/*! \brief Allocate storage for original matrix A
*/
void
zallocateA_dist(int_t n, int_t nnz, doublecomplex **a, int_t **asub, int_t **xa)
{
*a = (doublecomplex *) doublecomplexMalloc_dist(nnz);
*asub = (int_t *) intMalloc_dist(nnz);
*xa = (int_t *) intMalloc_dist(n+1);
}
/*! \brief
*
* <pre>
* Purpose
* =======
*
* GetDiagU extracts the main diagonal of matrix U of the LU factorization.
*
* Arguments
* =========
*
* n (input) int
* Dimension of the matrix.
*
* LUstruct (input) LUstruct_t*
* The data structures to store the distributed L and U factors.
* see superlu_ddefs.h for its definition.
*
* grid (input) gridinfo_t*
* The 2D process mesh. It contains the MPI communicator, the number
* of process rows (NPROW), the number of process columns (NPCOL),
* and my process rank. It is an input argument to all the
* parallel routines.
*
* diagU (output) double*, dimension (n)
* The main diagonal of matrix U.
* On exit, it is available on all processes.
*
*
* Note
* ====
*
* The diagonal blocks of the L and U matrices are stored in the L
* data structures, and are on the diagonal processes of the
* 2D process grid.
*
* This routine is modified from gather_diag_to_all() in pzgstrs_Bglobal.c.
* </pre>
*/
void pzGetDiagU(int_t n, LUstruct_t *LUstruct, gridinfo_t *grid,
doublecomplex *diagU)
{
int_t *xsup;
int iam, knsupc, pkk;
int nsupr; /* number of rows in the block L(:,k) (LDA) */
int_t i, j, jj, k, lk, lwork, nsupers, p;
int_t num_diag_procs, *diag_procs, *diag_len;
Glu_persist_t *Glu_persist = LUstruct->Glu_persist;
LocalLU_t *Llu = LUstruct->Llu;
doublecomplex *zblock, *zwork, *lusup;
iam = grid->iam;
nsupers = Glu_persist->supno[n-1] + 1;
xsup = Glu_persist->xsup;
get_diag_procs(n, Glu_persist, grid, &num_diag_procs,
&diag_procs, &diag_len);
jj = diag_len[0];
for (j = 1; j < num_diag_procs; ++j) jj = SUPERLU_MAX( jj, diag_len[j] );
if ( !(zwork = doublecomplexMalloc_dist(jj)) ) ABORT("Malloc fails for zwork[]");
for (p = 0; p < num_diag_procs; ++p) {
pkk = diag_procs[p];
if ( iam == pkk ) {
/* Copy diagonal into buffer dwork[]. */
lwork = 0;
for (k = p; k < nsupers; k += num_diag_procs) {
knsupc = SuperSize( k );
lk = LBj( k, grid );
nsupr = Llu->Lrowind_bc_ptr[lk][1]; /* LDA of lusup[] */
lusup = Llu->Lnzval_bc_ptr[lk];
for (i = 0; i < knsupc; ++i) /* Copy the diagonal. */
zwork[lwork+i] = lusup[i*(nsupr+1)];
lwork += knsupc;
}
MPI_Bcast( zwork, lwork, SuperLU_MPI_DOUBLE_COMPLEX, pkk, grid->comm );
} else {
MPI_Bcast( zwork, diag_len[p], SuperLU_MPI_DOUBLE_COMPLEX, pkk, grid->comm );
}
/* Scatter zwork[] into global diagU vector. */
lwork = 0;
for (k = p; k < nsupers; k += num_diag_procs) {
knsupc = SuperSize( k );
zblock = &diagU[FstBlockC( k )];
for (i = 0; i < knsupc; ++i) zblock[i] = zwork[lwork+i];
lwork += knsupc;
}
} /* for p = ... */
SUPERLU_FREE(diag_procs);
SUPERLU_FREE(diag_len);
SUPERLU_FREE(zwork);
}
int
zread_binary(FILE *fp, int_t *m, int_t *n, int_t *nnz,
doublecomplex **nzval, int_t **rowind, int_t **colptr)
{
size_t isize = sizeof(int_t), dsize = sizeof(double);
int nnz_read;
fread(n, isize, 1, fp);
fread(nnz, isize, 1, fp);
printf("fread n " IFMT "\tnnz " IFMT "\n", *n, *nnz);
*m = *n;
*colptr = intMalloc_dist(*n+1);
*rowind = intMalloc_dist(*nnz);
*nzval = doublecomplexMalloc_dist(*nnz);
fread(*colptr, isize, (size_t) (*n + 1), fp);
fread(*rowind, isize, (size_t) *nnz, fp);
nnz_read = fread(*nzval, dsize, (size_t) (2 * (*nnz)), fp);
printf("# of doubles fread: %d\n", nnz_read);
fclose(fp);
}
/*
* Convert a row compressed storage into a column compressed storage.
*/
void
zCompRow_to_CompCol_dist(int_t m, int_t n, int_t nnz,
doublecomplex *a, int_t *colind, int_t *rowptr,
doublecomplex **at, int_t **rowind, int_t **colptr)
{
register int i, j, col, relpos;
int_t *marker;
/* Allocate storage for another copy of the matrix. */
*at = (doublecomplex *) doublecomplexMalloc_dist(nnz);
*rowind = intMalloc_dist(nnz);
*colptr = intMalloc_dist(n+1);
marker = intCalloc_dist(n);
/* Get counts of each column of A, and set up column pointers */
for (i = 0; i < m; ++i)
for (j = rowptr[i]; j < rowptr[i+1]; ++j) ++marker[colind[j]];
(*colptr)[0] = 0;
for (j = 0; j < n; ++j) {
(*colptr)[j+1] = (*colptr)[j] + marker[j];
marker[j] = (*colptr)[j];
}
/* Transfer the matrix into the compressed column storage. */
for (i = 0; i < m; ++i) {
for (j = rowptr[i]; j < rowptr[i+1]; ++j) {
col = colind[j];
relpos = marker[col];
(*rowind)[relpos] = i;
(*at)[relpos] = a[j];
++marker[col];
}
}
SUPERLU_FREE(marker);
}
int_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_X_to_B(int_t n, doublecomplex *B, int_t m_loc, int_t ldb, int_t fst_row,
int_t nrhs, doublecomplex *x, int_t *ilsum,
ScalePermstruct_t *ScalePermstruct,
Glu_persist_t *Glu_persist, gridinfo_t *grid,
SOLVEstruct_t *SOLVEstruct)
{
/*
* Purpose
* =======
* Re-distribute X on the diagonal processes to B distributed on all
* the processes.
*
* 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.
*
*/
int_t i, ii, irow, j, jj, k, knsupc, nsupers, l, lk;
int_t *xsup, *supno;
int *SendCnt, *SendCnt_nrhs, *RecvCnt, *RecvCnt_nrhs;
int *sdispls, *rdispls, *sdispls_nrhs, *rdispls_nrhs;
int *ptr_to_ibuf, *ptr_to_dbuf;
int_t *send_ibuf, *recv_ibuf;
doublecomplex *send_dbuf, *recv_dbuf;
int_t *row_to_proc = SOLVEstruct->row_to_proc; /* row-process mapping */
pxgstrs_comm_t *gstrs_comm = SOLVEstruct->gstrs_comm;
int iam, p, q, pkk, procs;
int_t num_diag_procs, *diag_procs;
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(grid->iam, "Enter pzReDistribute_X_to_B()");
#endif
/* ------------------------------------------------------------
INITIALIZATION.
------------------------------------------------------------*/
xsup = Glu_persist->xsup;
supno = Glu_persist->supno;
nsupers = Glu_persist->supno[n-1] + 1;
iam = grid->iam;
procs = grid->nprow * grid->npcol;
SendCnt = gstrs_comm->X_to_B_SendCnt;
SendCnt_nrhs = gstrs_comm->X_to_B_SendCnt + procs;
RecvCnt = gstrs_comm->X_to_B_SendCnt + 2*procs;
RecvCnt_nrhs = gstrs_comm->X_to_B_SendCnt + 3*procs;
sdispls = gstrs_comm->X_to_B_SendCnt + 4*procs;
sdispls_nrhs = gstrs_comm->X_to_B_SendCnt + 5*procs;
rdispls = gstrs_comm->X_to_B_SendCnt + 6*procs;
rdispls_nrhs = gstrs_comm->X_to_B_SendCnt + 7*procs;
ptr_to_ibuf = gstrs_comm->ptr_to_ibuf;
ptr_to_dbuf = gstrs_comm->ptr_to_dbuf;
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)*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_nrhs[p];
}
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 );
l = X_BLK( lk );
for (i = 0; i < knsupc; ++i) {
#if 0
ii = inv_perm_c[irow]; /* Apply X <== Pc'*Y */
#else
ii = irow;
#endif
q = row_to_proc[ii];
jj = ptr_to_ibuf[q];
send_ibuf[jj] = ii;
jj = ptr_to_dbuf[q];
RHS_ITERATE(j) { /* RHS stored in row major in buffer. */
send_dbuf[jj++] = x[l + i + j*knsupc];
}
++ptr_to_ibuf[q];
ptr_to_dbuf[q] += nrhs;
++irow;
}
}
}
}
/* ------------------------------------------------------------
COMMUNICATE THE (PERMUTED) ROW INDICES AND NUMERICAL VALUES.
------------------------------------------------------------*/
MPI_Alltoallv(send_ibuf, SendCnt, sdispls, mpi_int_t,
recv_ibuf, RecvCnt, rdispls, mpi_int_t, grid->comm);
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 THE BUFFER INTO B.
------------------------------------------------------------*/
for (i = 0, k = 0; i < m_loc; ++i) {
irow = recv_ibuf[i];
irow -= fst_row; /* Relative row number */
RHS_ITERATE(j) { /* RHS is stored in row major in the buffer. */
B[irow + j*ldb] = recv_dbuf[k++];
}
}
SUPERLU_FREE(send_ibuf);
SUPERLU_FREE(send_dbuf);
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(grid->iam, "Exit pzReDistribute_X_to_B()");
#endif
return 0;
} /* pzReDistribute_X_to_B */
void
pzgstrs_Bglobal(int_t n, LUstruct_t *LUstruct, gridinfo_t *grid,
doublecomplex *B, int_t ldb, int nrhs,
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. */
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 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, *lsub, *usub;
int_t *ilsum; /* Starting position of each supernode in lsum (LOCAL)*/
int Pc, Pr, iam;
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;
#if defined (ISEND_IRECV) || defined (BSEND)
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
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 ) {
pxerr_dist("PZGSTRS_BGLOBAL", 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. */
stat->ops[SOLVE] = 0.0;
Llu->SolveMsgSent = 0;
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(iam, "Enter pzgstrs_Bglobal()");
#endif
/* Save the count to be altered so it can be used by
subsequent call to PDGSTRS_BGLOBAL. */
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;
#if defined (ISEND_IRECV) || defined (BSEND)
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(((size_t)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.
*---------------------------------------------------*/
/*
* Copy B into X on the diagonal processes.
*/
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;
kcol = PCOL( k, grid );
if ( mycol == kcol ) { /* Diagonal process. */
jj = X_BLK( lk );
x[jj - XK_H].r = k; /* Block number prepended in the header. */
x[jj - XK_H].i = 0;
RHS_ITERATE(j)
for (i = 0; i < knsupc; ++i) /* X is stored in blocks. */
x[i + jj + j*knsupc] = B[i + ii + j*ldb];
}
}
int main(int argc, char *argv[])
{
superlu_options_t options;
SuperLUStat_t stat;
SuperMatrix A;
NRformat_loc *Astore;
ScalePermstruct_t ScalePermstruct;
LUstruct_t LUstruct;
SOLVEstruct_t SOLVEstruct;
gridinfo_t grid;
double *berr;
doublecomplex *b, *b1, *xtrue, *nzval, *nzval1;
int_t *colind, *colind1, *rowptr, *rowptr1;
int_t i, j, m, n, nnz_loc, m_loc, fst_row;
int_t nprow, npcol;
int iam, info, ldb, ldx, nrhs;
char **cpp, c;
FILE *fp, *fopen();
nprow = 1; /* Default process rows. */
npcol = 1; /* Default process columns. */
nrhs = 1; /* Number of right-hand side. */
/* ------------------------------------------------------------
INITIALIZE MPI ENVIRONMENT.
------------------------------------------------------------*/
MPI_Init( &argc, &argv );
/* Parse command line argv[]. */
for (cpp = argv+1; *cpp; ++cpp) {
if ( **cpp == '-' ) {
c = *(*cpp+1);
++cpp;
switch (c) {
case 'h':
printf("Options:\n");
printf("\t-r <int>: process rows (default %d)\n", nprow);
printf("\t-c <int>: process columns (default %d)\n", npcol);
exit(0);
break;
case 'r': nprow = atoi(*cpp);
break;
case 'c': npcol = atoi(*cpp);
break;
}
} else { /* Last arg is considered a filename */
if ( !(fp = fopen(*cpp, "r")) ) {
ABORT("File does not exist");
}
break;
}
}
/* ------------------------------------------------------------
INITIALIZE THE SUPERLU PROCESS GRID.
------------------------------------------------------------*/
superlu_gridinit(MPI_COMM_WORLD, nprow, npcol, &grid);
/* Bail out if I do not belong in the grid. */
iam = grid.iam;
if ( iam >= nprow * npcol ) goto out;
if ( !iam ) printf("\tProcess grid\t%d X %d\n", grid.nprow, grid.npcol);
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(iam, "Enter main()");
#endif
/* ------------------------------------------------------------
GET THE MATRIX FROM FILE AND SETUP THE RIGHT HAND SIDE.
------------------------------------------------------------*/
zcreate_matrix(&A, nrhs, &b, &ldb, &xtrue, &ldx, fp, &grid);
if ( !(b1 = doublecomplexMalloc_dist(ldb * nrhs)) )
ABORT("Malloc fails for b1[]");
for (j = 0; j < nrhs; ++j)
for (i = 0; i < ldb; ++i) b1[i+j*ldb] = b[i+j*ldb];
if ( !(berr = doubleMalloc_dist(nrhs)) )
ABORT("Malloc fails for berr[].");
m = A.nrow;
n = A.ncol;
/* Save a copy of the matrix A. */
Astore = (NRformat_loc *) A.Store;
nnz_loc = Astore->nnz_loc;
m_loc = Astore->m_loc;
fst_row = Astore->fst_row;
nzval = Astore->nzval;
colind = Astore->colind;
rowptr = Astore->rowptr;
nzval1 = doublecomplexMalloc_dist(nnz_loc);
colind1 = intMalloc_dist(nnz_loc);
rowptr1 = intMalloc_dist(m_loc+1);
for (i = 0; i < nnz_loc; ++i) {
nzval1[i] = nzval[i];
colind1[i] = colind[i];
}
for (i = 0; i < m_loc+1; ++i) rowptr1[i] = rowptr[i];
/* ------------------------------------------------------------
WE SOLVE THE LINEAR SYSTEM FOR THE FIRST TIME.
------------------------------------------------------------*/
/* Set the default input options:
options.Fact = DOFACT;
options.Equil = YES;
options.ColPerm = MMD_AT_PLUS_A;
options.RowPerm = LargeDiag;
options.ReplaceTinyPivot = YES;
options.Trans = NOTRANS;
options.IterRefine = DOUBLE;
options.SolveInitialized = NO;
options.RefineInitialized = NO;
options.PrintStat = YES;
*/
set_default_options_dist(&options);
/* Initialize ScalePermstruct and LUstruct. */
ScalePermstructInit(m, n, &ScalePermstruct);
LUstructInit(m, n, &LUstruct);
/* Initialize the statistics variables. */
PStatInit(&stat);
/* Call the linear equation solver: factorize and solve. */
pzgssvx(&options, &A, &ScalePermstruct, b, ldb, nrhs, &grid,
&LUstruct, &SOLVEstruct, berr, &stat, &info);
/* Check the accuracy of the solution. */
pzinf_norm_error(iam, m_loc, nrhs, b, ldb, xtrue, ldx, &grid);
PStatPrint(&options, &stat, &grid); /* Print the statistics. */
PStatFree(&stat);
Destroy_CompRowLoc_Matrix_dist(&A); /* Deallocate storage of matrix A. */
SUPERLU_FREE(b); /* Free storage of right-hand side. */
/* ------------------------------------------------------------
NOW WE SOLVE ANOTHER LINEAR SYSTEM.
THE MATRIX A HAS THE SAME SPARSITY PATTERN AND THE SIMILAR
NUMERICAL VALUES AS THAT IN A PREVIOUS SYSTEM.
------------------------------------------------------------*/
options.Fact = SamePattern_SameRowPerm;
PStatInit(&stat); /* Initialize the statistics variables. */
/* Set up the local A in NR_loc format */
zCreate_CompRowLoc_Matrix_dist(&A, m, n, nnz_loc, m_loc, fst_row,
nzval1, colind1, rowptr1,
SLU_NR_loc, SLU_Z, SLU_GE);
/* Solve the linear system. */
pzgssvx(&options, &A, &ScalePermstruct, b1, ldb, nrhs, &grid,
&LUstruct, &SOLVEstruct, berr, &stat, &info);
/* Check the accuracy of the solution. */
if ( !iam )
printf("Solve a system with the same pattern and similar values.\n");
pzinf_norm_error(iam, m_loc, nrhs, b1, ldb, xtrue, ldx, &grid);
/* Print the statistics. */
PStatPrint(&options, &stat, &grid);
/* ------------------------------------------------------------
DEALLOCATE STORAGE.
------------------------------------------------------------*/
PStatFree(&stat);
Destroy_CompRowLoc_Matrix_dist(&A); /* Deallocate storage of matrix A. */
Destroy_LU(n, &grid, &LUstruct); /* Deallocate storage associated with
the L and U matrices. */
ScalePermstructFree(&ScalePermstruct);
LUstructFree(&LUstruct); /* Deallocate the structure of L and U.*/
if ( options.SolveInitialized ) {
zSolveFinalize(&options, &SOLVEstruct);
}
SUPERLU_FREE(b1); /* Free storage of right-hand side. */
SUPERLU_FREE(xtrue); /* Free storage of the exact solution. */
SUPERLU_FREE(berr);
/* ------------------------------------------------------------
RELEASE THE SUPERLU PROCESS GRID.
------------------------------------------------------------*/
out:
superlu_gridexit(&grid);
/* ------------------------------------------------------------
TERMINATES THE MPI EXECUTION ENVIRONMENT.
------------------------------------------------------------*/
MPI_Finalize();
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(iam, "Exit main()");
#endif
}
/*! \brief Gather A from the distributed compressed row format to global A in compressed column format.
*/
int pzCompRow_loc_to_CompCol_global
(
int_t need_value, /* Input. Whether need to gather numerical values */
SuperMatrix *A, /* Input. Distributed matrix in NRformat_loc format. */
gridinfo_t *grid, /* Input */
SuperMatrix *GA /* Output */
)
{
NRformat_loc *Astore;
NCformat *GAstore;
doublecomplex *a, *a_loc;
int_t *colind, *rowptr;
int_t *colptr_loc, *rowind_loc;
int_t m_loc, n, i, j, k, l;
int_t colnnz, fst_row, nnz_loc, nnz;
doublecomplex *a_recv; /* Buffer to receive the blocks of values. */
doublecomplex *a_buf; /* Buffer to merge blocks into block columns. */
int_t *itemp;
int_t *colptr_send; /* Buffer to redistribute the column pointers of the
local block rows.
Use n_loc+1 pointers for each block. */
int_t *colptr_blk; /* The column pointers for each block, after
redistribution to the local block columns.
Use n_loc+1 pointers for each block. */
int_t *rowind_recv; /* Buffer to receive the blocks of row indices. */
int_t *rowind_buf; /* Buffer to merge blocks into block columns. */
int_t *fst_rows, *n_locs;
int *sendcnts, *sdispls, *recvcnts, *rdispls, *itemp_32;
int it, n_loc, procs;
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(grid->iam, "Enter pzCompRow_loc_to_CompCol_global");
#endif
/* Initialization. */
n = A->ncol;
Astore = (NRformat_loc *) A->Store;
nnz_loc = Astore->nnz_loc;
m_loc = Astore->m_loc;
fst_row = Astore->fst_row;
a = Astore->nzval;
rowptr = Astore->rowptr;
colind = Astore->colind;
n_loc = m_loc; /* NOTE: CURRENTLY ONLY WORK FOR SQUARE MATRIX */
/* ------------------------------------------------------------
FIRST PHASE: TRANSFORM A INTO DISTRIBUTED COMPRESSED COLUMN.
------------------------------------------------------------*/
zCompRow_to_CompCol_dist(m_loc, n, nnz_loc, a, colind, rowptr, &a_loc,
&rowind_loc, &colptr_loc);
/* Change local row index numbers to global numbers. */
for (i = 0; i < nnz_loc; ++i) rowind_loc[i] += fst_row;
#if ( DEBUGlevel>=2 )
printf("Proc %d\n", grid->iam);
PrintInt10("rowind_loc", nnz_loc, rowind_loc);
PrintInt10("colptr_loc", n+1, colptr_loc);
#endif
procs = grid->nprow * grid->npcol;
if ( !(fst_rows = (int_t *) intMalloc_dist(2*procs)) )
ABORT("Malloc fails for fst_rows[]");
n_locs = fst_rows + procs;
MPI_Allgather(&fst_row, 1, mpi_int_t, fst_rows, 1, mpi_int_t,
grid->comm);
for (i = 0; i < procs-1; ++i) n_locs[i] = fst_rows[i+1] - fst_rows[i];
n_locs[procs-1] = n - fst_rows[procs-1];
if ( !(recvcnts = SUPERLU_MALLOC(5*procs * sizeof(int))) )
ABORT("Malloc fails for recvcnts[]");
sendcnts = recvcnts + procs;
rdispls = sendcnts + procs;
sdispls = rdispls + procs;
itemp_32 = sdispls + procs;
/* All-to-all transfer column pointers of each block.
Now the matrix view is P-by-P block-partition. */
/* n column starts for each column, and procs column ends for each block */
if ( !(colptr_send = intMalloc_dist(n + procs)) )
ABORT("Malloc fails for colptr_send[]");
if ( !(colptr_blk = intMalloc_dist( (((size_t) n_loc)+1)*procs)) )
ABORT("Malloc fails for colptr_blk[]");
for (i = 0, j = 0; i < procs; ++i) {
for (k = j; k < j + n_locs[i]; ++k) colptr_send[i+k] = colptr_loc[k];
colptr_send[i+k] = colptr_loc[k]; /* Add an END marker */
sendcnts[i] = n_locs[i] + 1;
#if ( DEBUGlevel>=1 )
assert(j == fst_rows[i]);
#endif
sdispls[i] = j + i;
recvcnts[i] = n_loc + 1;
rdispls[i] = i * (n_loc + 1);
j += n_locs[i]; /* First column of next block in colptr_loc[] */
}
MPI_Alltoallv(colptr_send, sendcnts, sdispls, mpi_int_t,
colptr_blk, recvcnts, rdispls, mpi_int_t, grid->comm);
/* Adjust colptr_blk[] so that they contain the local indices of the
column pointers in the receive buffer. */
nnz = 0; /* The running sum of the nonzeros counted by far */
k = 0;
for (i = 0; i < procs; ++i) {
for (j = rdispls[i]; j < rdispls[i] + n_loc; ++j) {
colnnz = colptr_blk[j+1] - colptr_blk[j];
/*assert(k<=j);*/
colptr_blk[k] = nnz;
nnz += colnnz; /* Start of the next column */
++k;
}
colptr_blk[k++] = nnz; /* Add an END marker for each block */
}
/*assert(k == (n_loc+1)*procs);*/
/* Now prepare to transfer row indices and values. */
sdispls[0] = 0;
for (i = 0; i < procs-1; ++i) {
sendcnts[i] = colptr_loc[fst_rows[i+1]] - colptr_loc[fst_rows[i]];
sdispls[i+1] = sdispls[i] + sendcnts[i];
}
sendcnts[procs-1] = colptr_loc[n] - colptr_loc[fst_rows[procs-1]];
for (i = 0; i < procs; ++i) {
j = rdispls[i]; /* Point to this block in colptr_blk[]. */
recvcnts[i] = colptr_blk[j+n_loc] - colptr_blk[j];
}
rdispls[0] = 0; /* Recompute rdispls[] for row indices. */
for (i = 0; i < procs-1; ++i) rdispls[i+1] = rdispls[i] + recvcnts[i];
k = rdispls[procs-1] + recvcnts[procs-1]; /* Total received */
if ( !(rowind_recv = (int_t *) intMalloc_dist(2*k)) )
ABORT("Malloc fails for rowind_recv[]");
rowind_buf = rowind_recv + k;
MPI_Alltoallv(rowind_loc, sendcnts, sdispls, mpi_int_t,
rowind_recv, recvcnts, rdispls, mpi_int_t, grid->comm);
if ( need_value ) {
if ( !(a_recv = (doublecomplex *) doublecomplexMalloc_dist(2*k)) )
ABORT("Malloc fails for rowind_recv[]");
a_buf = a_recv + k;
MPI_Alltoallv(a_loc, sendcnts, sdispls, SuperLU_MPI_DOUBLE_COMPLEX,
a_recv, recvcnts, rdispls, SuperLU_MPI_DOUBLE_COMPLEX,
grid->comm);
}
/* Reset colptr_loc[] to point to the n_loc global columns. */
colptr_loc[0] = 0;
itemp = colptr_send;
for (j = 0; j < n_loc; ++j) {
colnnz = 0;
for (i = 0; i < procs; ++i) {
k = i * (n_loc + 1) + j; /* j-th column in i-th block */
colnnz += colptr_blk[k+1] - colptr_blk[k];
}
colptr_loc[j+1] = colptr_loc[j] + colnnz;
itemp[j] = colptr_loc[j]; /* Save a copy of the column starts */
}
itemp[n_loc] = colptr_loc[n_loc];
/* Merge blocks of row indices into columns of row indices. */
for (i = 0; i < procs; ++i) {
k = i * (n_loc + 1);
for (j = 0; j < n_loc; ++j) { /* i-th block */
for (l = colptr_blk[k+j]; l < colptr_blk[k+j+1]; ++l) {
rowind_buf[itemp[j]] = rowind_recv[l];
++itemp[j];
}
}
}
if ( need_value ) {
for (j = 0; j < n_loc+1; ++j) itemp[j] = colptr_loc[j];
for (i = 0; i < procs; ++i) {
k = i * (n_loc + 1);
for (j = 0; j < n_loc; ++j) { /* i-th block */
for (l = colptr_blk[k+j]; l < colptr_blk[k+j+1]; ++l) {
a_buf[itemp[j]] = a_recv[l];
++itemp[j];
}
}
}
}
/* ------------------------------------------------------------
SECOND PHASE: GATHER TO GLOBAL A IN COMPRESSED COLUMN FORMAT.
------------------------------------------------------------*/
GA->nrow = A->nrow;
GA->ncol = A->ncol;
GA->Stype = SLU_NC;
GA->Dtype = A->Dtype;
GA->Mtype = A->Mtype;
GAstore = GA->Store = (NCformat *) SUPERLU_MALLOC ( sizeof(NCformat) );
if ( !GAstore ) ABORT ("SUPERLU_MALLOC fails for GAstore");
/* First gather the size of each piece. */
nnz_loc = colptr_loc[n_loc];
MPI_Allgather(&nnz_loc, 1, mpi_int_t, itemp, 1, mpi_int_t, grid->comm);
for (i = 0, nnz = 0; i < procs; ++i) nnz += itemp[i];
GAstore->nnz = nnz;
if ( !(GAstore->rowind = (int_t *) intMalloc_dist (nnz)) )
ABORT ("SUPERLU_MALLOC fails for GAstore->rowind[]");
if ( !(GAstore->colptr = (int_t *) intMalloc_dist (n+1)) )
ABORT ("SUPERLU_MALLOC fails for GAstore->colptr[]");
/* Allgatherv for row indices. */
rdispls[0] = 0;
for (i = 0; i < procs-1; ++i) {
rdispls[i+1] = rdispls[i] + itemp[i];
itemp_32[i] = itemp[i];
}
itemp_32[procs-1] = itemp[procs-1];
it = nnz_loc;
MPI_Allgatherv(rowind_buf, it, mpi_int_t, GAstore->rowind,
itemp_32, rdispls, mpi_int_t, grid->comm);
if ( need_value ) {
if ( !(GAstore->nzval = (doublecomplex *) doublecomplexMalloc_dist (nnz)) )
ABORT ("SUPERLU_MALLOC fails for GAstore->rnzval[]");
MPI_Allgatherv(a_buf, it, SuperLU_MPI_DOUBLE_COMPLEX, GAstore->nzval,
itemp_32, rdispls, SuperLU_MPI_DOUBLE_COMPLEX, grid->comm);
} else GAstore->nzval = NULL;
/* Now gather the column pointers. */
rdispls[0] = 0;
for (i = 0; i < procs-1; ++i) {
rdispls[i+1] = rdispls[i] + n_locs[i];
itemp_32[i] = n_locs[i];
}
itemp_32[procs-1] = n_locs[procs-1];
MPI_Allgatherv(colptr_loc, n_loc, mpi_int_t, GAstore->colptr,
itemp_32, rdispls, mpi_int_t, grid->comm);
/* Recompute column pointers. */
for (i = 1; i < procs; ++i) {
k = rdispls[i];
for (j = 0; j < n_locs[i]; ++j) GAstore->colptr[k++] += itemp[i-1];
itemp[i] += itemp[i-1]; /* prefix sum */
}
GAstore->colptr[n] = nnz;
#if ( DEBUGlevel>=2 )
if ( !grid->iam ) {
printf("After pdCompRow_loc_to_CompCol_global()\n");
zPrint_CompCol_Matrix_dist(GA);
}
#endif
SUPERLU_FREE(a_loc);
SUPERLU_FREE(rowind_loc);
SUPERLU_FREE(colptr_loc);
SUPERLU_FREE(fst_rows);
SUPERLU_FREE(recvcnts);
SUPERLU_FREE(colptr_send);
SUPERLU_FREE(colptr_blk);
SUPERLU_FREE(rowind_recv);
if ( need_value) SUPERLU_FREE(a_recv);
#if ( DEBUGlevel>=1 )
if ( !grid->iam ) printf("sizeof(NCformat) %lu\n", sizeof(NCformat));
CHECK_MALLOC(grid->iam, "Exit pzCompRow_loc_to_CompCol_global");
#endif
return 0;
} /* pzCompRow_loc_to_CompCol_global */
/*! \brief
*
* <pre>
* Purpose
* =======
*
* pzgssvx_ABglobal solves a system of linear equations A*X=B,
* by using Gaussian elimination with "static pivoting" to
* compute the LU factorization of A.
*
* Static pivoting is a technique that combines the numerical stability
* of partial pivoting with the scalability of Cholesky (no pivoting),
* to run accurately and efficiently on large numbers of processors.
*
* See our paper at http://www.nersc.gov/~xiaoye/SuperLU/ for a detailed
* description of the parallel algorithms.
*
* Here are the options for using this code:
*
* 1. Independent of all the other options specified below, the
* user must supply
*
* - B, the matrix of right hand sides, and its dimensions ldb and nrhs
* - grid, a structure describing the 2D processor mesh
* - options->IterRefine, which determines whether or not to
* improve the accuracy of the computed solution using
* iterative refinement
*
* On output, B is overwritten with the solution X.
*
* 2. Depending on options->Fact, the user has several options
* for solving A*X=B. The standard option is for factoring
* A "from scratch". (The other options, described below,
* are used when A is sufficiently similar to a previously
* solved problem to save time by reusing part or all of
* the previous factorization.)
*
* - options->Fact = DOFACT: A is factored "from scratch"
*
* In this case the user must also supply
*
* - A, the input matrix
*
* as well as the following options, which are described in more
* detail below:
*
* - options->Equil, to specify how to scale the rows and columns
* of A to "equilibrate" it (to try to reduce its
* condition number and so improve the
* accuracy of the computed solution)
*
* - options->RowPerm, to specify how to permute the rows of A
* (typically to control numerical stability)
*
* - options->ColPerm, to specify how to permute the columns of A
* (typically to control fill-in and enhance
* parallelism during factorization)
*
* - options->ReplaceTinyPivot, to specify how to deal with tiny
* pivots encountered during factorization
* (to control numerical stability)
*
* The outputs returned include
*
* - ScalePermstruct, modified to describe how the input matrix A
* was equilibrated and permuted:
* - ScalePermstruct->DiagScale, indicates whether the rows and/or
* columns of A were scaled
* - ScalePermstruct->R, array of row scale factors
* - ScalePermstruct->C, array of column scale factors
* - ScalePermstruct->perm_r, row permutation vector
* - ScalePermstruct->perm_c, column permutation vector
*
* (part of ScalePermstruct may also need to be supplied on input,
* depending on options->RowPerm and options->ColPerm as described
* later).
*
* - A, the input matrix A overwritten by the scaled and permuted matrix
* Pc*Pr*diag(R)*A*diag(C)
* where
* Pr and Pc are row and columns permutation matrices determined
* by ScalePermstruct->perm_r and ScalePermstruct->perm_c,
* respectively, and
* diag(R) and diag(C) are diagonal scaling matrices determined
* by ScalePermstruct->DiagScale, ScalePermstruct->R and
* ScalePermstruct->C
*
* - LUstruct, which contains the L and U factorization of A1 where
*
* A1 = Pc*Pr*diag(R)*A*diag(C)*Pc^T = L*U
*
* (Note that A1 = Aout * Pc^T, where Aout is the matrix stored
* in A on output.)
*
* 3. The second value of options->Fact assumes that a matrix with the same
* sparsity pattern as A has already been factored:
*
* - options->Fact = SamePattern: A is factored, assuming that it has
* the same nonzero pattern as a previously factored matrix. In this
* case the algorithm saves time by reusing the previously computed
* column permutation vector stored in ScalePermstruct->perm_c
* and the "elimination tree" of A stored in LUstruct->etree.
*
* In this case the user must still specify the following options
* as before:
*
* - options->Equil
* - options->RowPerm
* - options->ReplaceTinyPivot
*
* but not options->ColPerm, whose value is ignored. This is because the
* previous column permutation from ScalePermstruct->perm_c is used as
* input. The user must also supply
*
* - A, the input matrix
* - ScalePermstruct->perm_c, the column permutation
* - LUstruct->etree, the elimination tree
*
* The outputs returned include
*
* - A, the input matrix A overwritten by the scaled and permuted matrix
* as described above
* - ScalePermstruct, modified to describe how the input matrix A was
* equilibrated and row permuted
* - LUstruct, modified to contain the new L and U factors
*
* 4. The third value of options->Fact assumes that a matrix B with the same
* sparsity pattern as A has already been factored, and where the
* row permutation of B can be reused for A. This is useful when A and B
* have similar numerical values, so that the same row permutation
* will make both factorizations numerically stable. This lets us reuse
* all of the previously computed structure of L and U.
*
* - options->Fact = SamePattern_SameRowPerm: A is factored,
* assuming not only the same nonzero pattern as the previously
* factored matrix B, but reusing B's row permutation.
*
* In this case the user must still specify the following options
* as before:
*
* - options->Equil
* - options->ReplaceTinyPivot
*
* but not options->RowPerm or options->ColPerm, whose values are ignored.
* This is because the permutations from ScalePermstruct->perm_r and
* ScalePermstruct->perm_c are used as input.
*
* The user must also supply
*
* - A, the input matrix
* - ScalePermstruct->DiagScale, how the previous matrix was row and/or
* column scaled
* - ScalePermstruct->R, the row scalings of the previous matrix, if any
* - ScalePermstruct->C, the columns scalings of the previous matrix,
* if any
* - ScalePermstruct->perm_r, the row permutation of the previous matrix
* - ScalePermstruct->perm_c, the column permutation of the previous
* matrix
* - all of LUstruct, the previously computed information about L and U
* (the actual numerical values of L and U stored in
* LUstruct->Llu are ignored)
*
* The outputs returned include
*
* - A, the input matrix A overwritten by the scaled and permuted matrix
* as described above
* - ScalePermstruct, modified to describe how the input matrix A was
* equilibrated
* (thus ScalePermstruct->DiagScale, R and C may be modified)
* - LUstruct, modified to contain the new L and U factors
*
* 5. The fourth and last value of options->Fact assumes that A is
* identical to a matrix that has already been factored on a previous
* call, and reuses its entire LU factorization
*
* - options->Fact = Factored: A is identical to a previously
* factorized matrix, so the entire previous factorization
* can be reused.
*
* In this case all the other options mentioned above are ignored
* (options->Equil, options->RowPerm, options->ColPerm,
* options->ReplaceTinyPivot)
*
* The user must also supply
*
* - A, the unfactored matrix, only in the case that iterative refinment
* is to be done (specifically A must be the output A from
* the previous call, so that it has been scaled and permuted)
* - all of ScalePermstruct
* - all of LUstruct, including the actual numerical values of L and U
*
* all of which are unmodified on output.
*
* Arguments
* =========
*
* options (input) superlu_options_t*
* The structure defines the input parameters to control
* how the LU decomposition will be performed.
* The following fields should be defined for this structure:
*
* o Fact (fact_t)
* Specifies whether or not the factored form of the matrix
* A is supplied on entry, and if not, how the matrix A should
* be factorized based on the previous history.
*
* = DOFACT: The matrix A will be factorized from scratch.
* Inputs: A
* options->Equil, RowPerm, ColPerm, ReplaceTinyPivot
* Outputs: modified A
* (possibly row and/or column scaled and/or
* permuted)
* all of ScalePermstruct
* all of LUstruct
*
* = SamePattern: the matrix A will be factorized assuming
* that a factorization of a matrix with the same sparsity
* pattern was performed prior to this one. Therefore, this
* factorization will reuse column permutation vector
* ScalePermstruct->perm_c and the elimination tree
* LUstruct->etree
* Inputs: A
* options->Equil, RowPerm, ReplaceTinyPivot
* ScalePermstruct->perm_c
* LUstruct->etree
* Outputs: modified A
* (possibly row and/or column scaled and/or
* permuted)
* rest of ScalePermstruct (DiagScale, R, C, perm_r)
* rest of LUstruct (GLU_persist, Llu)
*
* = SamePattern_SameRowPerm: the matrix A will be factorized
* assuming that a factorization of a matrix with the same
* sparsity pattern and similar numerical values was performed
* prior to this one. Therefore, this factorization will reuse
* both row and column scaling factors R and C, and the
* both row and column permutation vectors perm_r and perm_c,
* distributed data structure set up from the previous symbolic
* factorization.
* Inputs: A
* options->Equil, ReplaceTinyPivot
* all of ScalePermstruct
* all of LUstruct
* Outputs: modified A
* (possibly row and/or column scaled and/or
* permuted)
* modified LUstruct->Llu
* = FACTORED: the matrix A is already factored.
* Inputs: all of ScalePermstruct
* all of LUstruct
*
* o Equil (yes_no_t)
* Specifies whether to equilibrate the system.
* = NO: no equilibration.
* = YES: scaling factors are computed to equilibrate the system:
* diag(R)*A*diag(C)*inv(diag(C))*X = diag(R)*B.
* Whether or not the system will be equilibrated depends
* on the scaling of the matrix A, but if equilibration is
* used, A is overwritten by diag(R)*A*diag(C) and B by
* diag(R)*B.
*
* o RowPerm (rowperm_t)
* Specifies how to permute rows of the matrix A.
* = NATURAL: use the natural ordering.
* = LargeDiag: use the Duff/Koster algorithm to permute rows of
* the original matrix to make the diagonal large
* relative to the off-diagonal.
* = MY_PERMR: use the ordering given in ScalePermstruct->perm_r
* input by the user.
*
* o ColPerm (colperm_t)
* Specifies what type of column permutation to use to reduce fill.
* = NATURAL: natural ordering.
* = MMD_AT_PLUS_A: minimum degree ordering on structure of A'+A.
* = MMD_ATA: minimum degree ordering on structure of A'*A.
* = MY_PERMC: the ordering given in ScalePermstruct->perm_c.
*
* o ReplaceTinyPivot (yes_no_t)
* = NO: do not modify pivots
* = YES: replace tiny pivots by sqrt(epsilon)*norm(A) during
* LU factorization.
*
* o IterRefine (IterRefine_t)
* Specifies how to perform iterative refinement.
* = NO: no iterative refinement.
* = SLU_DOUBLE: accumulate residual in double precision.
* = SLU_EXTRA: accumulate residual in extra precision.
*
* NOTE: all options must be indentical on all processes when
* calling this routine.
*
* A (input/output) SuperMatrix*
* On entry, matrix A in A*X=B, of dimension (A->nrow, A->ncol).
* The number of linear equations is A->nrow. The type of A must be:
* Stype = SLU_NC; Dtype = SLU_Z; Mtype = SLU_GE. That is, A is stored in
* compressed column format (also known as Harwell-Boeing format).
* See supermatrix.h for the definition of 'SuperMatrix'.
* This routine only handles square A, however, the LU factorization
* routine pzgstrf can factorize rectangular matrices.
* On exit, A may be overwritten by Pc*Pr*diag(R)*A*diag(C),
* depending on ScalePermstruct->DiagScale, options->RowPerm and
* options->colpem:
* if ScalePermstruct->DiagScale != NOEQUIL, A is overwritten by
* diag(R)*A*diag(C).
* if options->RowPerm != NATURAL, A is further overwritten by
* Pr*diag(R)*A*diag(C).
* if options->ColPerm != NATURAL, A is further overwritten by
* Pc*Pr*diag(R)*A*diag(C).
* If all the above condition are true, the LU decomposition is
* performed on the matrix Pc*Pr*diag(R)*A*diag(C)*Pc^T.
*
* NOTE: Currently, A must reside in all processes when calling
* this routine.
*
* ScalePermstruct (input/output) ScalePermstruct_t*
* The data structure to store the scaling and permutation vectors
* describing the transformations performed to the matrix A.
* It contains the following fields:
*
* o DiagScale (DiagScale_t)
* Specifies the form of equilibration that was done.
* = NOEQUIL: no equilibration.
* = ROW: row equilibration, i.e., A was premultiplied by
* diag(R).
* = COL: Column equilibration, i.e., A was postmultiplied
* by diag(C).
* = BOTH: both row and column equilibration, i.e., A was
* replaced by diag(R)*A*diag(C).
* If options->Fact = FACTORED or SamePattern_SameRowPerm,
* DiagScale is an input argument; otherwise it is an output
* argument.
*
* o perm_r (int*)
* Row permutation vector, which defines the permutation matrix Pr;
* perm_r[i] = j means row i of A is in position j in Pr*A.
* If options->RowPerm = MY_PERMR, or
* options->Fact = SamePattern_SameRowPerm, perm_r is an
* input argument; otherwise it is an output argument.
*
* o perm_c (int*)
* Column permutation vector, which defines the
* permutation matrix Pc; perm_c[i] = j means column i of A is
* in position j in A*Pc.
* If options->ColPerm = MY_PERMC or options->Fact = SamePattern
* or options->Fact = SamePattern_SameRowPerm, perm_c is an
* input argument; otherwise, it is an output argument.
* On exit, perm_c may be overwritten by the product of the input
* perm_c and a permutation that postorders the elimination tree
* of Pc*A'*A*Pc'; perm_c is not changed if the elimination tree
* is already in postorder.
*
* o R (double*) dimension (A->nrow)
* The row scale factors for A.
* If DiagScale = ROW or BOTH, A is multiplied on the left by
* diag(R).
* If DiagScale = NOEQUIL or COL, R is not defined.
* If options->Fact = FACTORED or SamePattern_SameRowPerm, R is
* an input argument; otherwise, R is an output argument.
*
* o C (double*) dimension (A->ncol)
* The column scale factors for A.
* If DiagScale = COL or BOTH, A is multiplied on the right by
* diag(C).
* If DiagScale = NOEQUIL or ROW, C is not defined.
* If options->Fact = FACTORED or SamePattern_SameRowPerm, C is
* an input argument; otherwise, C is an output argument.
*
* B (input/output) doublecomplex*
* On entry, the right-hand side matrix of dimension (A->nrow, nrhs).
* On exit, the solution matrix if info = 0;
*
* NOTE: Currently, B must reside in all processes when calling
* this routine.
*
* ldb (input) int (global)
* The leading dimension of matrix B.
*
* nrhs (input) int (global)
* The number of right-hand sides.
* If nrhs = 0, only LU decomposition is performed, the forward
* and back substitutions are skipped.
*
* 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_zdefs.h for the definition of 'gridinfo_t'.
*
* LUstruct (input/output) LUstruct_t*
* The data structures to store the distributed L and U factors.
* It contains the following fields:
*
* o etree (int*) dimension (A->ncol)
* Elimination tree of Pc*(A'+A)*Pc' or Pc*A'*A*Pc', dimension A->ncol.
* It is computed in sp_colorder() during the first factorization,
* and is reused in the subsequent factorizations of the matrices
* with the same nonzero pattern.
* On exit of sp_colorder(), the columns of A are permuted so that
* the etree is in a certain postorder. This postorder is reflected
* in ScalePermstruct->perm_c.
* NOTE:
* Etree is a vector of parent pointers for a forest whose vertices
* are the integers 0 to A->ncol-1; etree[root]==A->ncol.
*
* o Glu_persist (Glu_persist_t*)
* Global data structure (xsup, supno) replicated on all processes,
* describing the supernode partition in the factored matrices
* L and U:
* xsup[s] is the leading column of the s-th supernode,
* supno[i] is the supernode number to which column i belongs.
*
* o Llu (LocalLU_t*)
* The distributed data structures to store L and U factors.
* See superlu_ddefs.h for the definition of 'LocalLU_t'.
*
* berr (output) double*, dimension (nrhs)
* The componentwise relative backward error of each solution
* vector X(j) (i.e., the smallest relative change in
* any element of A or B that makes X(j) an exact solution).
*
* stat (output) SuperLUStat_t*
* Record the statistics on runtime and floating-point operation count.
* See util.h for the definition of 'SuperLUStat_t'.
*
* info (output) int*
* = 0: successful exit
* > 0: if info = i, and i is
* <= A->ncol: U(i,i) is exactly zero. The factorization has
* been completed, but the factor U is exactly singular,
* so the solution could not be computed.
* > A->ncol: number of bytes allocated when memory allocation
* failure occurred, plus A->ncol.
*
*
* See superlu_zdefs.h for the definitions of various data types.
* </pre>
*/
void
pzgssvx_ABglobal(superlu_options_t *options, SuperMatrix *A,
ScalePermstruct_t *ScalePermstruct,
doublecomplex B[], int ldb, int nrhs, gridinfo_t *grid,
LUstruct_t *LUstruct, double *berr,
SuperLUStat_t *stat, int *info)
{
SuperMatrix AC;
NCformat *Astore;
NCPformat *ACstore;
Glu_persist_t *Glu_persist = LUstruct->Glu_persist;
Glu_freeable_t *Glu_freeable;
/* The nonzero structures of L and U factors, which are
replicated on all processrs.
(lsub, xlsub) contains the compressed subscript of
supernodes in L.
(usub, xusub) contains the compressed subscript of
nonzero segments in U.
If options->Fact != SamePattern_SameRowPerm, they are
computed by SYMBFACT routine, and then used by DDISTRIBUTE
routine. They will be freed after DDISTRIBUTE routine.
If options->Fact == SamePattern_SameRowPerm, these
structures are not used. */
fact_t Fact;
doublecomplex *a;
int_t *perm_r; /* row permutations from partial pivoting */
int_t *perm_c; /* column permutation vector */
int_t *etree; /* elimination tree */
int_t *colptr, *rowind;
int_t colequ, Equil, factored, job, notran, rowequ;
int_t i, iinfo, j, irow, m, n, nnz, permc_spec, dist_mem_use;
int iam;
int ldx; /* LDA for matrix X (global). */
char equed[1], norm[1];
double *C, *R, *C1, *R1, amax, anorm, colcnd, rowcnd;
doublecomplex *X, *b_col, *b_work, *x_col;
double t;
static mem_usage_t num_mem_usage, symb_mem_usage;
#if ( PRNTlevel>= 2 )
double dmin, dsum, dprod;
#endif
/* Test input parameters. */
*info = 0;
Fact = options->Fact;
if ( Fact < 0 || Fact > FACTORED )
*info = -1;
else if ( options->RowPerm < 0 || options->RowPerm > MY_PERMR )
*info = -1;
else if ( options->ColPerm < 0 || options->ColPerm > MY_PERMC )
*info = -1;
else if ( options->IterRefine < 0 || options->IterRefine > SLU_EXTRA )
*info = -1;
else if ( options->IterRefine == SLU_EXTRA ) {
*info = -1;
fprintf(stderr, "Extra precise iterative refinement yet to support.");
} else if ( A->nrow != A->ncol || A->nrow < 0 ||
A->Stype != SLU_NC || A->Dtype != SLU_Z || A->Mtype != SLU_GE )
*info = -2;
else if ( ldb < A->nrow )
*info = -5;
else if ( nrhs < 0 )
*info = -6;
if ( *info ) {
i = -(*info);
pxerbla("pzgssvx_ABglobal", grid, -*info);
return;
}
/* Initialization */
factored = (Fact == FACTORED);
Equil = (!factored && options->Equil == YES);
notran = (options->Trans == NOTRANS);
iam = grid->iam;
job = 5;
m = A->nrow;
n = A->ncol;
Astore = A->Store;
nnz = Astore->nnz;
a = Astore->nzval;
colptr = Astore->colptr;
rowind = Astore->rowind;
if ( factored || (Fact == SamePattern_SameRowPerm && Equil) ) {
rowequ = (ScalePermstruct->DiagScale == ROW) ||
(ScalePermstruct->DiagScale == BOTH);
colequ = (ScalePermstruct->DiagScale == COL) ||
(ScalePermstruct->DiagScale == BOTH);
} else rowequ = colequ = FALSE;
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(iam, "Enter pzgssvx_ABglobal()");
#endif
perm_r = ScalePermstruct->perm_r;
perm_c = ScalePermstruct->perm_c;
etree = LUstruct->etree;
R = ScalePermstruct->R;
C = ScalePermstruct->C;
if ( Equil && Fact != SamePattern_SameRowPerm ) {
/* Allocate storage if not done so before. */
switch ( ScalePermstruct->DiagScale ) {
case NOEQUIL:
if ( !(R = (double *) doubleMalloc_dist(m)) )
ABORT("Malloc fails for R[].");
if ( !(C = (double *) doubleMalloc_dist(n)) )
ABORT("Malloc fails for C[].");
ScalePermstruct->R = R;
ScalePermstruct->C = C;
break;
case ROW:
if ( !(C = (double *) doubleMalloc_dist(n)) )
ABORT("Malloc fails for C[].");
ScalePermstruct->C = C;
break;
case COL:
if ( !(R = (double *) doubleMalloc_dist(m)) )
ABORT("Malloc fails for R[].");
ScalePermstruct->R = R;
break;
}
}
/* ------------------------------------------------------------
Diagonal scaling to equilibrate the matrix.
------------------------------------------------------------*/
if ( Equil ) {
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(iam, "Enter equil");
#endif
t = SuperLU_timer_();
if ( Fact == SamePattern_SameRowPerm ) {
/* Reuse R and C. */
switch ( ScalePermstruct->DiagScale ) {
case NOEQUIL:
break;
case ROW:
for (j = 0; j < n; ++j) {
for (i = colptr[j]; i < colptr[j+1]; ++i) {
irow = rowind[i];
zd_mult(&a[i], &a[i], R[i]); /* Scale rows. */
}
}
break;
case COL:
for (j = 0; j < n; ++j)
for (i = colptr[j]; i < colptr[j+1]; ++i)
zd_mult(&a[i], &a[i], C[j]); /* Scale columns. */
break;
case BOTH:
for (j = 0; j < n; ++j) {
for (i = colptr[j]; i < colptr[j+1]; ++i) {
irow = rowind[i];
zd_mult(&a[i], &a[i], R[irow]); /* Scale rows. */
zd_mult(&a[i], &a[i], C[j]); /* Scale columns. */
}
}
break;
}
} else {
if ( !iam ) {
/* Compute row and column scalings to equilibrate matrix A. */
zgsequ_dist(A, R, C, &rowcnd, &colcnd, &amax, &iinfo);
MPI_Bcast( &iinfo, 1, mpi_int_t, 0, grid->comm );
if ( iinfo == 0 ) {
MPI_Bcast( R, m, MPI_DOUBLE, 0, grid->comm );
MPI_Bcast( C, n, MPI_DOUBLE, 0, grid->comm );
MPI_Bcast( &rowcnd, 1, MPI_DOUBLE, 0, grid->comm );
MPI_Bcast( &colcnd, 1, MPI_DOUBLE, 0, grid->comm );
MPI_Bcast( &amax, 1, MPI_DOUBLE, 0, grid->comm );
} else {
if ( iinfo > 0 ) {
if ( iinfo <= m )
fprintf(stderr, "The %d-th row of A is exactly zero\n",
iinfo);
else fprintf(stderr, "The %d-th column of A is exactly zero\n",
iinfo-n);
exit(-1);
}
}
} else {
MPI_Bcast( &iinfo, 1, mpi_int_t, 0, grid->comm );
if ( iinfo == 0 ) {
MPI_Bcast( R, m, MPI_DOUBLE, 0, grid->comm );
MPI_Bcast( C, n, MPI_DOUBLE, 0, grid->comm );
MPI_Bcast( &rowcnd, 1, MPI_DOUBLE, 0, grid->comm );
MPI_Bcast( &colcnd, 1, MPI_DOUBLE, 0, grid->comm );
MPI_Bcast( &amax, 1, MPI_DOUBLE, 0, grid->comm );
} else {
ABORT("ZGSEQU failed\n");
}
}
/* Equilibrate matrix A. */
zlaqgs_dist(A, R, C, rowcnd, colcnd, amax, equed);
if ( lsame_(equed, "R") ) {
ScalePermstruct->DiagScale = rowequ = ROW;
} else if ( lsame_(equed, "C") ) {
ScalePermstruct->DiagScale = colequ = COL;
} else if ( lsame_(equed, "B") ) {
ScalePermstruct->DiagScale = BOTH;
rowequ = ROW;
colequ = COL;
} else ScalePermstruct->DiagScale = NOEQUIL;
#if ( PRNTlevel>=1 )
if ( !iam ) {
printf(".. equilibrated? *equed = %c\n", *equed);
/*fflush(stdout);*/
}
#endif
} /* if Fact ... */
stat->utime[EQUIL] = SuperLU_timer_() - t;
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(iam, "Exit equil");
#endif
} /* end if Equil ... */
/* ------------------------------------------------------------
Permute rows of A.
------------------------------------------------------------*/
if ( options->RowPerm != NO ) {
t = SuperLU_timer_();
if ( Fact == SamePattern_SameRowPerm /* Reuse perm_r. */
|| options->RowPerm == MY_PERMR ) { /* Use my perm_r. */
for (j = 0; j < n; ++j) {
for (i = colptr[j]; i < colptr[j+1]; ++i) {
irow = rowind[i];
rowind[i] = perm_r[irow];
}
}
} else if ( !factored ) {
if ( job == 5 ) {
/* Allocate storage for scaling factors. */
if ( !(R1 = (double *) SUPERLU_MALLOC(m * sizeof(double))) )
ABORT("SUPERLU_MALLOC fails for R1[]");
if ( !(C1 = (double *) SUPERLU_MALLOC(n * sizeof(double))) )
ABORT("SUPERLU_MALLOC fails for C1[]");
}
if ( !iam ) {
/* Process 0 finds a row permutation for large diagonal. */
zldperm(job, m, nnz, colptr, rowind, a, perm_r, R1, C1);
MPI_Bcast( perm_r, m, mpi_int_t, 0, grid->comm );
if ( job == 5 && Equil ) {
MPI_Bcast( R1, m, MPI_DOUBLE, 0, grid->comm );
MPI_Bcast( C1, n, MPI_DOUBLE, 0, grid->comm );
}
} else {
MPI_Bcast( perm_r, m, mpi_int_t, 0, grid->comm );
if ( job == 5 && Equil ) {
MPI_Bcast( R1, m, MPI_DOUBLE, 0, grid->comm );
MPI_Bcast( C1, n, MPI_DOUBLE, 0, grid->comm );
}
}
#if ( PRNTlevel>=2 )
dmin = dlamch_("Overflow");
dsum = 0.0;
dprod = 1.0;
#endif
if ( job == 5 ) {
if ( Equil ) {
for (i = 0; i < n; ++i) {
R1[i] = exp(R1[i]);
C1[i] = exp(C1[i]);
}
for (j = 0; j < n; ++j) {
for (i = colptr[j]; i < colptr[j+1]; ++i) {
irow = rowind[i];
zd_mult(&a[i], &a[i], R1[irow]); /* Scale rows. */
zd_mult(&a[i], &a[i], C1[j]); /* Scale columns. */
rowind[i] = perm_r[irow];
#if ( PRNTlevel>=2 )
if ( rowind[i] == j ) /* New diagonal */
dprod *= slud_z_abs1(&a[i]);
#endif
}
}
/* Multiply together the scaling factors. */
if ( rowequ ) for (i = 0; i < m; ++i) R[i] *= R1[i];
else for (i = 0; i < m; ++i) R[i] = R1[i];
if ( colequ ) for (i = 0; i < n; ++i) C[i] *= C1[i];
else for (i = 0; i < n; ++i) C[i] = C1[i];
ScalePermstruct->DiagScale = BOTH;
rowequ = colequ = 1;
} else { /* No equilibration. */
for (j = 0; j < n; ++j) {
for (i = colptr[j]; i < colptr[j+1]; ++i) {
irow = rowind[i];
rowind[i] = perm_r[irow];
}
}
}
SUPERLU_FREE (R1);
SUPERLU_FREE (C1);
} else { /* job = 2,3,4 */
for (j = 0; j < n; ++j) {
for (i = colptr[j]; i < colptr[j+1]; ++i) {
irow = rowind[i];
rowind[i] = perm_r[irow];
#if ( PRNTlevel>=2 )
if ( rowind[i] == j ) { /* New diagonal */
if ( job == 2 || job == 3 )
dmin = SUPERLU_MIN(dmin, slud_z_abs1(&a[i]));
else if ( job == 4 )
dsum += slud_z_abs1(&a[i]);
else if ( job == 5 )
dprod *= slud_z_abs1(&a[i]);
}
#endif
}
}
}
#if ( PRNTlevel>=2 )
if ( job == 2 || job == 3 ) {
if ( !iam ) printf("\tsmallest diagonal %e\n", dmin);
} else if ( job == 4 ) {
if ( !iam ) printf("\tsum of diagonal %e\n", dsum);
} else if ( job == 5 ) {
if ( !iam ) printf("\t product of diagonal %e\n", dprod);
}
#endif
} /* else !factored */
t = SuperLU_timer_() - t;
stat->utime[ROWPERM] = t;
} else { /* options->RowPerm == NOROWPERM */
for (i = 0; i < m; ++i) perm_r[i] = i;
}
if ( !factored || options->IterRefine ) {
/* Compute norm(A), which will be used to adjust small diagonal. */
if ( notran ) *(unsigned char *)norm = '1';
else *(unsigned char *)norm = 'I';
anorm = zlangs_dist(norm, A);
}
/* ------------------------------------------------------------
Perform the LU factorization.
------------------------------------------------------------*/
if ( !factored ) {
t = SuperLU_timer_();
/*
* Get column permutation vector perm_c[], according to permc_spec:
* permc_spec = NATURAL: natural ordering
* permc_spec = MMD_AT_PLUS_A: minimum degree on structure of A'+A
* permc_spec = MMD_ATA: minimum degree on structure of A'*A
* permc_spec = MY_PERMC: the ordering already supplied in perm_c[]
*/
permc_spec = options->ColPerm;
if ( permc_spec != MY_PERMC && Fact == DOFACT )
/* Use an ordering provided by SuperLU */
get_perm_c_dist(iam, permc_spec, A, perm_c);
/* Compute the elimination tree of Pc*(A'+A)*Pc' or Pc*A'*A*Pc'
(a.k.a. column etree), depending on the choice of ColPerm.
Adjust perm_c[] to be consistent with a postorder of etree.
Permute columns of A to form A*Pc'. */
sp_colorder(options, A, perm_c, etree, &AC);
/* Form Pc*A*Pc' to preserve the diagonal of the matrix Pr*A. */
ACstore = AC.Store;
for (j = 0; j < n; ++j)
for (i = ACstore->colbeg[j]; i < ACstore->colend[j]; ++i) {
irow = ACstore->rowind[i];
ACstore->rowind[i] = perm_c[irow];
}
stat->utime[COLPERM] = SuperLU_timer_() - t;
/* Perform a symbolic factorization on matrix A and set up the
nonzero data structures which are suitable for supernodal GENP. */
if ( Fact != SamePattern_SameRowPerm ) {
#if ( PRNTlevel>=1 )
if ( !iam )
printf(".. symbfact(): relax %4d, maxsuper %4d, fill %4d\n",
sp_ienv_dist(2), sp_ienv_dist(3), sp_ienv_dist(6));
#endif
t = SuperLU_timer_();
if ( !(Glu_freeable = (Glu_freeable_t *)
SUPERLU_MALLOC(sizeof(Glu_freeable_t))) )
ABORT("Malloc fails for Glu_freeable.");
iinfo = symbfact(options, iam, &AC, perm_c, etree,
Glu_persist, Glu_freeable);
stat->utime[SYMBFAC] = SuperLU_timer_() - t;
if ( iinfo < 0 ) {
QuerySpace_dist(n, -iinfo, Glu_freeable, &symb_mem_usage);
#if ( PRNTlevel>=1 )
if ( !iam ) {
printf("\tNo of supers %ld\n", Glu_persist->supno[n-1]+1);
printf("\tSize of G(L) %ld\n", Glu_freeable->xlsub[n]);
printf("\tSize of G(U) %ld\n", Glu_freeable->xusub[n]);
printf("\tint %d, short %d, float %d, double %d\n",
sizeof(int_t), sizeof(short), sizeof(float),
sizeof(double));
printf("\tSYMBfact (MB):\tL\\U %.2f\ttotal %.2f\texpansions %d\n",
symb_mem_usage.for_lu*1e-6,
symb_mem_usage.total*1e-6,
symb_mem_usage.expansions);
}
#endif
} else {
if ( !iam ) {
fprintf(stderr, "symbfact() error returns %d\n", iinfo);
exit(-1);
}
}
}
/* Distribute the L and U factors onto the process grid. */
t = SuperLU_timer_();
dist_mem_use = zdistribute(Fact, n, &AC, Glu_freeable, LUstruct, grid);
stat->utime[DIST] = SuperLU_timer_() - t;
/* Deallocate storage used in symbolic factor. */
if ( Fact != SamePattern_SameRowPerm ) {
iinfo = symbfact_SubFree(Glu_freeable);
SUPERLU_FREE(Glu_freeable);
}
/* Perform numerical factorization in parallel. */
t = SuperLU_timer_();
pzgstrf(options, m, n, anorm, LUstruct, grid, stat, info);
stat->utime[FACT] = SuperLU_timer_() - t;
#if ( PRNTlevel>=1 )
{
int_t TinyPivots;
float for_lu, total, max, avg, temp;
zQuerySpace_dist(n, LUstruct, grid, &num_mem_usage);
MPI_Reduce( &num_mem_usage.for_lu, &for_lu,
1, MPI_FLOAT, MPI_SUM, 0, grid->comm );
MPI_Reduce( &num_mem_usage.total, &total,
1, MPI_FLOAT, MPI_SUM, 0, grid->comm );
temp = SUPERLU_MAX(symb_mem_usage.total,
symb_mem_usage.for_lu +
(float)dist_mem_use + num_mem_usage.for_lu);
temp = SUPERLU_MAX(temp, num_mem_usage.total);
MPI_Reduce( &temp, &max,
1, MPI_FLOAT, MPI_MAX, 0, grid->comm );
MPI_Reduce( &temp, &avg,
1, MPI_FLOAT, MPI_SUM, 0, grid->comm );
MPI_Allreduce( &stat->TinyPivots, &TinyPivots, 1, mpi_int_t,
MPI_SUM, grid->comm );
stat->TinyPivots = TinyPivots;
if ( !iam ) {
printf("\tNUMfact (MB) all PEs:\tL\\U\t%.2f\tall\t%.2f\n",
for_lu*1e-6, total*1e-6);
printf("\tAll space (MB):"
"\t\ttotal\t%.2f\tAvg\t%.2f\tMax\t%.2f\n",
avg*1e-6, avg/grid->nprow/grid->npcol*1e-6, max*1e-6);
printf("\tNumber of tiny pivots: %10d\n", stat->TinyPivots);
}
}
#endif
#if ( PRNTlevel>=2 )
if ( !iam ) printf(".. pzgstrf INFO = %d\n", *info);
#endif
} else if ( options->IterRefine ) { /* options->Fact==FACTORED */
/* Permute columns of A to form A*Pc' using the existing perm_c.
* NOTE: rows of A were previously permuted to Pc*A.
*/
sp_colorder(options, A, perm_c, NULL, &AC);
} /* if !factored ... */
/* ------------------------------------------------------------
Compute the solution matrix X.
------------------------------------------------------------*/
if ( nrhs ) {
if ( !(b_work = doublecomplexMalloc_dist(n)) )
ABORT("Malloc fails for b_work[]");
/* ------------------------------------------------------------
Scale the right-hand side if equilibration was performed.
------------------------------------------------------------*/
if ( notran ) {
if ( rowequ ) {
b_col = B;
for (j = 0; j < nrhs; ++j) {
for (i = 0; i < m; ++i) zd_mult(&b_col[i], &b_col[i], R[i]);
b_col += ldb;
}
}
} else if ( colequ ) {
b_col = B;
for (j = 0; j < nrhs; ++j) {
for (i = 0; i < m; ++i) zd_mult(&b_col[i], &b_col[i], C[i]);
b_col += ldb;
}
}
/* ------------------------------------------------------------
Permute the right-hand side to form Pr*B.
------------------------------------------------------------*/
if ( options->RowPerm != NO ) {
if ( notran ) {
b_col = B;
for (j = 0; j < nrhs; ++j) {
for (i = 0; i < m; ++i) b_work[perm_r[i]] = b_col[i];
for (i = 0; i < m; ++i) b_col[i] = b_work[i];
b_col += ldb;
}
}
}
/* ------------------------------------------------------------
Permute the right-hand side to form Pc*B.
------------------------------------------------------------*/
if ( notran ) {
b_col = B;
for (j = 0; j < nrhs; ++j) {
for (i = 0; i < m; ++i) b_work[perm_c[i]] = b_col[i];
for (i = 0; i < m; ++i) b_col[i] = b_work[i];
b_col += ldb;
}
}
/* Save a copy of the right-hand side. */
ldx = ldb;
if ( !(X = doublecomplexMalloc_dist(((size_t)ldx) * nrhs)) )
ABORT("Malloc fails for X[]");
x_col = X; b_col = B;
for (j = 0; j < nrhs; ++j) {
for (i = 0; i < ldb; ++i) x_col[i] = b_col[i];
x_col += ldx; b_col += ldb;
}
/* ------------------------------------------------------------
Solve the linear system.
------------------------------------------------------------*/
pzgstrs_Bglobal(n, LUstruct, grid, X, ldb, nrhs, stat, info);
/* ------------------------------------------------------------
Use iterative refinement to improve the computed solution and
compute error bounds and backward error estimates for it.
------------------------------------------------------------*/
if ( options->IterRefine ) {
/* Improve the solution by iterative refinement. */
t = SuperLU_timer_();
pzgsrfs_ABXglobal(n, &AC, anorm, LUstruct, grid, B, ldb,
X, ldx, nrhs, berr, stat, info);
stat->utime[REFINE] = SuperLU_timer_() - t;
}
/* Permute the solution matrix X <= Pc'*X. */
for (j = 0; j < nrhs; j++) {
b_col = &B[j*ldb];
x_col = &X[j*ldx];
for (i = 0; i < n; ++i) b_col[i] = x_col[perm_c[i]];
}
/* Transform the solution matrix X to a solution of the original system
before the equilibration. */
if ( notran ) {
if ( colequ ) {
b_col = B;
for (j = 0; j < nrhs; ++j) {
for (i = 0; i < n; ++i) zd_mult(&b_col[i], &b_col[i], C[i]);
b_col += ldb;
}
}
} else if ( rowequ ) {
b_col = B;
for (j = 0; j < nrhs; ++j) {
for (i = 0; i < n; ++i) zd_mult(&b_col[i], &b_col[i], R[i]);
b_col += ldb;
}
}
SUPERLU_FREE(b_work);
SUPERLU_FREE(X);
} /* end if nrhs != 0 */
#if ( PRNTlevel>=1 )
if ( !iam ) printf(".. DiagScale = %d\n", ScalePermstruct->DiagScale);
#endif
/* Deallocate R and/or C if it is not used. */
if ( Equil && Fact != SamePattern_SameRowPerm ) {
switch ( ScalePermstruct->DiagScale ) {
case NOEQUIL:
SUPERLU_FREE(R);
SUPERLU_FREE(C);
break;
case ROW:
SUPERLU_FREE(C);
break;
case COL:
SUPERLU_FREE(R);
break;
}
}
if ( !factored || (factored && options->IterRefine) )
Destroy_CompCol_Permuted_dist(&AC);
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(iam, "Exit pzgssvx_ABglobal()");
#endif
}
/*! \brief
*
* <pre>
* Create the distributed modified sparse row (MSR) matrix: bindx/val.
* For a submatrix of size m-by-n, the MSR arrays are as follows:
* bindx[0] = m + 1
* bindx[0..m] = pointer to start of each row
* bindx[ks..ke] = column indices of the off-diagonal nonzeros in row k,
* where, ks = bindx[k], ke = bindx[k+1]-1
* val[k] = A(k,k), k < m, diagonal elements
* val[m] = not used
* val[ki] = A(k, bindx[ki]), where ks <= ki <= ke
* Both arrays are of length nnz + 1.
* </pre>
*/
static void zcreate_msr_matrix
(
SuperMatrix *A, /* Matrix A permuted by columns (input).
The type of A can be:
Stype = SLU_NCP; Dtype = SLU_Z; Mtype = SLU_GE. */
int_t update[], /* input (local) */
int_t N_update, /* input (local) */
doublecomplex **val, /* output */
int_t **bindx /* output */
)
{
int hi, i, irow, j, k, lo, n, nnz_local, nnz_diag;
NCPformat *Astore;
doublecomplex *nzval;
int_t *rowcnt;
doublecomplex zero = {0.0, 0.0};
if ( !N_update ) return;
n = A->ncol;
Astore = A->Store;
nzval = Astore->nzval;
/* One pass of original matrix A to count nonzeros of each row. */
if ( !(rowcnt = (int_t *) intCalloc_dist(N_update)) )
ABORT("Malloc fails for rowcnt[]");
lo = update[0];
hi = update[N_update-1];
nnz_local = 0;
nnz_diag = 0;
for (j = 0; j < n; ++j) {
for (i = Astore->colbeg[j]; i < Astore->colend[j]; ++i) {
irow = Astore->rowind[i];
if ( irow >= lo && irow <= hi ) {
if ( irow != j ) /* Exclude diagonal */
++rowcnt[irow - lo];
else ++nnz_diag; /* Count nonzero diagonal entries */
++nnz_local;
}
}
}
/* Add room for the logical diagonal zeros which are not counted
in nnz_local. */
nnz_local += (N_update - nnz_diag);
/* Allocate storage for bindx[] and val[]. */
if ( !(*val = (doublecomplex *) doublecomplexMalloc_dist(nnz_local+1)) )
ABORT("Malloc fails for val[]");
for (i = 0; i < N_update; ++i) (*val)[i] = zero; /* Initialize diagonal */
if ( !(*bindx = (int_t *) SUPERLU_MALLOC((nnz_local+1) * sizeof(int_t))) )
ABORT("Malloc fails for bindx[]");
/* Set up row pointers. */
(*bindx)[0] = N_update + 1;
for (j = 1; j <= N_update; ++j) {
(*bindx)[j] = (*bindx)[j-1] + rowcnt[j-1];
rowcnt[j-1] = (*bindx)[j-1];
}
/* One pass of original matrix A to fill in matrix entries. */
for (j = 0; j < n; ++j) {
for (i = Astore->colbeg[j]; i < Astore->colend[j]; ++i) {
irow = Astore->rowind[i];
if ( irow >= lo && irow <= hi ) {
if ( irow == j ) /* Diagonal */
(*val)[irow - lo] = nzval[i];
else {
irow -= lo;
k = rowcnt[irow];
(*bindx)[k] = j;
(*val)[k] = nzval[i];
++rowcnt[irow];
}
}
}
}
SUPERLU_FREE(rowcnt);
}
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 main(int argc, char *argv[])
{
superlu_options_t options;
SuperLUStat_t stat;
SuperMatrix A;
ScalePermstruct_t ScalePermstruct;
LUstruct_t LUstruct;
gridinfo_t grid;
double *berr;
doublecomplex *a, *a1, *b, *b1, *xtrue;
int_t *asub, *asub1, *xa, *xa1;
int_t i, j, m, n, nnz;
int_t nprow, npcol;
int iam, info, ldb, ldx, nrhs;
char trans[1];
char **cpp, c;
FILE *fp, *fopen();
extern int cpp_defs();
nprow = 1; /* Default process rows. */
npcol = 1; /* Default process columns. */
nrhs = 1; /* Number of right-hand side. */
/* ------------------------------------------------------------
INITIALIZE MPI ENVIRONMENT.
------------------------------------------------------------*/
MPI_Init( &argc, &argv );
/* Parse command line argv[]. */
for (cpp = argv+1; *cpp; ++cpp) {
if ( **cpp == '-' ) {
c = *(*cpp+1);
++cpp;
switch (c) {
case 'h':
printf("Options:\n");
printf("\t-r <int>: process rows (default %d)\n", nprow);
printf("\t-c <int>: process columns (default %d)\n", npcol);
exit(0);
break;
case 'r': nprow = atoi(*cpp);
break;
case 'c': npcol = atoi(*cpp);
break;
}
} else { /* Last arg is considered a filename */
if ( !(fp = fopen(*cpp, "r")) ) {
ABORT("File does not exist");
}
break;
}
}
/* ------------------------------------------------------------
INITIALIZE THE SUPERLU PROCESS GRID.
------------------------------------------------------------*/
superlu_gridinit(MPI_COMM_WORLD, nprow, npcol, &grid);
/* Bail out if I do not belong in the grid. */
iam = grid.iam;
if ( iam >= nprow * npcol )
goto out;
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(iam, "Enter main()");
#endif
/* ------------------------------------------------------------
Process 0 reads the matrix A, and then broadcasts it to all
the other processes.
------------------------------------------------------------*/
if ( !iam ) {
/* Print the CPP definitions. */
cpp_defs();
/* Read the matrix stored on disk in Harwell-Boeing format. */
zreadhb_dist(iam, fp, &m, &n, &nnz, &a, &asub, &xa);
printf("Input matrix file: %s\n", *cpp);
printf("\tDimension\t%dx%d\t # nonzeros %d\n", m, n, nnz);
printf("\tProcess grid\t%d X %d\n", grid.nprow, grid.npcol);
/* Broadcast matrix A to the other PEs. */
MPI_Bcast( &m, 1, mpi_int_t, 0, grid.comm );
MPI_Bcast( &n, 1, mpi_int_t, 0, grid.comm );
MPI_Bcast( &nnz, 1, mpi_int_t, 0, grid.comm );
MPI_Bcast( a, nnz, SuperLU_MPI_DOUBLE_COMPLEX, 0, grid.comm );
MPI_Bcast( asub, nnz, mpi_int_t, 0, grid.comm );
MPI_Bcast( xa, n+1, mpi_int_t, 0, grid.comm );
} else {
/* Receive matrix A from PE 0. */
MPI_Bcast( &m, 1, mpi_int_t, 0, grid.comm );
MPI_Bcast( &n, 1, mpi_int_t, 0, grid.comm );
MPI_Bcast( &nnz, 1, mpi_int_t, 0, grid.comm );
/* Allocate storage for compressed column representation. */
zallocateA_dist(n, nnz, &a, &asub, &xa);
MPI_Bcast( a, nnz, SuperLU_MPI_DOUBLE_COMPLEX, 0, grid.comm );
MPI_Bcast( asub, nnz, mpi_int_t, 0, grid.comm );
MPI_Bcast( xa, n+1, mpi_int_t, 0, grid.comm );
}
/* Create compressed column matrix for A. */
zCreate_CompCol_Matrix_dist(&A, m, n, nnz, a, asub, xa,
SLU_NC, SLU_Z, SLU_GE);
/* Generate the exact solution and compute the right-hand side. */
if (!(b=doublecomplexMalloc_dist(m * nrhs))) ABORT("Malloc fails for b[]");
if (!(xtrue=doublecomplexMalloc_dist(n*nrhs))) ABORT("Malloc fails for xtrue[]");
*trans = 'N';
ldx = n;
ldb = m;
zGenXtrue_dist(n, nrhs, xtrue, ldx);
zFillRHS_dist(trans, nrhs, xtrue, ldx, &A, b, ldb);
/* Save a copy of the right-hand side. */
if ( !(b1 = doublecomplexMalloc_dist(m * nrhs)) ) ABORT("Malloc fails for b1[]");
for (j = 0; j < nrhs; ++j)
for (i = 0; i < m; ++i) b1[i+j*ldb] = b[i+j*ldb];
if ( !(berr = doubleMalloc_dist(nrhs)) )
ABORT("Malloc fails for berr[].");
/* Save a copy of the matrix A. */
zallocateA_dist(n, nnz, &a1, &asub1, &xa1);
for (i = 0; i < nnz; ++i) { a1[i] = a[i]; asub1[i] = asub[i]; }
for (i = 0; i < n+1; ++i) xa1[i] = xa[i];
/* ------------------------------------------------------------
WE SOLVE THE LINEAR SYSTEM FOR THE FIRST TIME.
------------------------------------------------------------*/
/* Set the default input options:
options.Fact = DOFACT;
options.Equil = YES;
options.ColPerm = METIS_AT_PLUS_A;
options.RowPerm = LargeDiag;
options.ReplaceTinyPivot = YES;
options.Trans = NOTRANS;
options.IterRefine = DOUBLE;
options.SolveInitialized = NO;
options.RefineInitialized = NO;
options.PrintStat = YES;
*/
set_default_options_dist(&options);
if (!iam) {
print_sp_ienv_dist(&options);
print_options_dist(&options);
}
/* Initialize ScalePermstruct and LUstruct. */
ScalePermstructInit(m, n, &ScalePermstruct);
LUstructInit(n, &LUstruct);
/* Initialize the statistics variables. */
PStatInit(&stat);
/* Call the linear equation solver: factorize and solve. */
pzgssvx_ABglobal(&options, &A, &ScalePermstruct, b, ldb, nrhs, &grid,
&LUstruct, berr, &stat, &info);
/* Check the accuracy of the solution. */
if ( !iam ) {
zinf_norm_error_dist(n, nrhs, b, ldb, xtrue, ldx, &grid);
}
PStatPrint(&options, &stat, &grid); /* Print the statistics. */
PStatFree(&stat);
Destroy_CompCol_Matrix_dist(&A); /* Deallocate storage of matrix A. */
Destroy_LU(n, &grid, &LUstruct); /* Deallocate storage associated with
the L and U matrices. */
SUPERLU_FREE(b); /* Free storage of right-hand side. */
/* ------------------------------------------------------------
NOW WE SOLVE ANOTHER LINEAR SYSTEM.
ONLY THE SPARSITY PATTERN OF MATRIX A IS THE SAME.
------------------------------------------------------------*/
options.Fact = SamePattern;
PStatInit(&stat); /* Initialize the statistics variables. */
/* Create compressed column matrix for A. */
zCreate_CompCol_Matrix_dist(&A, m, n, nnz, a1, asub1, xa1,
SLU_NC, SLU_Z, SLU_GE);
/* Solve the linear system. */
pzgssvx_ABglobal(&options, &A, &ScalePermstruct, b1, ldb, nrhs, &grid,
&LUstruct, berr, &stat, &info);
/* Check the accuracy of the solution. */
if ( !iam ) {
printf("Solve the system with the same sparsity pattern.\n");
zinf_norm_error_dist(n, nrhs, b1, ldb, xtrue, ldx, &grid);
}
/* Print the statistics. */
PStatPrint(&options, &stat, &grid);
/* ------------------------------------------------------------
DEALLOCATE STORAGE.
------------------------------------------------------------*/
PStatFree(&stat);
Destroy_CompCol_Matrix_dist(&A); /* Deallocate storage of matrix A. */
Destroy_LU(n, &grid, &LUstruct); /* Deallocate storage associated with
the L and U matrices. */
ScalePermstructFree(&ScalePermstruct);
LUstructFree(&LUstruct); /* Deallocate the structure of L and U.*/
SUPERLU_FREE(b1); /* Free storage of right-hand side. */
SUPERLU_FREE(xtrue); /* Free storage of the exact solution. */
SUPERLU_FREE(berr);
/* ------------------------------------------------------------
RELEASE THE SUPERLU PROCESS GRID.
------------------------------------------------------------*/
out:
superlu_gridexit(&grid);
/* ------------------------------------------------------------
TERMINATES THE MPI EXECUTION ENVIRONMENT.
------------------------------------------------------------*/
MPI_Finalize();
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(iam, "Exit main()");
#endif
}
void pzgsmv_init
(
SuperMatrix *A, /* Matrix A permuted by columns (input/output).
The type of A can be:
Stype = SLU_NR_loc; Dtype = SLU_Z; Mtype = SLU_GE. */
int_t *row_to_proc, /* Input. Mapping between rows and processes. */
gridinfo_t *grid, /* Input */
pzgsmv_comm_t *gsmv_comm /* Output. The data structure for communication. */
)
{
NRformat_loc *Astore;
int iam, p, procs;
int *SendCounts, *RecvCounts;
int_t i, j, k, l, m, m_loc, n, fst_row, jcol;
int_t TotalIndSend, TotalValSend;
int_t *colind, *rowptr;
int_t *ind_tosend = NULL, *ind_torecv = NULL;
int_t *ptr_ind_tosend, *ptr_ind_torecv;
int_t *extern_start, *spa, *itemp;
doublecomplex *nzval, *val_tosend = NULL, *val_torecv = NULL, t;
MPI_Request *send_req, *recv_req;
MPI_Status status;
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(grid->iam, "Enter pzgsmv_init()");
#endif
/* ------------------------------------------------------------
INITIALIZATION.
------------------------------------------------------------*/
iam = grid->iam;
procs = grid->nprow * grid->npcol;
Astore = (NRformat_loc *) A->Store;
m = A->nrow;
n = A->ncol;
m_loc = Astore->m_loc;
fst_row = Astore->fst_row;
colind = Astore->colind;
rowptr = Astore->rowptr;
nzval = Astore->nzval;
if ( !(SendCounts = SUPERLU_MALLOC(2*procs * sizeof(int))) )
ABORT("Malloc fails for SendCounts[]");
/*for (i = 0; i < 2*procs; ++i) SendCounts[i] = 0;*/
RecvCounts = SendCounts + procs;
if ( !(ptr_ind_tosend = intMalloc_dist(2*(procs+1))) )
ABORT("Malloc fails for ptr_ind_tosend[]");
ptr_ind_torecv = ptr_ind_tosend + procs + 1;
if ( !(extern_start = intMalloc_dist(m_loc)) )
ABORT("Malloc fails for extern_start[]");
for (i = 0; i < m_loc; ++i) extern_start[i] = rowptr[i];
/* ------------------------------------------------------------
COUNT THE NUMBER OF X ENTRIES TO BE SENT TO EACH PROCESS.
THIS IS THE UNION OF THE COLUMN INDICES OF MY ROWS.
SWAP TO THE BEGINNING THE PART OF A CORRESPONDING TO THE
LOCAL PART OF X.
THIS ACCOUNTS FOR THE FIRST PASS OF ACCESSING MATRIX A.
------------------------------------------------------------*/
if ( !(spa = intCalloc_dist(n)) ) /* Aid in global to local translation */
ABORT("Malloc fails for spa[]");
for (p = 0; p < procs; ++p) SendCounts[p] = 0;
for (i = 0; i < m_loc; ++i) { /* Loop through each row */
k = extern_start[i];
for (j = rowptr[i]; j < rowptr[i+1]; ++j) {/* Each nonzero in row i */
jcol = colind[j];
p = row_to_proc[jcol];
if ( p != iam ) { /* External */
if ( spa[jcol] == 0 ) { /* First time see this index */
++SendCounts[p];
spa[jcol] = 1;
}
} else { /* Swap to beginning the part of A corresponding
to the local part of X */
l = colind[k];
t = nzval[k];
colind[k] = jcol;
nzval[k] = nzval[j];
colind[j] = l;
nzval[j] = t;
++k;
}
}
extern_start[i] = k;
}
/* ------------------------------------------------------------
LOAD THE X-INDICES TO BE SENT TO THE OTHER PROCESSES.
THIS ACCOUNTS FOR THE SECOND PASS OF ACCESSING MATRIX A.
------------------------------------------------------------*/
/* Build pointers to ind_tosend[]. */
ptr_ind_tosend[0] = 0;
for (p = 0, TotalIndSend = 0; p < procs; ++p) {
TotalIndSend += SendCounts[p]; /* Total to send. */
ptr_ind_tosend[p+1] = ptr_ind_tosend[p] + SendCounts[p];
}
#if 0
ptr_ind_tosend[iam] = 0; /* Local part of X */
#endif
if ( TotalIndSend ) {
if ( !(ind_tosend = intMalloc_dist(TotalIndSend)) )
ABORT("Malloc fails for ind_tosend[]"); /* Exclude local part of X */
}
/* Build SPA to aid global to local translation. */
for (i = 0; i < n; ++i) spa[i] = EMPTY;
for (i = 0; i < m_loc; ++i) { /* Loop through each row of A */
for (j = rowptr[i]; j < rowptr[i+1]; ++j) {
jcol = colind[j];
if ( spa[jcol] == EMPTY ) { /* First time see this index */
p = row_to_proc[jcol];
if ( p == iam ) { /* Local */
/*assert(jcol>=fst_row);*/
spa[jcol] = jcol - fst_row; /* Relative position in local X */
} else { /* External */
ind_tosend[ptr_ind_tosend[p]] = jcol; /* Still global */
spa[jcol] = ptr_ind_tosend[p]; /* Position in ind_tosend[] */
++ptr_ind_tosend[p];
}
}
}
}
/* ------------------------------------------------------------
TRANSFORM THE COLUMN INDICES OF MATRIX A INTO LOCAL INDICES.
THIS ACCOUNTS FOR THE THIRD PASS OF ACCESSING MATRIX A.
------------------------------------------------------------*/
for (i = 0; i < m_loc; ++i) {
for (j = rowptr[i]; j < rowptr[i+1]; ++j) {
jcol = colind[j];
colind[j] = spa[jcol];
}
}
/* ------------------------------------------------------------
COMMUNICATE THE EXTERNAL INDICES OF X.
------------------------------------------------------------*/
MPI_Alltoall(SendCounts, 1, MPI_INT, RecvCounts, 1, MPI_INT,
grid->comm);
/* Build pointers to ind_torecv[]. */
ptr_ind_torecv[0] = 0;
for (p = 0, TotalValSend = 0; p < procs; ++p) {
TotalValSend += RecvCounts[p]; /* Total to receive. */
ptr_ind_torecv[p+1] = ptr_ind_torecv[p] + RecvCounts[p];
}
if ( TotalValSend ) {
if ( !(ind_torecv = intMalloc_dist(TotalValSend)) )
ABORT("Malloc fails for ind_torecv[]");
}
if ( !(send_req = (MPI_Request *)
SUPERLU_MALLOC(2*procs *sizeof(MPI_Request))))
ABORT("Malloc fails for recv_req[].");
recv_req = send_req + procs;
for (p = 0; p < procs; ++p) {
ptr_ind_tosend[p] -= SendCounts[p]; /* Reset pointer to beginning */
if ( SendCounts[p] ) {
MPI_Isend(&ind_tosend[ptr_ind_tosend[p]], SendCounts[p],
mpi_int_t, p, iam, grid->comm, &send_req[p]);
}
if ( RecvCounts[p] ) {
MPI_Irecv(&ind_torecv[ptr_ind_torecv[p]], RecvCounts[p],
mpi_int_t, p, p, grid->comm, &recv_req[p]);
}
}
for (p = 0; p < procs; ++p) {
if ( SendCounts[p] ) MPI_Wait(&send_req[p], &status);
if ( RecvCounts[p] ) MPI_Wait(&recv_req[p], &status);
}
/* Allocate storage for the X values to to transferred. */
if ( TotalIndSend &&
!(val_torecv = doublecomplexMalloc_dist(TotalIndSend)) )
ABORT("Malloc fails for val_torecv[].");
if ( TotalValSend &&
!(val_tosend = doublecomplexMalloc_dist(TotalValSend)) )
ABORT("Malloc fails for val_tosend[].");
gsmv_comm->extern_start = extern_start;
gsmv_comm->ind_tosend = ind_tosend;
gsmv_comm->ind_torecv = ind_torecv;
gsmv_comm->ptr_ind_tosend = ptr_ind_tosend;
gsmv_comm->ptr_ind_torecv = ptr_ind_torecv;
gsmv_comm->SendCounts = SendCounts;
gsmv_comm->RecvCounts = RecvCounts;
gsmv_comm->val_tosend = val_tosend;
gsmv_comm->val_torecv = val_torecv;
gsmv_comm->TotalIndSend = TotalIndSend;
gsmv_comm->TotalValSend = TotalValSend;
SUPERLU_FREE(spa);
SUPERLU_FREE(send_req);
#if ( DEBUGlevel>=2 )
PrintInt10("pzgsmv_init::rowptr", m_loc+1, rowptr);
PrintInt10("pzgsmv_init::extern_start", m_loc, extern_start);
#endif
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(iam, "Exit pzgsmv_init()");
#endif
} /* PZGSMV_INIT */
void
pzgsrfs_ABXglobal(int_t n, SuperMatrix *A, double anorm, LUstruct_t *LUstruct,
gridinfo_t *grid, doublecomplex *B, int_t ldb, doublecomplex *X, int_t ldx,
int nrhs, double *berr, SuperLUStat_t *stat, int *info)
{
#define ITMAX 20
Glu_persist_t *Glu_persist = LUstruct->Glu_persist;
LocalLU_t *Llu = LUstruct->Llu;
/*
* Data structures used by matrix-vector multiply routine.
*/
int_t N_update; /* Number of variables updated on this process */
int_t *update; /* vector elements (global index) updated
on this processor. */
int_t *bindx;
doublecomplex *val;
int_t *mv_sup_to_proc; /* Supernode to process mapping in
matrix-vector multiply. */
/*-- end data structures for matrix-vector multiply --*/
doublecomplex *b, *ax, *R, *B_col, *temp, *work, *X_col,
*x_trs, *dx_trs;
double *rwork;
int_t notran;
int_t count, ii, j, jj, k, knsupc, lk, lwork,
nprow, nsupers, nz, p;
int i, iam, pkk;
int_t *ilsum, *xsup;
double eps, lstres;
double s, safmin, safe1, safe2;
/* NEW STUFF */
int_t num_diag_procs, *diag_procs; /* Record diagonal process numbers. */
int_t *diag_len; /* Length of the X vector on diagonal processes. */
/*-- Function prototypes --*/
extern void pzgstrs1(int_t, LUstruct_t *, gridinfo_t *,
doublecomplex *, int, SuperLUStat_t *, int *);
/*extern double dlamch_(char *);*/
/* Test the input parameters. */
*info = 0;
if ( n < 0 ) *info = -1;
else if ( A->nrow != A->ncol || A->nrow < 0 ||
A->Stype != SLU_NCP || A->Dtype != SLU_Z || A->Mtype != SLU_GE )
*info = -2;
else if ( ldb < SUPERLU_MAX(0, n) ) *info = -10;
else if ( ldx < SUPERLU_MAX(0, n) ) *info = -12;
else if ( nrhs < 0 ) *info = -13;
if (*info != 0) {
i = -(*info);
xerbla_("pzgsrfs_ABXglobal", &i);
return;
}
/* Quick return if possible. */
if ( n == 0 || nrhs == 0 ) {
return;
}
/* Initialization. */
iam = grid->iam;
nprow = grid->nprow;
nsupers = Glu_persist->supno[n-1] + 1;
xsup = Glu_persist->xsup;
ilsum = Llu->ilsum;
notran = 1;
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(iam, "Enter pzgsrfs_ABXglobal()");
#endif
get_diag_procs(n, Glu_persist, grid, &num_diag_procs,
&diag_procs, &diag_len);
#if ( PRNTlevel>=1 )
if ( !iam ) {
printf(".. number of diag processes = %d\n", num_diag_procs);
PrintInt10("diag_procs", num_diag_procs, diag_procs);
PrintInt10("diag_len", num_diag_procs, diag_len);
}
#endif
if ( !(mv_sup_to_proc = intCalloc_dist(nsupers)) )
ABORT("Calloc fails for mv_sup_to_proc[]");
pzgsmv_AXglobal_setup(A, Glu_persist, grid, &N_update, &update,
&val, &bindx, mv_sup_to_proc);
i = CEILING( nsupers, nprow ); /* Number of local block rows */
ii = Llu->ldalsum + i * XK_H;
k = SUPERLU_MAX(N_update, sp_ienv_dist(3));
jj = diag_len[0];
for (j = 1; j < num_diag_procs; ++j) jj = SUPERLU_MAX( jj, diag_len[j] );
jj = SUPERLU_MAX( jj, N_update );
lwork = N_update /* For ax and R */
+ ii /* For dx_trs */
+ ii /* For x_trs */
+ k /* For b */
+ jj; /* for temp */
if ( !(work = doublecomplexMalloc_dist(lwork)) )
ABORT("Malloc fails for work[]");
ax = R = work;
dx_trs = work + N_update;
x_trs = dx_trs + ii;
b = x_trs + ii;
temp = b + k;
if ( !(rwork = SUPERLU_MALLOC(N_update * sizeof(double))) )
ABORT("Malloc fails for rwork[]");
#if ( DEBUGlevel>=2 )
{
doublecomplex *dwork = doublecomplexMalloc_dist(n);
for (i = 0; i < n; ++i) {
if ( i & 1 ) dwork[i].r = 1.;
else dwork[i].r = 2.;
dwork[i].i = 0.;
}
/* Check correctness of matrix-vector multiply. */
pzgsmv_AXglobal(N_update, update, val, bindx, dwork, ax);
PrintDouble5("Mult A*x", N_update, ax);
SUPERLU_FREE(dwork);
}
#endif
/* NZ = maximum number of nonzero elements in each row of A, plus 1 */
nz = A->ncol + 1;
eps = dlamch_("Epsilon");
safmin = dlamch_("Safe minimum");
/* Set SAFE1 essentially to be the underflow threshold times the
number of additions in each row. */
safe1 = nz * safmin;
safe2 = safe1 / eps;
#if ( DEBUGlevel>=1 )
if ( !iam ) printf(".. eps = %e\tanorm = %e\tsafe1 = %e\tsafe2 = %e\n",
eps, anorm, safe1, safe2);
#endif
/* Do for each right-hand side ... */
for (j = 0; j < nrhs; ++j) {
count = 0;
lstres = 3.;
/* Copy X into x on the diagonal processes. */
B_col = &B[j*ldb];
X_col = &X[j*ldx];
for (p = 0; p < num_diag_procs; ++p) {
pkk = diag_procs[p];
if ( iam == pkk ) {
for (k = p; k < nsupers; k += num_diag_procs) {
knsupc = SuperSize( k );
lk = LBi( k, grid );
ii = ilsum[lk] + (lk+1)*XK_H;
jj = FstBlockC( k );
for (i = 0; i < knsupc; ++i) x_trs[i+ii] = X_col[i+jj];
dx_trs[ii-XK_H].r = k;/* Block number prepended in header. */
}
}
}
/* Copy B into b distributed the same way as matrix-vector product. */
if ( N_update ) ii = update[0];
for (i = 0; i < N_update; ++i) b[i] = B_col[i + ii];
while (1) { /* Loop until stopping criterion is satisfied. */
/* Compute residual R = B - op(A) * X,
where op(A) = A, A**T, or A**H, depending on TRANS. */
/* Matrix-vector multiply. */
pzgsmv_AXglobal(N_update, update, val, bindx, X_col, ax);
/* Compute residual. */
for (i = 0; i < N_update; ++i) z_sub(&R[i], &b[i], &ax[i]);
/* Compute abs(op(A))*abs(X) + abs(B). */
pzgsmv_AXglobal_abs(N_update, update, val, bindx, X_col, rwork);
for (i = 0; i < N_update; ++i) rwork[i] += slud_z_abs1(&b[i]);
s = 0.0;
for (i = 0; i < N_update; ++i) {
if ( rwork[i] > safe2 ) {
s = SUPERLU_MAX(s, slud_z_abs1(&R[i]) / rwork[i]);
} else if ( rwork[i] != 0.0 ) {
s = SUPERLU_MAX(s, (safe1 + slud_z_abs1(&R[i])) / rwork[i]);
}
/* If temp[i] is exactly 0.0 (computed by PxGSMV), then
we know the true residual also must be exactly 0.0. */
}
MPI_Allreduce( &s, &berr[j], 1, MPI_DOUBLE, MPI_MAX, grid->comm );
#if ( PRNTlevel>= 1 )
if ( !iam )
printf("(%2d) .. Step %2d: berr[j] = %e\n", iam, count, berr[j]);
#endif
if ( berr[j] > eps && berr[j] * 2 <= lstres && count < ITMAX ) {
/* Compute new dx. */
redist_all_to_diag(n, R, Glu_persist, Llu, grid,
mv_sup_to_proc, dx_trs);
pzgstrs1(n, LUstruct, grid, dx_trs, 1, stat, info);
/* Update solution. */
for (p = 0; p < num_diag_procs; ++p)
if ( iam == diag_procs[p] )
for (k = p; k < nsupers; k += num_diag_procs) {
lk = LBi( k, grid );
ii = ilsum[lk] + (lk+1)*XK_H;
knsupc = SuperSize( k );
for (i = 0; i < knsupc; ++i)
z_add(&x_trs[i + ii], &x_trs[i + ii],
&dx_trs[i + ii]);
}
lstres = berr[j];
++count;
/* Transfer x_trs (on diagonal processes) into X
(on all processes). */
gather_1rhs_diag_to_all(n, x_trs, Glu_persist, Llu, grid,
num_diag_procs, diag_procs, diag_len,
X_col, temp);
} else {
break;
}
} /* end while */
stat->RefineSteps = count;
} /* for j ... */
/* Deallocate storage used by matrix-vector multiplication. */
SUPERLU_FREE(diag_procs);
SUPERLU_FREE(diag_len);
if ( N_update ) {
SUPERLU_FREE(update);
SUPERLU_FREE(bindx);
SUPERLU_FREE(val);
}
SUPERLU_FREE(mv_sup_to_proc);
SUPERLU_FREE(work);
SUPERLU_FREE(rwork);
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(iam, "Exit pzgsrfs_ABXglobal()");
#endif
} /* PZGSRFS_ABXGLOBAL */
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;
}
}
}
void
pzgsrfs_ABXglobal(int_t n, SuperMatrix *A, double anorm, LUstruct_t *LUstruct,
gridinfo_t *grid, doublecomplex *B, int_t ldb,
doublecomplex *X, int_t ldx, int nrhs, double *berr,
SuperLUStat_t *stat, int *info)
{
/*
* Purpose
* =======
*
* pzgsrfs_ABXglobal improves the computed solution to a system of linear
* equations and provides error bounds and backward error estimates
* for the solution.
*
* Arguments
* =========
*
* n (input) int (global)
* The order of the system of linear equations.
*
* A (input) SuperMatrix*
* The original matrix A, or the scaled A if equilibration was done.
* A is also permuted into the form Pc*Pr*A*Pc', where Pr and Pc
* are permutation matrices. The type of A can be:
* Stype = NCP; Dtype = Z; Mtype = GE.
*
* NOTE: Currently, A must reside in all processes when calling
* this routine.
*
* anorm (input) double
* The norm of the original matrix A, or the scaled A if
* equilibration was done.
*
* LUstruct (input) LUstruct_t*
* The distributed data structures storing L and U factors.
* The L and U factors are obtained from pzgstrf for
* the possibly scaled and permuted matrix A.
* See superlu_ddefs.h for the definition of 'LUstruct_t'.
*
* 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_ddefs.h for the definition of 'gridinfo_t'.
*
* B (input) doublecomplex* (global)
* The N-by-NRHS right-hand side matrix of the possibly equilibrated
* and row permuted system.
*
* NOTE: Currently, B must reside on all processes when calling
* this routine.
*
* ldb (input) int (global)
* Leading dimension of matrix B.
*
* X (input/output) doublecomplex* (global)
* On entry, the solution matrix X, as computed by pzgstrs.
* On exit, the improved solution matrix X.
* If DiagScale = COL or BOTH, X should be premultiplied by diag(C)
* in order to obtain the solution to the original system.
*
* NOTE: Currently, X must reside on all processes when calling
* this routine.
*
* ldx (input) int (global)
* Leading dimension of matrix X.
*
* nrhs (input) int
* Number of right-hand sides.
*
* berr (output) double*, dimension (nrhs)
* The componentwise relative backward error of each solution
* vector X(j) (i.e., the smallest relative change in
* any element of A or B that makes X(j) an exact solution).
*
* stat (output) SuperLUStat_t*
* Record the statistics about the refinement steps.
* See util.h for the definition of SuperLUStat_t.
*
* info (output) int*
* = 0: successful exit
* < 0: if info = -i, the i-th argument had an illegal value
*
* Internal Parameters
* ===================
*
* ITMAX is the maximum number of steps of iterative refinement.
*
*/
#define ITMAX 20
Glu_persist_t *Glu_persist = LUstruct->Glu_persist;
LocalLU_t *Llu = LUstruct->Llu;
/*
* Data structures used by matrix-vector multiply routine.
*/
int_t N_update; /* Number of variables updated on this process */
int_t *update; /* vector elements (global index) updated
on this processor. */
int_t *bindx;
doublecomplex *val;
int_t *mv_sup_to_proc; /* Supernode to process mapping in
matrix-vector multiply. */
/*-- end data structures for matrix-vector multiply --*/
doublecomplex *b, *ax, *R, *B_col, *temp, *work, *X_col,
*x_trs, *dx_trs;
double *rwork;
int_t count, ii, j, jj, k, knsupc, lk, lwork,
nprow, nsupers, notran, nz, p;
int i, iam, pkk;
int_t *ilsum, *xsup;
double eps, lstres;
double s, safmin, safe1, safe2;
/* NEW STUFF */
int_t num_diag_procs, *diag_procs; /* Record diagonal process numbers. */
int_t *diag_len; /* Length of the X vector on diagonal processes. */
/*-- Function prototypes --*/
extern void pzgstrs1(int_t, LUstruct_t *, gridinfo_t *,
doublecomplex *, int, SuperLUStat_t *, int *);
extern double dlamch_(char *);
/* Test the input parameters. */
*info = 0;
if ( n < 0 ) *info = -1;
else if ( A->nrow != A->ncol || A->nrow < 0 ||
A->Stype != SLU_NCP || A->Dtype != SLU_Z || A->Mtype != SLU_GE )
*info = -2;
else if ( ldb < SUPERLU_MAX(0, n) ) *info = -10;
else if ( ldx < SUPERLU_MAX(0, n) ) *info = -12;
else if ( nrhs < 0 ) *info = -13;
if (*info != 0) {
i = -(*info);
xerbla_("pzgsrfs_ABXglobal", &i);
return;
}
/* Quick return if possible. */
if ( n == 0 || nrhs == 0 ) {
return;
}
/* Initialization. */
iam = grid->iam;
nprow = grid->nprow;
nsupers = Glu_persist->supno[n-1] + 1;
xsup = Glu_persist->xsup;
ilsum = Llu->ilsum;
notran = 1;
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(iam, "Enter pzgsrfs_ABXglobal()");
#endif
get_diag_procs(n, Glu_persist, grid, &num_diag_procs,
&diag_procs, &diag_len);
#if ( PRNTlevel>=1 )
if ( !iam ) {
printf(".. number of diag processes = %d\n", num_diag_procs);
PrintInt10("diag_procs", num_diag_procs, diag_procs);
PrintInt10("diag_len", num_diag_procs, diag_len);
}
#endif
if ( !(mv_sup_to_proc = intCalloc_dist(nsupers)) )
ABORT("Calloc fails for mv_sup_to_proc[]");
pzgsmv_AXglobal_setup(A, Glu_persist, grid, &N_update, &update,
&val, &bindx, mv_sup_to_proc);
i = CEILING( nsupers, nprow ); /* Number of local block rows */
ii = Llu->ldalsum + i * XK_H;
k = SUPERLU_MAX(N_update, sp_ienv_dist(3));
jj = diag_len[0];
for (j = 1; j < num_diag_procs; ++j) jj = SUPERLU_MAX( jj, diag_len[j] );
jj = SUPERLU_MAX( jj, N_update );
lwork = N_update /* For ax and R */
+ ii /* For dx_trs */
+ ii /* For x_trs */
+ k /* For b */
+ jj; /* for temp */
if ( !(work = doublecomplexMalloc_dist(lwork)) )
ABORT("Malloc fails for work[]");
ax = R = work;
dx_trs = work + N_update;
x_trs = dx_trs + ii;
b = x_trs + ii;
temp = b + k;
if ( !(rwork = SUPERLU_MALLOC(N_update * sizeof(double))) )
ABORT("Malloc fails for rwork[]");
#if ( DEBUGlevel>=2 )
{
doublecomplex *dwork = doublecomplexMalloc_dist(n);
for (i = 0; i < n; ++i) {
if ( i & 1 ) dwork[i].r = 1.;
else dwork[i].r = 2.;
dwork[i].i = 0.;
}
/* Check correctness of matrix-vector multiply. */
pzgsmv_AXglobal(N_update, update, val, bindx, dwork, ax);
PrintDouble5("Mult A*x", N_update, ax);
SUPERLU_FREE(dwork);
}
#endif
/* NZ = maximum number of nonzero elements in each row of A, plus 1 */
nz = A->ncol + 1;
eps = dlamch_("Epsilon");
safmin = dlamch_("Safe minimum");
safe1 = nz * safmin;
safe2 = safe1 / eps;
#if ( DEBUGlevel>=1 )
if ( !iam ) printf(".. eps = %e\tanorm = %e\tsafe1 = %e\tsafe2 = %e\n",
eps, anorm, safe1, safe2);
#endif
/* Do for each right-hand side ... */
for (j = 0; j < nrhs; ++j) {
count = 0;
lstres = 3.;
/* Copy X into x on the diagonal processes. */
B_col = &B[j*ldb];
X_col = &X[j*ldx];
for (p = 0; p < num_diag_procs; ++p) {
pkk = diag_procs[p];
if ( iam == pkk ) {
for (k = p; k < nsupers; k += num_diag_procs) {
knsupc = SuperSize( k );
lk = LBi( k, grid );
ii = ilsum[lk] + (lk+1)*XK_H;
jj = FstBlockC( k );
for (i = 0; i < knsupc; ++i) x_trs[i+ii] = X_col[i+jj];
dx_trs[ii-XK_H].r = k;/* Block number prepended in header. */
}
}
}
/* Copy B into b distributed the same way as matrix-vector product. */
ii = update[0];
for (i = 0; i < N_update; ++i) b[i] = B_col[i + ii];
while (1) { /* Loop until stopping criterion is satisfied. */
/* Compute residual R = B - op(A) * X,
where op(A) = A, A**T, or A**H, depending on TRANS. */
/* Matrix-vector multiply. */
pzgsmv_AXglobal(N_update, update, val, bindx, X_col, ax);
/* Compute residual. */
for (i = 0; i < N_update; ++i) z_sub(&R[i], &b[i], &ax[i]);
/* Compute abs(op(A))*abs(X) + abs(B). */
pzgsmv_AXglobal_abs(N_update, update, val, bindx, X_col, rwork);
for (i = 0; i < N_update; ++i) rwork[i] += z_abs1(&b[i]);
s = 0.0;
for (i = 0; i < N_update; ++i) {
if ( rwork[i] > safe2 )
s = SUPERLU_MAX(s, z_abs1(&R[i]) / rwork[i]);
else
s = SUPERLU_MAX(s, (z_abs1(&R[i])+safe1)/(rwork[i]+safe1));
}
MPI_Allreduce( &s, &berr[j], 1, MPI_DOUBLE, MPI_MAX, grid->comm );
#if ( PRNTlevel>= 1 )
if ( !iam )
printf("(%2d) .. Step %2d: berr[j] = %e\n", iam, count, berr[j]);
#endif
if ( berr[j] > eps && berr[j] * 2 <= lstres && count < ITMAX ) {
/* Compute new dx. */
redist_all_to_diag(n, R, Glu_persist, Llu, grid,
mv_sup_to_proc, dx_trs);
pzgstrs1(n, LUstruct, grid, dx_trs, 1, stat, info);
/* Update solution. */
for (p = 0; p < num_diag_procs; ++p)
if ( iam == diag_procs[p] )
for (k = p; k < nsupers; k += num_diag_procs) {
lk = LBi( k, grid );
ii = ilsum[lk] + (lk+1)*XK_H;
knsupc = SuperSize( k );
for (i = 0; i < knsupc; ++i)
z_add(&x_trs[i + ii], &x_trs[i + ii],
&dx_trs[i + ii]);
}
lstres = berr[j];
++count;
/* Transfer x_trs (on diagonal processes) into X
(on all processes). */
gather_1rhs_diag_to_all(n, x_trs, Glu_persist, Llu, grid,
num_diag_procs, diag_procs, diag_len,
X_col, temp);
} else {
break;
}
} /* end while */
stat->RefineSteps = count;
} /* for j ... */
/* Deallocate storage used by matrix-vector multiplication. */
SUPERLU_FREE(diag_procs);
SUPERLU_FREE(diag_len);
if ( N_update ) {
SUPERLU_FREE(update);
SUPERLU_FREE(bindx);
SUPERLU_FREE(val);
}
SUPERLU_FREE(mv_sup_to_proc);
SUPERLU_FREE(work);
SUPERLU_FREE(rwork);
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(iam, "Exit pzgsrfs_ABXglobal()");
#endif
} /* PZGSRFS_ABXGLOBAL */
void pzgstrf
/************************************************************************/
(
superlu_options_t_Distributed *options, int m, int n, double anorm,
LUstruct_t *LUstruct, gridinfo_t *grid, SuperLUStat_t *stat, int *info
)
/*
* Purpose
* =======
*
* pzgstrf performs the LU factorization in parallel.
*
* Arguments
* =========
*
* options (input) superlu_options_t_Distributed*
* The structure defines the input parameters to control
* how the LU decomposition will be performed.
* The following field should be defined:
* o ReplaceTinyPivot (yes_no_t)
* Specifies whether to replace the tiny diagonals by
* sqrt(epsilon)*norm(A) during LU factorization.
*
* m (input) int
* Number of rows in the matrix.
*
* n (input) int
* Number of columns in the matrix.
*
* anorm (input) double
* The norm of the original matrix A, or the scaled A if
* equilibration was done.
*
* LUstruct (input/output) LUstruct_t*
* The data structures to store the distributed L and U factors.
* The following fields should be defined:
*
* o Glu_persist (input) Glu_persist_t*
* Global data structure (xsup, supno) replicated on all processes,
* describing the supernode partition in the factored matrices
* L and U:
* xsup[s] is the leading column of the s-th supernode,
* supno[i] is the supernode number to which column i belongs.
*
* o Llu (input/output) LocalLU_t*
* The distributed data structures to store L and U factors.
* See superlu_zdefs.h for the definition of 'LocalLU_t'.
*
* 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_zdefs.h for the definition of 'gridinfo_t'.
*
* stat (output) SuperLUStat_t*
* Record the statistics on runtime and floating-point operation count.
* See util.h for the definition of 'SuperLUStat_t'.
*
* info (output) int*
* = 0: successful exit
* < 0: if info = -i, the i-th argument had an illegal value
* > 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.
*
*/
{
#ifdef _CRAY
_fcd ftcs = _cptofcd("N", strlen("N"));
_fcd ftcs1 = _cptofcd("L", strlen("L"));
_fcd ftcs2 = _cptofcd("N", strlen("N"));
_fcd ftcs3 = _cptofcd("U", strlen("U"));
#endif
doublecomplex zero = {0.0, 0.0};
doublecomplex alpha = {1.0, 0.0}, beta = {0.0, 0.0};
int_t *xsup;
int_t *lsub, *lsub1, *usub, *Usub_buf,
*Lsub_buf_2[2]; /* Need 2 buffers to implement Irecv. */
doublecomplex *lusup, *lusup1, *uval, *Uval_buf,
*Lval_buf_2[2]; /* Need 2 buffers to implement Irecv. */
int_t fnz, i, ib, ijb, ilst, it, iukp, jb, jj, klst, knsupc,
lb, lib, ldv, ljb, lptr, lptr0, lptrj, luptr, luptr0, luptrj,
nlb, nub, nsupc, rel, rukp;
int_t Pc, Pr;
int iam, kcol, krow, mycol, myrow, pi, pj;
int j, k, lk, nsupers;
int nsupr, nbrow, segsize;
int msgcnt[4]; /* Count the size of the message xfer'd in each buffer:
* 0 : transferred in Lsub_buf[]
* 1 : transferred in Lval_buf[]
* 2 : transferred in Usub_buf[]
* 3 : transferred in Uval_buf[]
*/
int_t msg0, msg2;
int_t **Ufstnz_br_ptr, **Lrowind_bc_ptr;
doublecomplex **Unzval_br_ptr, **Lnzval_bc_ptr;
int_t *index;
doublecomplex *nzval;
int_t *iuip, *ruip;/* Pointers to U index/nzval; size ceil(NSUPERS/Pr). */
doublecomplex *ucol;
int_t *indirect;
doublecomplex *tempv, *tempv2d;
int_t iinfo;
int_t *ToRecv, *ToSendD, **ToSendR;
Glu_persist_t *Glu_persist = LUstruct->Glu_persist;
LocalLU_t *Llu = LUstruct->Llu;
superlu_scope_t *scp;
double s_eps, thresh;
doublecomplex *tempU2d, *tempu;
int full, ldt, ldu, lead_zero, ncols;
MPI_Request recv_req[4], *send_req;
MPI_Status status;
#if ( DEBUGlevel>=1 )
int_t num_copy=0, num_update=0;
#endif
#if ( PRNTlevel==3 )
int_t zero_msg = 0, total_msg = 0;
#endif
#if ( PROFlevel>=1 )
double t1, t2;
float msg_vol = 0, msg_cnt = 0;
int_t iword = sizeof(int_t), zword = sizeof(doublecomplex);
#endif
/* Test the input parameters. */
*info = 0;
if ( m < 0 ) *info = -2;
else if ( n < 0 ) *info = -3;
if ( *info ) {
pxerbla("pzgstrf", grid, -*info);
return;
}
/* Quick return if possible. */
if ( m == 0 || n == 0 ) 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;
s_eps = slamch_("Epsilon");
thresh = s_eps * anorm / 256.;
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(iam, "Enter pzgstrf()");
#endif
stat->ops[FACT] = 0.0;
if ( Pr*Pc > 1) {
i = Llu->bufmax[0];
if ( !(Llu->Lsub_buf_2[0] = intMalloc_dist(2 * i)) )
ABORT("Malloc fails for Lsub_buf.");
Llu->Lsub_buf_2[1] = Llu->Lsub_buf_2[0] + i;
i = Llu->bufmax[1];
if ( !(Llu->Lval_buf_2[0] = doublecomplexMalloc_dist(2 * i)) )
ABORT("Malloc fails for Lval_buf[].");
Llu->Lval_buf_2[1] = Llu->Lval_buf_2[0] + i;
if ( Llu->bufmax[2] != 0 )
if ( !(Llu->Usub_buf = intMalloc_dist(Llu->bufmax[2])) )
ABORT("Malloc fails for Usub_buf[].");
if ( Llu->bufmax[3] != 0 )
if ( !(Llu->Uval_buf = doublecomplexMalloc_dist(Llu->bufmax[3])) )
ABORT("Malloc fails for Uval_buf[].");
if ( !(send_req =
(MPI_Request *) SUPERLU_MALLOC(2*Pc*sizeof(MPI_Request))))
ABORT("Malloc fails for send_req[].");
}
if ( !(Llu->ujrow = doublecomplexMalloc_dist(sp_ienv_dist(3))) )
ABORT("Malloc fails for ujrow[].");
#if ( PRNTlevel>=1 )
if ( !iam ) {
printf(".. thresh = s_eps %e * anorm %e / 256. = %e\n", s_eps, anorm, thresh);
printf(".. Buffer size: Lsub %d\tLval %d\tUsub %d\tUval %d\tLDA %d\n",
Llu->bufmax[0], Llu->bufmax[1],
Llu->bufmax[2], Llu->bufmax[3], Llu->bufmax[4]);
}
#endif
Lsub_buf_2[0] = Llu->Lsub_buf_2[0];
Lsub_buf_2[1] = Llu->Lsub_buf_2[1];
Lval_buf_2[0] = Llu->Lval_buf_2[0];
Lval_buf_2[1] = Llu->Lval_buf_2[1];
Usub_buf = Llu->Usub_buf;
Uval_buf = Llu->Uval_buf;
Lrowind_bc_ptr = Llu->Lrowind_bc_ptr;
Lnzval_bc_ptr = Llu->Lnzval_bc_ptr;
Ufstnz_br_ptr = Llu->Ufstnz_br_ptr;
Unzval_br_ptr = Llu->Unzval_br_ptr;
ToRecv = Llu->ToRecv;
ToSendD = Llu->ToSendD;
ToSendR = Llu->ToSendR;
ldt = sp_ienv_dist(3); /* Size of maximum supernode */
if ( !(tempv2d = doublecomplexCalloc_dist(2*ldt*ldt)) )
ABORT("Calloc fails for tempv2d[].");
tempU2d = tempv2d + ldt*ldt;
if ( !(indirect = intMalloc_dist(ldt)) )
ABORT("Malloc fails for indirect[].");
k = CEILING( nsupers, Pr ); /* Number of local block rows */
if ( !(iuip = intMalloc_dist(k)) )
ABORT("Malloc fails for iuip[].");
if ( !(ruip = intMalloc_dist(k)) )
ABORT("Malloc fails for ruip[].");
/* ---------------------------------------------------------------
Handle the first block column separately to start the pipeline.
--------------------------------------------------------------- */
if ( mycol == 0 ) {
pzgstrf2(options, 0, thresh, Glu_persist, grid, Llu, stat, info);
scp = &grid->rscp; /* The scope of process row. */
/* Process column *kcol* multicasts numeric values of L(:,k)
to process rows. */
lsub = Lrowind_bc_ptr[0];
lusup = Lnzval_bc_ptr[0];
if ( lsub ) {
msgcnt[0] = lsub[1] + BC_HEADER + lsub[0]*LB_DESCRIPTOR;
msgcnt[1] = lsub[1] * SuperSize( 0 );
} else {
msgcnt[0] = msgcnt[1] = 0;
}
for (pj = 0; pj < Pc; ++pj) {
if ( ToSendR[0][pj] != EMPTY ) {
#if ( PROFlevel>=1 )
TIC(t1);
#endif
MPI_Isend( lsub, msgcnt[0], mpi_int_t, pj, 0, scp->comm,
&send_req[pj] );
MPI_Isend( lusup, msgcnt[1], SuperLU_MPI_DOUBLE_COMPLEX,
pj, 1, scp->comm, &send_req[pj+Pc] );
#if ( DEBUGlevel>=2 )
printf("(%d) Send L(:,%4d): lsub %4d, lusup %4d to Pc %2d\n",
iam, 0, msgcnt[0], msgcnt[1], pj);
#endif
#if ( PROFlevel>=1 )
TOC(t2, t1);
stat->utime[COMM] += t2;
msg_cnt += 2;
msg_vol += msgcnt[0]*iword + msgcnt[1]*zword;
#endif
}
} /* for pj ... */
} else { /* Post immediate receives. */
if ( ToRecv[0] >= 1 ) { /* Recv block column L(:,0). */
scp = &grid->rscp; /* The scope of process row. */
MPI_Irecv( Lsub_buf_2[0], Llu->bufmax[0], mpi_int_t, 0,
0, scp->comm, &recv_req[0] );
MPI_Irecv( Lval_buf_2[0], Llu->bufmax[1],
SuperLU_MPI_DOUBLE_COMPLEX, 0,
1, scp->comm, &recv_req[1] );
#if ( DEBUGlevel>=2 )
printf("(%d) Post Irecv L(:,%4d)\n", iam, 0);
#endif
}
} /* if mycol == 0 */
/* ------------------------------------------
MAIN LOOP: Loop through all block columns.
------------------------------------------ */
for (k = 0; k < nsupers; ++k) {
knsupc = SuperSize( k );
krow = PROW( k, grid );
kcol = PCOL( k, grid );
if ( mycol == kcol ) {
lk = LBj( k, grid ); /* Local block number. */
for (pj = 0; pj < Pc; ++pj) {
/* Wait for Isend to complete before using lsub/lusup. */
if ( ToSendR[lk][pj] != EMPTY ) {
MPI_Wait( &send_req[pj], &status );
MPI_Wait( &send_req[pj+Pc], &status );
}
}
lsub = Lrowind_bc_ptr[lk];
lusup = Lnzval_bc_ptr[lk];
} else {
if ( ToRecv[k] >= 1 ) { /* Recv block column L(:,k). */
scp = &grid->rscp; /* The scope of process row. */
#if ( PROFlevel>=1 )
TIC(t1);
#endif
/*probe_recv(iam, kcol, (4*k)%NTAGS, mpi_int_t, scp->comm,
Llu->bufmax[0]);*/
/*MPI_Recv( Lsub_buf, Llu->bufmax[0], mpi_int_t, kcol,
(4*k)%NTAGS, scp->comm, &status );*/
MPI_Wait( &recv_req[0], &status );
MPI_Get_count( &status, mpi_int_t, &msgcnt[0] );
/*probe_recv(iam, kcol, (4*k+1)%NTAGS, MPI_DOUBLE, scp->comm,
Llu->bufmax[1]);*/
/*MPI_Recv( Lval_buf, Llu->bufmax[1], SuperLU_MPI_DOUBLE_COMPLEX,
kcol, (4*k+1)%NTAGS, scp->comm, &status );*/
MPI_Wait( &recv_req[1], &status );
MPI_Get_count(&status, SuperLU_MPI_DOUBLE_COMPLEX, &msgcnt[1]);
#if ( PROFlevel>=1 )
TOC(t2, t1);
stat->utime[COMM] += t2;
#endif
#if ( DEBUGlevel>=2 )
printf("(%d) Recv L(:,%4d): lsub %4d, lusup %4d from Pc %2d\n",
iam, k, msgcnt[0], msgcnt[1], kcol);
#endif
lsub = Lsub_buf_2[k%2];
lusup = Lval_buf_2[k%2];
#if ( PRNTlevel==3 )
++total_msg;
if ( !msgcnt[0] ) ++zero_msg;
#endif
} else msgcnt[0] = 0;
} /* if mycol = Pc(k) */
scp = &grid->cscp; /* The scope of process column. */
if ( myrow == krow ) {
/* Parallel triangular solve across process row *krow* --
U(k,j) = L(k,k) \ A(k,j). */
#ifdef _CRAY
pzgstrs2(n, k, Glu_persist, grid, Llu, stat, ftcs1, ftcs2, ftcs3);
#else
pzgstrs2(n, k, Glu_persist, grid, Llu, stat);
#endif
/* Multicasts U(k,:) to process columns. */
lk = LBi( k, grid );
usub = Ufstnz_br_ptr[lk];
uval = Unzval_br_ptr[lk];
if ( usub ) {
msgcnt[2] = usub[2];
msgcnt[3] = usub[1];
} else {
msgcnt[2] = msgcnt[3] = 0;
}
if ( ToSendD[lk] == YES ) {
for (pi = 0; pi < Pr; ++pi)
if ( pi != myrow ) {
#if ( PROFlevel>=1 )
TIC(t1);
#endif
MPI_Send( usub, msgcnt[2], mpi_int_t, pi,
(4*k+2)%NTAGS, scp->comm);
MPI_Send( uval, msgcnt[3], SuperLU_MPI_DOUBLE_COMPLEX,
pi, (4*k+3)%NTAGS, scp->comm);
#if ( PROFlevel>=1 )
TOC(t2, t1);
stat->utime[COMM] += t2;
msg_cnt += 2;
msg_vol += msgcnt[2]*iword + msgcnt[3]*zword;
#endif
#if ( DEBUGlevel>=2 )
printf("(%d) Send U(%4d,:) to Pr %2d\n", iam, k, pi);
#endif
} /* if pi ... */
} /* if ToSendD ... */
} else { /* myrow != krow */
if ( ToRecv[k] == 2 ) { /* Recv block row U(k,:). */
#if ( PROFlevel>=1 )
TIC(t1);
#endif
/*probe_recv(iam, krow, (4*k+2)%NTAGS, mpi_int_t, scp->comm,
Llu->bufmax[2]);*/
MPI_Recv( Usub_buf, Llu->bufmax[2], mpi_int_t, krow,
(4*k+2)%NTAGS, scp->comm, &status );
MPI_Get_count( &status, mpi_int_t, &msgcnt[2] );
/*probe_recv(iam, krow, (4*k+3)%NTAGS,
SuperLU_MPI_DOUBLE_COMPLEX, scp->comm,
Llu->bufmax[3]);*/
MPI_Recv( Uval_buf, Llu->bufmax[3], SuperLU_MPI_DOUBLE_COMPLEX,
krow, (4*k+3)%NTAGS, scp->comm, &status );
MPI_Get_count(&status, SuperLU_MPI_DOUBLE_COMPLEX, &msgcnt[3]);
#if ( PROFlevel>=1 )
TOC(t2, t1);
stat->utime[COMM] += t2;
#endif
usub = Usub_buf;
uval = Uval_buf;
#if ( DEBUGlevel>=2 )
printf("(%d) Recv U(%4d,:) from Pr %2d\n", iam, k, krow);
#endif
#if ( PRNTlevel==3 )
++total_msg;
if ( !msgcnt[2] ) ++zero_msg;
#endif
} else msgcnt[2] = 0;
} /* if myrow == Pr(k) */
/*
* Parallel rank-k update; pair up blocks L(i,k) and U(k,j).
* for (j = k+1; k < N; ++k) {
* for (i = k+1; i < N; ++i)
* if ( myrow == PROW( i, grid ) && mycol == PCOL( j, grid )
* && L(i,k) != 0 && U(k,j) != 0 )
* A(i,j) = A(i,j) - L(i,k) * U(k,j);
*/
msg0 = msgcnt[0];
msg2 = msgcnt[2];
if ( msg0 && msg2 ) { /* L(:,k) and U(k,:) are not empty. */
nsupr = lsub[1]; /* LDA of lusup. */
if ( myrow == krow ) { /* Skip diagonal block L(k,k). */
lptr0 = BC_HEADER + LB_DESCRIPTOR + lsub[BC_HEADER+1];
luptr0 = knsupc;
nlb = lsub[0] - 1;
} else {
lptr0 = BC_HEADER;
luptr0 = 0;
nlb = lsub[0];
}
lptr = lptr0;
for (lb = 0; lb < nlb; ++lb) { /* Initialize block row pointers. */
ib = lsub[lptr];
lib = LBi( ib, grid );
iuip[lib] = BR_HEADER;
ruip[lib] = 0;
lptr += LB_DESCRIPTOR + lsub[lptr+1];
}
nub = usub[0]; /* Number of blocks in the block row U(k,:) */
iukp = BR_HEADER; /* Skip header; Pointer to index[] of U(k,:) */
rukp = 0; /* Pointer to nzval[] of U(k,:) */
klst = FstBlockC( k+1 );
/*
* Update the first block column A(:,k+1).
*/
jb = usub[iukp]; /* Global block number of block U(k,j). */
if ( jb == k+1 ) { /* First update (k+1)-th block. */
--nub;
lptr = lptr0;
luptr = luptr0;
ljb = LBj( jb, grid ); /* Local block number of U(k,j). */
nsupc = SuperSize( jb );
iukp += UB_DESCRIPTOR; /* Start fstnz of block U(k,j). */
/* Prepare to call DGEMM. */
jj = iukp;
while ( usub[jj] == klst ) ++jj;
ldu = klst - usub[jj++];
ncols = 1;
full = 1;
for (; jj < iukp+nsupc; ++jj) {
segsize = klst - usub[jj];
if ( segsize ) {
++ncols;
if ( segsize != ldu ) full = 0;
if ( segsize > ldu ) ldu = segsize;
}
}
#if ( DEBUGlevel>=1 )
++num_update;
#endif
if ( full ) {
tempu = &uval[rukp];
} else { /* Copy block U(k,j) into tempU2d. */
#if ( DEBUGlevel>=1 )
printf("(%d) full=%d,k=%d,jb=%d,ldu=%d,ncols=%d,nsupc=%d\n",
iam, full, k, jb, ldu, ncols, nsupc);
++num_copy;
#endif
tempu = tempU2d;
for (jj = iukp; jj < iukp+nsupc; ++jj) {
segsize = klst - usub[jj];
if ( segsize ) {
lead_zero = ldu - segsize;
for (i = 0; i < lead_zero; ++i) tempu[i] = zero;
tempu += lead_zero;
for (i = 0; i < segsize; ++i)
tempu[i] = uval[rukp+i];
rukp += segsize;
tempu += segsize;
}
}
tempu = tempU2d;
rukp -= usub[iukp - 1]; /* Return to start of U(k,j). */
} /* if full ... */
for (lb = 0; lb < nlb; ++lb) {
ib = lsub[lptr]; /* Row block L(i,k). */
nbrow = lsub[lptr+1]; /* Number of full rows. */
lptr += LB_DESCRIPTOR; /* Skip descriptor. */
tempv = tempv2d;
#ifdef _CRAY
CGEMM(ftcs, ftcs, &nbrow, &ncols, &ldu, &alpha,
&lusup[luptr+(knsupc-ldu)*nsupr], &nsupr,
tempu, &ldu, &beta, tempv, &ldt);
#else
zgemm_("N", "N", &nbrow, &ncols, &ldu, &alpha,
&lusup[luptr+(knsupc-ldu)*nsupr], &nsupr,
tempu, &ldu, &beta, tempv, &ldt);
#endif
stat->ops[FACT] += 8 * nbrow * ldu * ncols;
/* Now gather the result into the destination block. */
if ( ib < jb ) { /* A(i,j) is in U. */
ilst = FstBlockC( ib+1 );
lib = LBi( ib, grid );
index = Ufstnz_br_ptr[lib];
ijb = index[iuip[lib]];
while ( ijb < jb ) { /* Search for dest block. */
ruip[lib] += index[iuip[lib]+1];
iuip[lib] += UB_DESCRIPTOR + SuperSize( ijb );
ijb = index[iuip[lib]];
}
iuip[lib] += UB_DESCRIPTOR; /* Skip descriptor. */
tempv = tempv2d;
for (jj = 0; jj < nsupc; ++jj) {
segsize = klst - usub[iukp + jj];
fnz = index[iuip[lib]++];
if ( segsize ) { /* Nonzero segment in U(k.j). */
ucol = &Unzval_br_ptr[lib][ruip[lib]];
for (i = 0, it = 0; i < nbrow; ++i) {
rel = lsub[lptr + i] - fnz;
z_sub(&ucol[rel], &ucol[rel], &tempv[it]);
++it;
}
tempv += ldt;
}
ruip[lib] += ilst - fnz;
}
} else { /* A(i,j) is in L. */
index = Lrowind_bc_ptr[ljb];
ldv = index[1]; /* LDA of the dest lusup. */
lptrj = BC_HEADER;
luptrj = 0;
ijb = index[lptrj];
while ( ijb != ib ) { /* Search for dest block --
blocks are not ordered! */
luptrj += index[lptrj+1];
lptrj += LB_DESCRIPTOR + index[lptrj+1];
ijb = index[lptrj];
}
/*
* Build indirect table. This is needed because the
* indices are not sorted.
*/
fnz = FstBlockC( ib );
lptrj += LB_DESCRIPTOR;
for (i = 0; i < index[lptrj-1]; ++i) {
rel = index[lptrj + i] - fnz;
indirect[rel] = i;
}
nzval = Lnzval_bc_ptr[ljb] + luptrj;
tempv = tempv2d;
for (jj = 0; jj < nsupc; ++jj) {
segsize = klst - usub[iukp + jj];
if ( segsize ) {
/*#pragma _CRI cache_bypass nzval,tempv*/
for (it = 0, i = 0; i < nbrow; ++i) {
rel = lsub[lptr + i] - fnz;
z_sub(&nzval[indirect[rel]],
&nzval[indirect[rel]],
&tempv[it]);
++it;
}
tempv += ldt;
}
nzval += ldv;
}
} /* if ib < jb ... */
lptr += nbrow;
luptr += nbrow;
} /* for lb ... */
rukp += usub[iukp - 1]; /* Move to block U(k,j+1) */
iukp += nsupc;
} /* if jb == k+1 */
} /* if L(:,k) and U(k,:) not empty */
if ( k+1 < nsupers ) {
kcol = PCOL( k+1, grid );
if ( mycol == kcol ) {
/* Factor diagonal and subdiagonal blocks and test for exact
singularity. */
pzgstrf2(options, k+1, thresh, Glu_persist, grid, Llu, stat, info);
/* Process column *kcol+1* multicasts numeric values of L(:,k+1)
to process rows. */
lk = LBj( k+1, grid ); /* Local block number. */
lsub1 = Lrowind_bc_ptr[lk];
if ( lsub1 ) {
msgcnt[0] = lsub1[1] + BC_HEADER + lsub1[0]*LB_DESCRIPTOR;
msgcnt[1] = lsub1[1] * SuperSize( k+1 );
} else {
msgcnt[0] = 0;
msgcnt[1] = 0;
}
scp = &grid->rscp; /* The scope of process row. */
for (pj = 0; pj < Pc; ++pj) {
if ( ToSendR[lk][pj] != EMPTY ) {
lusup1 = Lnzval_bc_ptr[lk];
#if ( PROFlevel>=1 )
TIC(t1);
#endif
MPI_Isend( lsub1, msgcnt[0], mpi_int_t, pj,
(4*(k+1))%NTAGS, scp->comm, &send_req[pj] );
MPI_Isend( lusup1, msgcnt[1], SuperLU_MPI_DOUBLE_COMPLEX,
pj, (4*(k+1)+1)%NTAGS, scp->comm,
&send_req[pj+Pc] );
#if ( PROFlevel>=1 )
TOC(t2, t1);
stat->utime[COMM] += t2;
msg_cnt += 2;
msg_vol += msgcnt[0]*iword + msgcnt[1]*zword;
#endif
#if ( DEBUGlevel>=2 )
printf("(%d) Send L(:,%4d): lsub %4d, lusup %4d to Pc %2d\n",
iam, k+1, msgcnt[0], msgcnt[1], pj);
#endif
}
} /* for pj ... */
} else { /* Post Recv of block column L(:,k+1). */
if ( ToRecv[k+1] >= 1 ) {
scp = &grid->rscp; /* The scope of process row. */
MPI_Irecv(Lsub_buf_2[(k+1)%2], Llu->bufmax[0], mpi_int_t, kcol,
(4*(k+1))%NTAGS, scp->comm, &recv_req[0]);
MPI_Irecv(Lval_buf_2[(k+1)%2], Llu->bufmax[1],
SuperLU_MPI_DOUBLE_COMPLEX, kcol,
(4*(k+1)+1)%NTAGS, scp->comm, &recv_req[1]);
}
} /* if mycol == Pc(k+1) */
} /* if k+1 < nsupers */
if ( msg0 && msg2 ) { /* L(:,k) and U(k,:) are not empty. */
/*
* Update all other blocks using block row U(k,:)
*/
for (j = 0; j < nub; ++j) {
lptr = lptr0;
luptr = luptr0;
jb = usub[iukp]; /* Global block number of block U(k,j). */
ljb = LBj( jb, grid ); /* Local block number of U(k,j). */
nsupc = SuperSize( jb );
iukp += UB_DESCRIPTOR; /* Start fstnz of block U(k,j). */
/* Prepare to call DGEMM. */
jj = iukp;
while ( usub[jj] == klst ) ++jj;
ldu = klst - usub[jj++];
ncols = 1;
full = 1;
for (; jj < iukp+nsupc; ++jj) {
segsize = klst - usub[jj];
if ( segsize ) {
++ncols;
if ( segsize != ldu ) full = 0;
if ( segsize > ldu ) ldu = segsize;
}
}
#if ( DEBUGlevel>=2 )
printf("(%d) full=%d,k=%d,jb=%d,ldu=%d,ncols=%d,nsupc=%d\n",
iam, full, k, jb, ldu, ncols, nsupc);
++num_update;
#endif
if ( full ) {
tempu = &uval[rukp];
} else { /* Copy block U(k,j) into tempU2d. */
#if ( DEBUGlevel>=1 )
++num_copy;
#endif
tempu = tempU2d;
for (jj = iukp; jj < iukp+nsupc; ++jj) {
segsize = klst - usub[jj];
if ( segsize ) {
lead_zero = ldu - segsize;
for (i = 0; i < lead_zero; ++i) tempu[i] = zero;
tempu += lead_zero;
for (i = 0; i < segsize; ++i)
tempu[i] = uval[rukp+i];
rukp += segsize;
tempu += segsize;
}
}
tempu = tempU2d;
rukp -= usub[iukp - 1]; /* Return to start of U(k,j). */
} /* if full ... */
for (lb = 0; lb < nlb; ++lb) {
ib = lsub[lptr]; /* Row block L(i,k). */
nbrow = lsub[lptr+1]; /* Number of full rows. */
lptr += LB_DESCRIPTOR; /* Skip descriptor. */
tempv = tempv2d;
#ifdef _CRAY
CGEMM(ftcs, ftcs, &nbrow, &ncols, &ldu, &alpha,
&lusup[luptr+(knsupc-ldu)*nsupr], &nsupr,
tempu, &ldu, &beta, tempv, &ldt);
#else
zgemm_("N", "N", &nbrow, &ncols, &ldu, &alpha,
&lusup[luptr+(knsupc-ldu)*nsupr], &nsupr,
tempu, &ldu, &beta, tempv, &ldt);
#endif
stat->ops[FACT] += 8 * nbrow * ldu * ncols;
/* Now gather the result into the destination block. */
if ( ib < jb ) { /* A(i,j) is in U. */
ilst = FstBlockC( ib+1 );
lib = LBi( ib, grid );
index = Ufstnz_br_ptr[lib];
ijb = index[iuip[lib]];
while ( ijb < jb ) { /* Search for dest block. */
ruip[lib] += index[iuip[lib]+1];
iuip[lib] += UB_DESCRIPTOR + SuperSize( ijb );
ijb = index[iuip[lib]];
}
iuip[lib] += UB_DESCRIPTOR; /* Skip descriptor. */
tempv = tempv2d;
for (jj = 0; jj < nsupc; ++jj) {
segsize = klst - usub[iukp + jj];
fnz = index[iuip[lib]++];
if ( segsize ) { /* Nonzero segment in U(k.j). */
ucol = &Unzval_br_ptr[lib][ruip[lib]];
for (i = 0, it = 0; i < nbrow; ++i) {
rel = lsub[lptr + i] - fnz;
z_sub(&ucol[rel], &ucol[rel], &tempv[it]);
++it;
}
tempv += ldt;
}
ruip[lib] += ilst - fnz;
}
} else { /* A(i,j) is in L. */
index = Lrowind_bc_ptr[ljb];
ldv = index[1]; /* LDA of the dest lusup. */
lptrj = BC_HEADER;
luptrj = 0;
ijb = index[lptrj];
while ( ijb != ib ) { /* Search for dest block --
blocks are not ordered! */
luptrj += index[lptrj+1];
lptrj += LB_DESCRIPTOR + index[lptrj+1];
ijb = index[lptrj];
}
/*
* Build indirect table. This is needed because the
* indices are not sorted.
*/
fnz = FstBlockC( ib );
lptrj += LB_DESCRIPTOR;
for (i = 0; i < index[lptrj-1]; ++i) {
rel = index[lptrj + i] - fnz;
indirect[rel] = i;
}
nzval = Lnzval_bc_ptr[ljb] + luptrj;
tempv = tempv2d;
for (jj = 0; jj < nsupc; ++jj) {
segsize = klst - usub[iukp + jj];
if ( segsize ) {
/*#pragma _CRI cache_bypass nzval,tempv*/
for (it = 0, i = 0; i < nbrow; ++i) {
rel = lsub[lptr + i] - fnz;
z_sub(&nzval[indirect[rel]],
&nzval[indirect[rel]],
&tempv[it]);
++it;
}
tempv += ldt;
}
nzval += ldv;
}
} /* if ib < jb ... */
lptr += nbrow;
luptr += nbrow;
} /* for lb ... */
rukp += usub[iukp - 1]; /* Move to block U(k,j+1) */
iukp += nsupc;
} /* for j ... */
} /* if k L(:,k) and U(k,:) are not empty */
}
/* ------------------------------------------
END MAIN LOOP: for k = ...
------------------------------------------ */
if ( Pr*Pc > 1 ) {
SUPERLU_FREE(Lsub_buf_2[0]); /* also free Lsub_buf_2[1] */
SUPERLU_FREE(Lval_buf_2[0]); /* also free Lval_buf_2[1] */
if ( Llu->bufmax[2] != 0 ) SUPERLU_FREE(Usub_buf);
if ( Llu->bufmax[3] != 0 ) SUPERLU_FREE(Uval_buf);
SUPERLU_FREE(send_req);
}
SUPERLU_FREE(Llu->ujrow);
SUPERLU_FREE(tempv2d);
SUPERLU_FREE(indirect);
SUPERLU_FREE(iuip);
SUPERLU_FREE(ruip);
/* Prepare error message. */
if ( *info == 0 ) *info = n + 1;
#if ( PROFlevel>=1 )
TIC(t1);
#endif
MPI_Allreduce( info, &iinfo, 1, mpi_int_t, MPI_MIN, grid->comm );
#if ( PROFlevel>=1 )
TOC(t2, t1);
stat->utime[COMM] += t2;
{
float msg_vol_max, msg_vol_sum, msg_cnt_max, msg_cnt_sum;
MPI_Reduce( &msg_cnt, &msg_cnt_sum,
1, MPI_FLOAT, MPI_SUM, 0, grid->comm );
MPI_Reduce( &msg_cnt, &msg_cnt_max,
1, MPI_FLOAT, MPI_MAX, 0, grid->comm );
MPI_Reduce( &msg_vol, &msg_vol_sum,
1, MPI_FLOAT, MPI_SUM, 0, grid->comm );
MPI_Reduce( &msg_vol, &msg_vol_max,
1, MPI_FLOAT, MPI_MAX, 0, grid->comm );
if ( !iam ) {
printf("\tPZGSTRF comm stat:"
"\tAvg\tMax\t\tAvg\tMax\n"
"\t\t\tCount:\t%.0f\t%.0f\tVol(MB)\t%.2f\t%.2f\n",
msg_cnt_sum/Pr/Pc, msg_cnt_max,
msg_vol_sum/Pr/Pc*1e-6, msg_vol_max*1e-6);
}
}
#endif
if ( iinfo == n + 1 ) *info = 0;
else *info = iinfo;
#if ( PRNTlevel==3 )
MPI_Allreduce( &zero_msg, &iinfo, 1, mpi_int_t, MPI_SUM, grid->comm );
if ( !iam ) printf(".. # msg of zero size\t%d\n", iinfo);
MPI_Allreduce( &total_msg, &iinfo, 1, mpi_int_t, MPI_SUM, grid->comm );
if ( !iam ) printf(".. # total msg\t%d\n", iinfo);
#endif
#if ( PRNTlevel==2 )
for (i = 0; i < Pr * Pc; ++i) {
if ( iam == i ) {
PrintLblocks(iam, nsupers, grid, Glu_persist, Llu);
PrintUblocks(iam, nsupers, grid, Glu_persist, Llu);
printf("(%d)\n", iam);
PrintInt10("Recv", nsupers, Llu->ToRecv);
}
MPI_Barrier( grid->comm );
}
#endif
#if ( DEBUGlevel>=1 )
printf("(%d) num_copy=%d, num_update=%d\n", iam, num_copy, num_update);
CHECK_MALLOC(iam, "Exit pzgstrf()");
#endif
} /* PZGSTRF_AGLOBAL */
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 */
int main(int argc, char *argv[])
{
superlu_dist_options_t options;
SuperLUStat_t stat;
SuperMatrix A;
ScalePermstruct_t ScalePermstruct;
LUstruct_t LUstruct;
gridinfo_t grid;
double *berr;
doublecomplex *a, *b, *xtrue;
int_t *asub, *xa;
int_t m, n, nnz;
int_t nprow, npcol;
int iam, info, ldb, ldx, nrhs;
char trans[1];
char **cpp, c;
FILE *fp, *fopen();
extern int cpp_defs();
/* prototypes */
extern void LUstructInit(const int_t, LUstruct_t *);
extern void LUstructFree(LUstruct_t *);
extern void Destroy_LU(int_t, gridinfo_t *, LUstruct_t *);
nprow = 1; /* Default process rows. */
npcol = 1; /* Default process columns. */
nrhs = 1; /* Number of right-hand side. */
/* ------------------------------------------------------------
INITIALIZE MPI ENVIRONMENT.
------------------------------------------------------------*/
MPI_Init( &argc, &argv );
/* Parse command line argv[]. */
for (cpp = argv+1; *cpp; ++cpp) {
if ( **cpp == '-' ) {
c = *(*cpp+1);
++cpp;
switch (c) {
case 'h':
printf("Options:\n");
printf("\t-r <int>: process rows (default " IFMT ")\n", nprow);
printf("\t-c <int>: process columns (default " IFMT ")\n", npcol);
exit(0);
break;
case 'r': nprow = atoi(*cpp);
break;
case 'c': npcol = atoi(*cpp);
break;
}
} else { /* Last arg is considered a filename */
if ( !(fp = fopen(*cpp, "r")) ) {
ABORT("File does not exist");
}
break;
}
}
/* ------------------------------------------------------------
INITIALIZE THE SUPERLU PROCESS GRID.
------------------------------------------------------------*/
superlu_gridinit(MPI_COMM_WORLD, nprow, npcol, &grid);
/* Bail out if I do not belong in the grid. */
iam = grid.iam;
if ( iam >= nprow * npcol )
goto out;
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(iam, "Enter main()");
#endif
/* ------------------------------------------------------------
PROCESS 0 READS THE MATRIX A, AND THEN BROADCASTS IT TO ALL
THE OTHER PROCESSES.
------------------------------------------------------------*/
if ( !iam ) {
/* Print the CPP definitions. */
cpp_defs();
/* Read the matrix stored on disk in Harwell-Boeing format. */
zreadhb_dist(iam, fp, &m, &n, &nnz, &a, &asub, &xa);
printf("Input matrix file: %s\n", *cpp);
printf("\tDimension\t" IFMT "x" IFMT "\t # nonzeros " IFMT "\n", m, n, nnz);
printf("\tProcess grid\t%d X %d\n", (int) grid.nprow, (int) grid.npcol);
/* Broadcast matrix A to the other PEs. */
MPI_Bcast( &m, 1, mpi_int_t, 0, grid.comm );
MPI_Bcast( &n, 1, mpi_int_t, 0, grid.comm );
MPI_Bcast( &nnz, 1, mpi_int_t, 0, grid.comm );
MPI_Bcast( a, nnz, SuperLU_MPI_DOUBLE_COMPLEX, 0, grid.comm );
MPI_Bcast( asub, nnz, mpi_int_t, 0, grid.comm );
MPI_Bcast( xa, n+1, mpi_int_t, 0, grid.comm );
} else {
/* Receive matrix A from PE 0. */
MPI_Bcast( &m, 1, mpi_int_t, 0, grid.comm );
MPI_Bcast( &n, 1, mpi_int_t, 0, grid.comm );
MPI_Bcast( &nnz, 1, mpi_int_t, 0, grid.comm );
/* Allocate storage for compressed column representation. */
zallocateA_dist(n, nnz, &a, &asub, &xa);
MPI_Bcast( a, nnz, SuperLU_MPI_DOUBLE_COMPLEX, 0, grid.comm );
MPI_Bcast( asub, nnz, mpi_int_t, 0, grid.comm );
MPI_Bcast( xa, n+1, mpi_int_t, 0, grid.comm );
}
/* Create compressed column matrix for A. */
zCreate_CompCol_Matrix_dist(&A, m, n, nnz, a, asub, xa,
SLU_NC, SLU_Z, SLU_GE);
/* Generate the exact solution and compute the right-hand side. */
if (!(b=doublecomplexMalloc_dist(m*nrhs))) ABORT("Malloc fails for b[]");
if (!(xtrue=doublecomplexMalloc_dist(n*nrhs))) ABORT("Malloc fails for xtrue[]");
*trans = 'N';
ldx = n;
ldb = m;
zGenXtrue_dist(n, nrhs, xtrue, ldx);
zFillRHS_dist(trans, nrhs, xtrue, ldx, &A, b, ldb);
if ( !(berr = doubleMalloc_dist(nrhs)) )
ABORT("Malloc fails for berr[].");
/* ------------------------------------------------------------
NOW WE SOLVE THE LINEAR SYSTEM.
------------------------------------------------------------*/
/* Set the default input options:
options.Fact = DOFACT;
options.Equil = YES;
options.ColPerm = METIS_AT_PLUS_A;
options.RowPerm = LargeDiag_MC64;
options.ReplaceTinyPivot = YES;
options.Trans = NOTRANS;
options.IterRefine = DOUBLE;
options.SolveInitialized = NO;
options.RefineInitialized = NO;
options.PrintStat = YES;
*/
set_default_options_dist(&options);
if (!iam) {
print_sp_ienv_dist(&options);
print_options_dist(&options);
}
/* Initialize ScalePermstruct and LUstruct. */
ScalePermstructInit(m, n, &ScalePermstruct);
LUstructInit(n, &LUstruct);
/* Initialize the statistics variables. */
PStatInit(&stat);
/* Call the linear equation solver. */
pzgssvx_ABglobal(&options, &A, &ScalePermstruct, b, ldb, nrhs, &grid,
&LUstruct, berr, &stat, &info);
/* Check the accuracy of the solution. */
if ( !iam ) {
zinf_norm_error_dist(n, nrhs, b, ldb, xtrue, ldx, &grid);
}
PStatPrint(&options, &stat, &grid); /* Print the statistics. */
/* ------------------------------------------------------------
DEALLOCATE STORAGE.
------------------------------------------------------------*/
PStatFree(&stat);
Destroy_CompCol_Matrix_dist(&A);
Destroy_LU(n, &grid, &LUstruct);
ScalePermstructFree(&ScalePermstruct);
LUstructFree(&LUstruct);
SUPERLU_FREE(b);
SUPERLU_FREE(xtrue);
SUPERLU_FREE(berr);
/* ------------------------------------------------------------
RELEASE THE SUPERLU PROCESS GRID.
------------------------------------------------------------*/
out:
superlu_gridexit(&grid);
/* ------------------------------------------------------------
TERMINATES THE MPI EXECUTION ENVIRONMENT.
------------------------------------------------------------*/
MPI_Finalize();
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(iam, "Exit main()");
#endif
}
/*! \brief Permute the distributed dense matrix: B <= perm(X). perm[i] = j means the i-th row of X is in the j-th row of B.
*/
int pzPermute_Dense_Matrix
(
int_t fst_row,
int_t m_loc,
int_t row_to_proc[],
int_t perm[],
doublecomplex X[], int ldx,
doublecomplex B[], int ldb,
int nrhs,
gridinfo_t *grid
)
{
int_t i, j, k, l;
int p, procs;
int *sendcnts, *sendcnts_nrhs, *recvcnts, *recvcnts_nrhs;
int *sdispls, *sdispls_nrhs, *rdispls, *rdispls_nrhs;
int *ptr_to_ibuf, *ptr_to_dbuf;
int_t *send_ibuf, *recv_ibuf;
doublecomplex *send_dbuf, *recv_dbuf;
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(grid->iam, "Enter pzPermute_Dense_Matrix()");
#endif
procs = grid->nprow * grid->npcol;
if ( !(sendcnts = SUPERLU_MALLOC(10*procs * sizeof(int))) )
ABORT("Malloc fails for sendcnts[].");
sendcnts_nrhs = sendcnts + procs;
recvcnts = sendcnts_nrhs + procs;
recvcnts_nrhs = recvcnts + procs;
sdispls = recvcnts_nrhs + procs;
sdispls_nrhs = sdispls + procs;
rdispls = sdispls_nrhs + procs;
rdispls_nrhs = rdispls + procs;
ptr_to_ibuf = rdispls_nrhs + procs;
ptr_to_dbuf = ptr_to_ibuf + procs;
for (i = 0; i < procs; ++i) sendcnts[i] = 0;
/* Count the number of X entries to be sent to each process.*/
for (i = fst_row; i < fst_row + m_loc; ++i) {
p = row_to_proc[perm[i]];
++sendcnts[p];
}
MPI_Alltoall(sendcnts, 1, MPI_INT, recvcnts, 1, MPI_INT, grid->comm);
sdispls[0] = rdispls[0] = 0;
sdispls_nrhs[0] = rdispls_nrhs[0] = 0;
sendcnts_nrhs[0] = sendcnts[0] * nrhs;
recvcnts_nrhs[0] = recvcnts[0] * nrhs;
for (i = 1; i < procs; ++i) {
sdispls[i] = sdispls[i-1] + sendcnts[i-1];
sdispls_nrhs[i] = sdispls[i] * nrhs;
rdispls[i] = rdispls[i-1] + recvcnts[i-1];
rdispls_nrhs[i] = rdispls[i] * nrhs;
sendcnts_nrhs[i] = sendcnts[i] * nrhs;
recvcnts_nrhs[i] = recvcnts[i] * nrhs;
}
k = sdispls[procs-1] + sendcnts[procs-1];/* Total number of sends */
l = rdispls[procs-1] + recvcnts[procs-1];/* Total number of recvs */
/*assert(k == m_loc);*/
/*assert(l == m_loc);*/
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)*nrhs)) )
ABORT("Malloc fails for send_dbuf[].");
recv_dbuf = send_dbuf + k * nrhs;
for (i = 0; i < procs; ++i) {
ptr_to_ibuf[i] = sdispls[i];
ptr_to_dbuf[i] = sdispls_nrhs[i];
}
/* Fill in the send buffers: send_ibuf[] and send_dbuf[]. */
for (i = fst_row; i < fst_row + m_loc; ++i) {
j = perm[i];
p = row_to_proc[j];
send_ibuf[ptr_to_ibuf[p]] = j;
j = ptr_to_dbuf[p];
RHS_ITERATE(k) { /* RHS stored in row major in the buffer */
send_dbuf[j++] = X[i-fst_row + k*ldx];
}
++ptr_to_ibuf[p];
ptr_to_dbuf[p] += nrhs;
}
/* Transfer the (permuted) row indices and numerical values. */
MPI_Alltoallv(send_ibuf, sendcnts, sdispls, mpi_int_t,
recv_ibuf, recvcnts, rdispls, mpi_int_t, grid->comm);
MPI_Alltoallv(send_dbuf, sendcnts_nrhs, sdispls_nrhs, SuperLU_MPI_DOUBLE_COMPLEX,
recv_dbuf, recvcnts_nrhs, rdispls_nrhs, SuperLU_MPI_DOUBLE_COMPLEX,
grid->comm);
/* Copy the buffer into b. */
for (i = 0, l = 0; i < m_loc; ++i) {
j = recv_ibuf[i] - fst_row; /* Relative row number */
RHS_ITERATE(k) { /* RHS stored in row major in the buffer */
B[j + k*ldb] = recv_dbuf[l++];
}
}
SUPERLU_FREE(sendcnts);
SUPERLU_FREE(send_ibuf);
SUPERLU_FREE(send_dbuf);
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(grid->iam, "Exit pzPermute_Dense_Matrix()");
#endif
return 0;
} /* pzPermute_Dense_Matrix */
int zcreate_dist_matrix(SuperMatrix *A, int_t m, int_t n, int_t nnz,
doublecomplex *nzval_g, int_t *rowind_g, int_t *colptr_g,
gridinfo_t *grid)
{
SuperMatrix GA; /* global A */
int_t *rowind, *colptr; /* global */
doublecomplex *nzval; /* global */
doublecomplex *nzval_loc; /* local */
int_t *colind, *rowptr; /* local */
int_t m_loc, fst_row, nnz_loc;
int_t m_loc_fst; /* Record m_loc of the first p-1 processors,
when mod(m, p) is not zero. */
int_t iam, row, col, i, j, relpos;
char trans[1];
int_t *marker;
iam = grid->iam;
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(iam, "Enter zcreate_dist_matrix()");
#endif
if ( !iam ) {
/* Allocate storage for compressed column representation. */
zallocateA_dist(n, nnz, &nzval, &rowind, &colptr);
/* Copy the global matrix. */
#if 0
/* and ADJUST to 0-based indexing
which is required by the C routines.*/
#endif
for(i=0; i<nnz; i++){
nzval[i]=nzval_g[i];
rowind[i]=rowind_g[i]; /* - 1;*/
}
for(i=0; i<n+1; i++)
colptr[i]=colptr_g[i]; /* - 1;*/
/* Broadcast matrix A to the other PEs. */
MPI_Bcast( &m, 1, mpi_int_t, 0, grid->comm );
MPI_Bcast( &n, 1, mpi_int_t, 0, grid->comm );
MPI_Bcast( &nnz, 1, mpi_int_t, 0, grid->comm );
MPI_Bcast( nzval, nnz, SuperLU_MPI_DOUBLE_COMPLEX, 0, grid->comm );
MPI_Bcast( rowind, nnz, mpi_int_t, 0, grid->comm );
MPI_Bcast( colptr, n+1, mpi_int_t, 0, grid->comm );
} else {
/* Receive matrix A from PE 0. */
MPI_Bcast( &m, 1, mpi_int_t, 0, grid->comm );
MPI_Bcast( &n, 1, mpi_int_t, 0, grid->comm );
MPI_Bcast( &nnz, 1, mpi_int_t, 0, grid->comm );
/* Allocate storage for compressed column representation. */
zallocateA_dist(n, nnz, &nzval, &rowind, &colptr);
MPI_Bcast( nzval, nnz, SuperLU_MPI_DOUBLE_COMPLEX, 0, grid->comm );
MPI_Bcast( rowind, nnz, mpi_int_t, 0, grid->comm );
MPI_Bcast( colptr, n+1, mpi_int_t, 0, grid->comm );
}
#if 0
nzval[0]=0.1;
#endif
/* Compute the number of rows to be distributed to local process */
m_loc = m / (grid->nprow * grid->npcol);
m_loc_fst = m_loc;
/* When m / procs is not an integer */
if ((m_loc * grid->nprow * grid->npcol) != m) {
m_loc = m_loc+1;
m_loc_fst = m_loc;
if (iam == (grid->nprow * grid->npcol - 1))
m_loc = m - m_loc_fst * (grid->nprow * grid->npcol - 1);
}
/* Create compressed column matrix for GA. */
zCreate_CompCol_Matrix_dist(&GA, m, n, nnz, nzval, rowind, colptr,
SLU_NC, SLU_Z, SLU_GE);
/*************************************************
* Change GA to a local A with NR_loc format *
*************************************************/
rowptr = (int_t *) intMalloc_dist(m_loc+1);
marker = (int_t *) intCalloc_dist(n);
/* Get counts of each row of GA */
for (i = 0; i < n; ++i)
for (j = colptr[i]; j < colptr[i+1]; ++j) ++marker[rowind[j]];
/* Set up row pointers */
rowptr[0] = 0;
fst_row = iam * m_loc_fst;
nnz_loc = 0;
for (j = 0; j < m_loc; ++j) {
row = fst_row + j;
rowptr[j+1] = rowptr[j] + marker[row];
marker[j] = rowptr[j];
}
nnz_loc = rowptr[m_loc];
nzval_loc = (doublecomplex *) doublecomplexMalloc_dist(nnz_loc);
colind = (int_t *) intMalloc_dist(nnz_loc);
/* Transfer the matrix into the compressed row storage */
for (i = 0; i < n; ++i) {
for (j = colptr[i]; j < colptr[i+1]; ++j) {
row = rowind[j];
if ( (row>=fst_row) && (row<fst_row+m_loc) ) {
row = row - fst_row;
relpos = marker[row];
colind[relpos] = i;
nzval_loc[relpos] = nzval[j];
++marker[row];
}
}
}
#if ( DEBUGlevel>=1 )
if ( !iam ) dPrint_CompCol_Matrix_dist(&GA);
#endif
/* Destroy GA */
Destroy_CompCol_Matrix_dist(&GA);
/******************************************************/
/* Change GA to a local A with NR_loc format */
/******************************************************/
/* Set up the local A in NR_loc format */
zCreate_CompRowLoc_Matrix_dist(A, m, n, nnz_loc, m_loc, fst_row,
nzval_loc, colind, rowptr,
SLU_NR_loc, SLU_Z, SLU_GE);
SUPERLU_FREE(marker);
#if ( DEBUGlevel>=1 )
printf("sizeof(NRforamt_loc) %d\n", sizeof(NRformat_loc));
CHECK_MALLOC(iam, "Exit dcreate_dist_matrix()");
#endif
return 0;
}
