back solve Ux = y.
*
* The Y components from the forward solve is already
* on the diagonal processes.
*---------------------------------------------------*/
/* Save the count to be altered so it can be used by
subsequent call to PDGSTRS1. */
if ( !(bmod = intMalloc_dist(nlb)) )
ABORT("Calloc fails for bmod[].");
for (i = 0; i < nlb; ++i) bmod[i] = Llu->bmod[i];
if ( !(brecv = intMalloc_dist(nlb)) )
ABORT("Malloc fails for brecv[].");
Llu->brecv = brecv;
/*
* Compute brecv[] and nbrecvmod counts on the diagonal processes.
*/
{
superlu_scope_t *scp = &grid->rscp;
for (k = 0; k < nsupers; ++k) {
krow = PROW( k, grid );
if ( myrow == krow ) {
lk = LBi( k, grid ); /* Local block number. */
kcol = PCOL( k, grid ); /* Root process in this row scope. */
if ( mycol != kcol && bmod[lk] )
i = 1; /* Contribution from non-diagonal process. */
else i = 0;
MPI_Reduce( &i, &brecv[lk], 1, mpi_int_t,
MPI_SUM, kcol, scp->comm );
if ( mycol == kcol ) { /* Diagonal process. */
nbrecvmod += brecv[lk];
if ( !brecv[lk] && !bmod[lk] ) ++nroot;
#if ( DEBUGlevel>=2 )
printf("(%2d) brecv[%4d] %2d\n", iam, k, brecv[lk]);
assert( brecv[lk] < Pc );
#endif
}
}
}
}
/* Re-initialize lsum to zero. Each block header is already in place. */
for (k = 0; k < nsupers; ++k) {
krow = PROW( k, grid );
if ( myrow == krow ) {
knsupc = SuperSize( k );
lk = LBi( k, grid );
il = LSUM_BLK( lk );
dest = &lsum[il];
RHS_ITERATE(j)
for (i = 0; i < knsupc; ++i) dest[i + j*knsupc] = 0.0;
}
}