/*! \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);
}
/*
* Gather the components of x vector on the diagonal processes
* onto all processes, and combine them into the global vector y.
*/
static void
gather_1rhs_diag_to_all(int_t n, doublecomplex x[],
Glu_persist_t *Glu_persist, LocalLU_t *Llu,
gridinfo_t *grid, int_t num_diag_procs,
int_t diag_procs[], int_t diag_len[],
doublecomplex y[], doublecomplex work[])
{
int_t i, ii, k, lk, lwork, nsupers, p;
int_t *ilsum, *xsup;
int iam, knsupc, pkk;
iam = grid->iam;
nsupers = Glu_persist->supno[n-1] + 1;
xsup = Glu_persist->xsup;
ilsum = Llu->ilsum;
for (p = 0; p < num_diag_procs; ++p) {
pkk = diag_procs[p];
if ( iam == pkk ) {
/* Copy x vector into a buffer. */
lwork = 0;
for (k = p; k < nsupers; k += num_diag_procs) {
knsupc = SuperSize( k );
lk = LBi( k, grid );
ii = ilsum[lk] + (lk+1)*XK_H;
for (i = 0; i < knsupc; ++i) work[i+lwork] = x[i+ii];
lwork += knsupc;
}
MPI_Bcast( work, lwork, SuperLU_MPI_DOUBLE_COMPLEX,
pkk, grid->comm );
} else {
MPI_Bcast( work, diag_len[p], SuperLU_MPI_DOUBLE_COMPLEX,
pkk, grid->comm );
}
/* Scatter work[] into global y vector. */
lwork = 0;
for (k = p; k < nsupers; k += num_diag_procs) {
knsupc = SuperSize( k );
ii = FstBlockC( k );
for (i = 0; i < knsupc; ++i) y[i+ii] = work[i+lwork];
lwork += knsupc;
}
}
} /* GATHER_1RHS_DIAG_TO_ALL */
static void pdgstrf2
/************************************************************************/
(
superlu_options_t *options,
int_t k, double thresh, Glu_persist_t *Glu_persist, gridinfo_t *grid,
LocalLU_t *Llu, MPI_Request *U_diag_blk_send_req,
SuperLUStat_t *stat, int* info
)
/*
* Purpose
* =======
*
* Panel factorization -- block column k
* Factor diagonal and subdiagonal blocks and test for exact singularity.
* Only the column processes that owns block column *k* participate
* in the work.
*
* Arguments
* =========
*
* k (input) int (global)
* The column number of the block column to be factorized.
*
* thresh (input) double (global)
* The threshold value = s_eps * anorm.
*
* Glu_persist (input) Glu_persist_t*
* Global data structures (xsup, supno) replicated on all processes.
*
* grid (input) gridinfo_t*
* The 2D process mesh.
*
* Llu (input/output) LocalLU_t*
* Local data structures to store distributed L and U matrices.
*
* U_diag_blk_send_req (input/output) MPI_Request*
* List of send requests to send down the diagonal block of U.
*
* stat (output) SuperLUStat_t*
* Record the statistics about the factorization.
* See SuperLUStat_t structure defined in util.h.
*
* info (output) int*
* = 0: successful exit
* < 0: if info = -i, the i-th argument had an illegal value
* > 0: if info = i, U(i,i) is exactly zero. The factorization has
* been completed, but the factor U is exactly singular,
* and division by zero will occur if it is used to solve a
* system of equations.
*
*/
{
int cols_left, iam, l, pkk, pr;
int incx = 1, incy = 1;
int nsupr; /* number of rows in the block (LDA) */
int luptr;
int_t i, krow, j, jfst, jlst, u_diag_cnt;
int_t nsupc; /* number of columns in the block */
int_t *xsup = Glu_persist->xsup;
int_t Pr;
MPI_Status status;
MPI_Comm comm = (grid->cscp).comm;
double *lusup, temp;
double *ujrow, *ublk_ptr; /* pointer to the U block */
double alpha = -1;
*info = 0;
/* Quick return. */
/* Initialization. */
iam = grid->iam;
Pr = grid->nprow;
krow = PROW( k, grid );
pkk = PNUM( PROW(k, grid), PCOL(k, grid), grid );
j = LBj( k, grid ); /* Local block number */
jfst = FstBlockC( k );
jlst = FstBlockC( k+1 );
lusup = Llu->Lnzval_bc_ptr[j];
nsupc = SuperSize( k );
if ( Llu->Lrowind_bc_ptr[j] ) nsupr = Llu->Lrowind_bc_ptr[j][1];
ublk_ptr = ujrow = Llu->ujrow;
luptr = 0; /* point to the diagonal entries. */
cols_left = nsupc; /* supernode size */
u_diag_cnt = 0;
if ( iam == pkk ) { /* diagonal process */
if ( U_diag_blk_send_req && U_diag_blk_send_req[krow] ) {
/* There are pending sends - wait for all Isend to complete */
for (pr = 0; pr < Pr; ++pr)
if (pr != krow)
MPI_Wait(U_diag_blk_send_req + pr, &status);
}
for (j = 0; j < jlst - jfst; ++j) { /* for each column in panel */
/* Diagonal pivot */
i = luptr;
if ( options->ReplaceTinyPivot == YES || lusup[i] == 0.0 ) {
if ( fabs(lusup[i]) < thresh ) {
#if ( PRNTlevel>=2 )
printf("(%d) .. col %d, tiny pivot %e ",
iam, jfst+j, lusup[i]);
#endif
/* Keep the new diagonal entry with the same sign. */
if ( lusup[i] < 0 ) lusup[i] = -thresh;
else lusup[i] = thresh;
#if ( PRNTlevel>=2 )
printf("replaced by %e\n", lusup[i]);
#endif
++(stat->TinyPivots);
}
}
for (l = 0; l < cols_left; ++l, i += nsupr, ++u_diag_cnt)
ublk_ptr[u_diag_cnt] = lusup[i]; /* copy one row of U */
if ( ujrow[0] == 0.0 ) { /* Test for singularity. */
*info = j+jfst+1;
} else { /* Scale the j-th column. */
temp = 1.0 / ujrow[0];
for (i = luptr+1; i < luptr-j+nsupr; ++i) lusup[i] *= temp;
stat->ops[FACT] += nsupr-j-1;
}
/* Rank-1 update of the trailing submatrix. */
if ( --cols_left ) {
l = nsupr - j - 1;
#ifdef _CRAY
SGER(&l, &cols_left, &alpha, &lusup[luptr+1], &incx,
&ujrow[1], &incy, &lusup[luptr+nsupr+1], &nsupr);
#else
dger_(&l, &cols_left, &alpha, &lusup[luptr+1], &incx,
&ujrow[1], &incy, &lusup[luptr+nsupr+1], &nsupr);
#endif
stat->ops[FACT] += 2 * l * cols_left;
}
ujrow = ublk_ptr + u_diag_cnt; /* move to next row of U */
luptr += nsupr + 1; /* move to next column */
} /* for column j ... */
if ( U_diag_blk_send_req && iam == pkk ) { /* Send the U block */
/** ALWAYS SEND TO ALL OTHERS - TO FIX **/
for (pr = 0; pr < Pr; ++pr)
if (pr != krow)
MPI_Isend(ublk_ptr, u_diag_cnt, MPI_DOUBLE, pr,
((k<<2)+2)%NTAGS, comm, U_diag_blk_send_req + pr);
U_diag_blk_send_req[krow] = 1; /* flag outstanding Isend */
}
} else { /* non-diagonal process */
/* Receive the diagonal block of U */
MPI_Recv(ublk_ptr, (nsupc*(nsupc+1))>>1, MPI_DOUBLE,
krow, ((k<<2)+2)%NTAGS, comm, &status);
for (j = 0; j < jlst - jfst; ++j) { /* for each column in panel */
u_diag_cnt += cols_left;
if ( !lusup ) { /* empty block column */
--cols_left;
if ( ujrow[0] == 0.0 ) *info = j+jfst+1;
continue;
}
/* Test for singularity. */
if ( ujrow[0] == 0.0 ) {
*info = j+jfst+1;
} else {
/* Scale the j-th column. */
temp = 1.0 / ujrow[0];
for (i = luptr; i < luptr+nsupr; ++i) lusup[i] *= temp;
stat->ops[FACT] += nsupr;
}
/* Rank-1 update of the trailing submatrix. */
if ( --cols_left ) {
#ifdef _CRAY
SGER(&nsupr, &cols_left, &alpha, &lusup[luptr], &incx,
&ujrow[1], &incy, &lusup[luptr+nsupr], &nsupr);
#else
dger_(&nsupr, &cols_left, &alpha, &lusup[luptr], &incx,
&ujrow[1], &incy, &lusup[luptr+nsupr], &nsupr);
#endif
stat->ops[FACT] += 2 * nsupr * cols_left;
}
ujrow = ublk_ptr + u_diag_cnt; /* move to next row of U */
luptr += nsupr; /* move to next column */
} /* for column j ... */
} /* end if pkk ... */
} /* PDGSTRF2 */
float
ddistribute(fact_t fact, int_t n, SuperMatrix *A,
Glu_freeable_t *Glu_freeable,
LUstruct_t *LUstruct, gridinfo_t *grid)
{
Glu_persist_t *Glu_persist = LUstruct->Glu_persist;
LocalLU_t *Llu = LUstruct->Llu;
int_t bnnz, fsupc, fsupc1, i, ii, irow, istart, j, jb, jj, k,
len, len1, nsupc;
int_t ljb; /* local block column number */
int_t nrbl; /* number of L blocks in current block column */
int_t nrbu; /* number of U blocks in current block column */
int_t gb; /* global block number; 0 < gb <= nsuper */
int_t lb; /* local block number; 0 < lb <= ceil(NSUPERS/Pr) */
int iam, jbrow, kcol, mycol, myrow, pc, pr;
int_t mybufmax[NBUFFERS];
NCPformat *Astore;
double *a;
int_t *asub;
int_t *xa_begin, *xa_end;
int_t *xsup = Glu_persist->xsup; /* supernode and column mapping */
int_t *supno = Glu_persist->supno;
int_t *lsub, *xlsub, *usub, *xusub;
int_t nsupers;
int_t next_lind; /* next available position in index[*] */
int_t next_lval; /* next available position in nzval[*] */
int_t *index; /* indices consist of headers and row subscripts */
int *index1; /* temporary pointer to array of int */
double *lusup, *uval; /* nonzero values in L and U */
double **Lnzval_bc_ptr; /* size ceil(NSUPERS/Pc) */
int_t **Lrowind_bc_ptr; /* size ceil(NSUPERS/Pc) */
double **Unzval_br_ptr; /* size ceil(NSUPERS/Pr) */
int_t **Ufstnz_br_ptr; /* size ceil(NSUPERS/Pr) */
/*-- Counts to be used in factorization. --*/
int *ToRecv, *ToSendD, **ToSendR;
/*-- Counts to be used in lower triangular solve. --*/
int_t *fmod; /* Modification count for L-solve. */
int_t **fsendx_plist; /* Column process list to send down Xk. */
int_t nfrecvx = 0; /* Number of Xk I will receive. */
int_t nfsendx = 0; /* Number of Xk I will send */
int_t kseen;
/*-- Counts to be used in upper triangular solve. --*/
int_t *bmod; /* Modification count for U-solve. */
int_t **bsendx_plist; /* Column process list to send down Xk. */
int_t nbrecvx = 0; /* Number of Xk I will receive. */
int_t nbsendx = 0; /* Number of Xk I will send */
int_t *ilsum; /* starting position of each supernode in
the full array (local) */
/*-- Auxiliary arrays; freed on return --*/
int_t *rb_marker; /* block hit marker; size ceil(NSUPERS/Pr) */
int_t *Urb_length; /* U block length; size ceil(NSUPERS/Pr) */
int_t *Urb_indptr; /* pointers to U index[]; size ceil(NSUPERS/Pr) */
int_t *Urb_fstnz; /* # of fstnz in a block row; size ceil(NSUPERS/Pr) */
int_t *Ucbs; /* number of column blocks in a block row */
int_t *Lrb_length; /* L block length; size ceil(NSUPERS/Pr) */
int_t *Lrb_number; /* global block number; size ceil(NSUPERS/Pr) */
int_t *Lrb_indptr; /* pointers to L index[]; size ceil(NSUPERS/Pr) */
int_t *Lrb_valptr; /* pointers to L nzval[]; size ceil(NSUPERS/Pr) */
double *dense, *dense_col; /* SPA */
double zero = 0.0;
int_t ldaspa; /* LDA of SPA */
int_t iword, dword;
float mem_use = 0.0;
#if ( PRNTlevel>=1 )
int_t nLblocks = 0, nUblocks = 0;
#endif
#if ( PROFlevel>=1 )
double t, t_u, t_l;
int_t u_blks;
#endif
/* Initialization. */
iam = grid->iam;
myrow = MYROW( iam, grid );
mycol = MYCOL( iam, grid );
for (i = 0; i < NBUFFERS; ++i) mybufmax[i] = 0;
nsupers = supno[n-1] + 1;
Astore = A->Store;
a = Astore->nzval;
asub = Astore->rowind;
xa_begin = Astore->colbeg;
xa_end = Astore->colend;
#if ( PRNTlevel>=1 )
iword = sizeof(int_t);
dword = sizeof(double);
#endif
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(iam, "Enter ddistribute()");
#endif
if ( fact == SamePattern_SameRowPerm ) {
/* ---------------------------------------------------------------
* REUSE THE L AND U DATA STRUCTURES FROM A PREVIOUS FACTORIZATION.
* --------------------------------------------------------------- */
#if ( PROFlevel>=1 )
t_l = t_u = 0; u_blks = 0;
#endif
/* We can propagate the new values of A into the existing
L and U data structures. */
ilsum = Llu->ilsum;
ldaspa = Llu->ldalsum;
if ( !(dense = doubleCalloc_dist(((size_t)ldaspa) * sp_ienv_dist(3))) )
ABORT("Calloc fails for SPA dense[].");
nrbu = CEILING( nsupers, grid->nprow ); /* No. of local block rows */
if ( !(Urb_length = intCalloc_dist(nrbu)) )
ABORT("Calloc fails for Urb_length[].");
if ( !(Urb_indptr = intMalloc_dist(nrbu)) )
ABORT("Malloc fails for Urb_indptr[].");
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;
#if ( PRNTlevel>=1 )
mem_use += 2.0*nrbu*iword + ldaspa*sp_ienv_dist(3)*dword;
#endif
#if ( PROFlevel>=1 )
t = SuperLU_timer_();
#endif
/* Initialize Uval to zero. */
for (lb = 0; lb < nrbu; ++lb) {
Urb_indptr[lb] = BR_HEADER; /* Skip header in U index[]. */
index = Ufstnz_br_ptr[lb];
if ( index ) {
uval = Unzval_br_ptr[lb];
len = index[1];
for (i = 0; i < len; ++i) uval[i] = zero;
} /* if index != NULL */
} /* for lb ... */
for (jb = 0; jb < nsupers; ++jb) { /* Loop through each block column */
pc = PCOL( jb, grid );
if ( mycol == pc ) { /* Block column jb in my process column */
fsupc = FstBlockC( jb );
nsupc = SuperSize( jb );
/* Scatter A into SPA (for L), or into U directly. */
for (j = fsupc, dense_col = dense; j < FstBlockC(jb+1); ++j) {
for (i = xa_begin[j]; i < xa_end[j]; ++i) {
irow = asub[i];
gb = BlockNum( irow );
if ( myrow == PROW( gb, grid ) ) {
lb = LBi( gb, grid );
if ( gb < jb ) { /* in U */
index = Ufstnz_br_ptr[lb];
uval = Unzval_br_ptr[lb];
while ( (k = index[Urb_indptr[lb]]) < jb ) {
/* Skip nonzero values in this block */
Urb_length[lb] += index[Urb_indptr[lb]+1];
/* Move pointer to the next block */
Urb_indptr[lb] += UB_DESCRIPTOR
+ SuperSize( k );
}
/*assert(k == jb);*/
/* start fstnz */
istart = Urb_indptr[lb] + UB_DESCRIPTOR;
len = Urb_length[lb];
fsupc1 = FstBlockC( gb+1 );
k = j - fsupc;
/* Sum the lengths of the leading columns */
for (jj = 0; jj < k; ++jj)
len += fsupc1 - index[istart++];
/*assert(irow>=index[istart]);*/
uval[len + irow - index[istart]] = a[i];
} else { /* in L; put in SPA first */
irow = ilsum[lb] + irow - FstBlockC( gb );
dense_col[irow] = a[i];
}
}
} /* for i ... */
dense_col += ldaspa;
} /* for j ... */
#if ( PROFlevel>=1 )
t_u += SuperLU_timer_() - t;
t = SuperLU_timer_();
#endif
/* Gather the values of A from SPA into Lnzval[]. */
ljb = LBj( jb, grid ); /* Local block number */
index = Lrowind_bc_ptr[ljb];
if ( index ) {
nrbl = index[0]; /* Number of row blocks. */
len = index[1]; /* LDA of lusup[]. */
lusup = Lnzval_bc_ptr[ljb];
next_lind = BC_HEADER;
next_lval = 0;
for (jj = 0; jj < nrbl; ++jj) {
gb = index[next_lind++];
len1 = index[next_lind++]; /* Rows in the block. */
lb = LBi( gb, grid );
for (bnnz = 0; bnnz < len1; ++bnnz) {
irow = index[next_lind++]; /* Global index. */
irow = ilsum[lb] + irow - FstBlockC( gb );
k = next_lval++;
for (j = 0, dense_col = dense; j < nsupc; ++j) {
lusup[k] = dense_col[irow];
dense_col[irow] = zero;
k += len;
dense_col += ldaspa;
}
} /* for bnnz ... */
} /* for jj ... */
} /* if index ... */
#if ( PROFlevel>=1 )
t_l += SuperLU_timer_() - t;
#endif
} /* if mycol == pc */
} /* for jb ... */
SUPERLU_FREE(dense);
SUPERLU_FREE(Urb_length);
SUPERLU_FREE(Urb_indptr);
#if ( PROFlevel>=1 )
if ( !iam ) printf(".. 2nd distribute time: L %.2f\tU %.2f\tu_blks %d\tnrbu %d\n",
t_l, t_u, u_blks, nrbu);
#endif
} else {
/* --------------------------------------------------
* FIRST TIME CREATING THE L AND U DATA STRUCTURE.
* -------------------------------------------------- */
#if ( PROFlevel>=1 )
t_l = t_u = 0; u_blks = 0;
#endif
/* No L and U data structures are available yet.
We need to set up the L and U data structures and propagate
the values of A into them. */
lsub = Glu_freeable->lsub; /* compressed L subscripts */
xlsub = Glu_freeable->xlsub;
usub = Glu_freeable->usub; /* compressed U subscripts */
xusub = Glu_freeable->xusub;
if ( !(ToRecv = SUPERLU_MALLOC(nsupers * sizeof(int))) )
ABORT("Malloc fails for ToRecv[].");
for (i = 0; i < nsupers; ++i) ToRecv[i] = 0;
k = CEILING( nsupers, grid->npcol );/* Number of local column blocks */
if ( !(ToSendR = (int **) SUPERLU_MALLOC(k*sizeof(int*))) )
ABORT("Malloc fails for ToSendR[].");
j = k * grid->npcol;
if ( !(index1 = SUPERLU_MALLOC(j * sizeof(int))) )
ABORT("Malloc fails for index[].");
#if ( PRNTlevel>=1 )
mem_use += (float) k*sizeof(int_t*) + (j + nsupers)*iword;
#endif
for (i = 0; i < j; ++i) index1[i] = EMPTY;
for (i = 0,j = 0; i < k; ++i, j += grid->npcol) ToSendR[i] = &index1[j];
k = CEILING( nsupers, grid->nprow ); /* Number of local block rows */
/* Pointers to the beginning of each block row of U. */
if ( !(Unzval_br_ptr =
(double**)SUPERLU_MALLOC(k * sizeof(double*))) )
ABORT("Malloc fails for Unzval_br_ptr[].");
if ( !(Ufstnz_br_ptr = (int_t**)SUPERLU_MALLOC(k * sizeof(int_t*))) )
ABORT("Malloc fails for Ufstnz_br_ptr[].");
if ( !(ToSendD = SUPERLU_MALLOC(k * sizeof(int))) )
ABORT("Malloc fails for ToSendD[].");
for (i = 0; i < k; ++i) ToSendD[i] = NO;
if ( !(ilsum = intMalloc_dist(k+1)) )
ABORT("Malloc fails for ilsum[].");
/* Auxiliary arrays used to set up U block data structures.
They are freed on return. */
if ( !(rb_marker = intCalloc_dist(k)) )
ABORT("Calloc fails for rb_marker[].");
if ( !(Urb_length = intCalloc_dist(k)) )
ABORT("Calloc fails for Urb_length[].");
if ( !(Urb_indptr = intMalloc_dist(k)) )
ABORT("Malloc fails for Urb_indptr[].");
if ( !(Urb_fstnz = intCalloc_dist(k)) )
ABORT("Calloc fails for Urb_fstnz[].");
if ( !(Ucbs = intCalloc_dist(k)) )
ABORT("Calloc fails for Ucbs[].");
#if ( PRNTlevel>=1 )
mem_use += 2.0*k*sizeof(int_t*) + (7.0*k+1)*iword;
#endif
/* Compute ldaspa and ilsum[]. */
ldaspa = 0;
ilsum[0] = 0;
for (gb = 0; gb < nsupers; ++gb) {
if ( myrow == PROW( gb, grid ) ) {
i = SuperSize( gb );
ldaspa += i;
lb = LBi( gb, grid );
ilsum[lb + 1] = ilsum[lb] + i;
}
}
/* ------------------------------------------------------------
COUNT NUMBER OF ROW BLOCKS AND THE LENGTH OF EACH BLOCK IN U.
THIS ACCOUNTS FOR ONE-PASS PROCESSING OF G(U).
------------------------------------------------------------*/
/* Loop through each supernode column. */
for (jb = 0; jb < nsupers; ++jb) {
pc = PCOL( jb, grid );
fsupc = FstBlockC( jb );
nsupc = SuperSize( jb );
/* Loop through each column in the block. */
for (j = fsupc; j < fsupc + nsupc; ++j) {
/* usub[*] contains only "first nonzero" in each segment. */
for (i = xusub[j]; i < xusub[j+1]; ++i) {
irow = usub[i]; /* First nonzero of the segment. */
gb = BlockNum( irow );
kcol = PCOL( gb, grid );
ljb = LBj( gb, grid );
if ( mycol == kcol && mycol != pc ) ToSendR[ljb][pc] = YES;
pr = PROW( gb, grid );
lb = LBi( gb, grid );
if ( mycol == pc ) {
if ( myrow == pr ) {
ToSendD[lb] = YES;
/* Count nonzeros in entire block row. */
Urb_length[lb] += FstBlockC( gb+1 ) - irow;
if (rb_marker[lb] <= jb) {/* First see the block */
rb_marker[lb] = jb + 1;
Urb_fstnz[lb] += nsupc;
++Ucbs[lb]; /* Number of column blocks
in block row lb. */
#if ( PRNTlevel>=1 )
++nUblocks;
#endif
}
ToRecv[gb] = 1;
} else ToRecv[gb] = 2; /* Do I need 0, 1, 2 ? */
}
} /* for i ... */
} /* for j ... */
} /* for jb ... */
/* Set up the initial pointers for each block row in U. */
nrbu = CEILING( nsupers, grid->nprow );/* Number of local block rows */
for (lb = 0; lb < nrbu; ++lb) {
len = Urb_length[lb];
rb_marker[lb] = 0; /* Reset block marker. */
if ( len ) {
/* Add room for descriptors */
len1 = Urb_fstnz[lb] + BR_HEADER + Ucbs[lb] * UB_DESCRIPTOR;
if ( !(index = intMalloc_dist(len1+1)) )
ABORT("Malloc fails for Uindex[].");
Ufstnz_br_ptr[lb] = index;
if ( !(Unzval_br_ptr[lb] = doubleMalloc_dist(len)) )
ABORT("Malloc fails for Unzval_br_ptr[*][].");
mybufmax[2] = SUPERLU_MAX( mybufmax[2], len1 );
mybufmax[3] = SUPERLU_MAX( mybufmax[3], len );
index[0] = Ucbs[lb]; /* Number of column blocks */
index[1] = len; /* Total length of nzval[] */
index[2] = len1; /* Total length of index[] */
index[len1] = -1; /* End marker */
} else {
Ufstnz_br_ptr[lb] = NULL;
Unzval_br_ptr[lb] = NULL;
}
Urb_length[lb] = 0; /* Reset block length. */
Urb_indptr[lb] = BR_HEADER; /* Skip header in U index[]. */
Urb_fstnz[lb] = BR_HEADER;
} /* for lb ... */
SUPERLU_FREE(Ucbs);
#if ( PROFlevel>=1 )
t = SuperLU_timer_() - t;
if ( !iam) printf(".. Phase 2 - setup U strut time: %.2f\t\n", t);
#endif
#if ( PRNTlevel>=1 )
mem_use -= 2.0*k * iword;
#endif
/* Auxiliary arrays used to set up L block data structures.
They are freed on return.
k is the number of local row blocks. */
if ( !(Lrb_length = intCalloc_dist(k)) )
ABORT("Calloc fails for Lrb_length[].");
if ( !(Lrb_number = intMalloc_dist(k)) )
ABORT("Malloc fails for Lrb_number[].");
if ( !(Lrb_indptr = intMalloc_dist(k)) )
ABORT("Malloc fails for Lrb_indptr[].");
if ( !(Lrb_valptr = intMalloc_dist(k)) )
ABORT("Malloc fails for Lrb_valptr[].");
if (!(dense=doubleCalloc_dist(SUPERLU_MAX(1,((size_t)ldaspa)
*sp_ienv_dist(3)))))
ABORT("Calloc fails for SPA dense[].");
/* These counts will be used for triangular solves. */
if ( !(fmod = intCalloc_dist(k)) )
ABORT("Calloc fails for fmod[].");
if ( !(bmod = intCalloc_dist(k)) )
ABORT("Calloc fails for bmod[].");
#if ( PRNTlevel>=1 )
mem_use += 6.0*k*iword + ldaspa*sp_ienv_dist(3)*dword;
#endif
k = CEILING( nsupers, grid->npcol );/* Number of local block columns */
/* Pointers to the beginning of each block column of L. */
if ( !(Lnzval_bc_ptr = (double**)SUPERLU_MALLOC(k * sizeof(double*))) )
ABORT("Malloc fails for Lnzval_bc_ptr[].");
if ( !(Lrowind_bc_ptr = (int_t**)SUPERLU_MALLOC(k * sizeof(int_t*))) )
ABORT("Malloc fails for Lrowind_bc_ptr[].");
Lrowind_bc_ptr[k-1] = NULL;
/* These lists of processes will be used for triangular solves. */
if ( !(fsendx_plist = (int_t **) SUPERLU_MALLOC(k*sizeof(int_t*))) )
ABORT("Malloc fails for fsendx_plist[].");
len = k * grid->nprow;
if ( !(index = intMalloc_dist(len)) )
ABORT("Malloc fails for fsendx_plist[0]");
for (i = 0; i < len; ++i) index[i] = EMPTY;
for (i = 0, j = 0; i < k; ++i, j += grid->nprow)
fsendx_plist[i] = &index[j];
if ( !(bsendx_plist = (int_t **) SUPERLU_MALLOC(k*sizeof(int_t*))) )
ABORT("Malloc fails for bsendx_plist[].");
if ( !(index = intMalloc_dist(len)) )
ABORT("Malloc fails for bsendx_plist[0]");
for (i = 0; i < len; ++i) index[i] = EMPTY;
for (i = 0, j = 0; i < k; ++i, j += grid->nprow)
bsendx_plist[i] = &index[j];
#if ( PRNTlevel>=1 )
mem_use += 4.0*k*sizeof(int_t*) + 2.0*len*iword;
#endif
/*------------------------------------------------------------
PROPAGATE ROW SUBSCRIPTS AND VALUES OF A INTO L AND U BLOCKS.
THIS ACCOUNTS FOR ONE-PASS PROCESSING OF A, L AND U.
------------------------------------------------------------*/
for (jb = 0; jb < nsupers; ++jb) {
pc = PCOL( jb, grid );
if ( mycol == pc ) { /* Block column jb in my process column */
fsupc = FstBlockC( jb );
nsupc = SuperSize( jb );
ljb = LBj( jb, grid ); /* Local block number */
/* Scatter A into SPA. */
for (j = fsupc, dense_col = dense; j < FstBlockC( jb+1 ); ++j){
for (i = xa_begin[j]; i < xa_end[j]; ++i) {
irow = asub[i];
gb = BlockNum( irow );
if ( myrow == PROW( gb, grid ) ) {
lb = LBi( gb, grid );
irow = ilsum[lb] + irow - FstBlockC( gb );
dense_col[irow] = a[i];
}
}
dense_col += ldaspa;
}
jbrow = PROW( jb, grid );
#if ( PROFlevel>=1 )
t = SuperLU_timer_();
#endif
/*------------------------------------------------
* SET UP U BLOCKS.
*------------------------------------------------*/
kseen = 0;
dense_col = dense;
/* Loop through each column in the block column. */
for (j = fsupc; j < FstBlockC( jb+1 ); ++j) {
istart = xusub[j];
/* NOTE: Only the first nonzero index of the segment
is stored in usub[]. */
for (i = istart; i < xusub[j+1]; ++i) {
irow = usub[i]; /* First nonzero in the segment. */
gb = BlockNum( irow );
pr = PROW( gb, grid );
if ( pr != jbrow &&
myrow == jbrow && /* diag. proc. owning jb */
bsendx_plist[ljb][pr] == EMPTY ) {
bsendx_plist[ljb][pr] = YES;
++nbsendx;
}
if ( myrow == pr ) {
lb = LBi( gb, grid ); /* Local block number */
index = Ufstnz_br_ptr[lb];
uval = Unzval_br_ptr[lb];
fsupc1 = FstBlockC( gb+1 );
if (rb_marker[lb] <= jb) { /* First time see
the block */
rb_marker[lb] = jb + 1;
Urb_indptr[lb] = Urb_fstnz[lb];;
index[Urb_indptr[lb]] = jb; /* Descriptor */
Urb_indptr[lb] += UB_DESCRIPTOR;
/* Record the first location in index[] of the
next block */
Urb_fstnz[lb] = Urb_indptr[lb] + nsupc;
len = Urb_indptr[lb];/* Start fstnz in index */
index[len-1] = 0;
for (k = 0; k < nsupc; ++k)
index[len+k] = fsupc1;
if ( gb != jb )/* Exclude diagonal block. */
++bmod[lb];/* Mod. count for back solve */
if ( kseen == 0 && myrow != jbrow ) {
++nbrecvx;
kseen = 1;
}
} else { /* Already saw the block */
len = Urb_indptr[lb];/* Start fstnz in index */
}
jj = j - fsupc;
index[len+jj] = irow;
/* Load the numerical values */
k = fsupc1 - irow; /* No. of nonzeros in segment */
index[len-1] += k; /* Increment block length in
Descriptor */
irow = ilsum[lb] + irow - FstBlockC( gb );
for (ii = 0; ii < k; ++ii) {
uval[Urb_length[lb]++] = dense_col[irow + ii];
dense_col[irow + ii] = zero;
}
} /* if myrow == pr ... */
} /* for i ... */
dense_col += ldaspa;
} /* for j ... */
#if ( PROFlevel>=1 )
t_u += SuperLU_timer_() - t;
t = SuperLU_timer_();
#endif
/*------------------------------------------------
* SET UP L BLOCKS.
*------------------------------------------------*/
/* Count number of blocks and length of each block. */
nrbl = 0;
len = 0; /* Number of row subscripts I own. */
kseen = 0;
istart = xlsub[fsupc];
for (i = istart; i < xlsub[fsupc+1]; ++i) {
irow = lsub[i];
gb = BlockNum( irow ); /* Global block number */
pr = PROW( gb, grid ); /* Process row owning this block */
if ( pr != jbrow &&
myrow == jbrow && /* diag. proc. owning jb */
fsendx_plist[ljb][pr] == EMPTY /* first time */ ) {
fsendx_plist[ljb][pr] = YES;
++nfsendx;
}
if ( myrow == pr ) {
lb = LBi( gb, grid ); /* Local block number */
if (rb_marker[lb] <= jb) { /* First see this block */
rb_marker[lb] = jb + 1;
Lrb_length[lb] = 1;
Lrb_number[nrbl++] = gb;
if ( gb != jb ) /* Exclude diagonal block. */
++fmod[lb]; /* Mod. count for forward solve */
if ( kseen == 0 && myrow != jbrow ) {
++nfrecvx;
kseen = 1;
}
#if ( PRNTlevel>=1 )
++nLblocks;
#endif
} else {
++Lrb_length[lb];
}
++len;
}
} /* for i ... */
if ( nrbl ) { /* Do not ensure the blocks are sorted! */
/* Set up the initial pointers for each block in
index[] and nzval[]. */
/* Add room for descriptors */
len1 = len + BC_HEADER + nrbl * LB_DESCRIPTOR;
if ( !(index = intMalloc_dist(len1)) )
ABORT("Malloc fails for index[]");
Lrowind_bc_ptr[ljb] = index;
if (!(Lnzval_bc_ptr[ljb] = doubleMalloc_dist(((size_t)len)*nsupc))) {
fprintf(stderr, "col block " IFMT " ", jb);
ABORT("Malloc fails for Lnzval_bc_ptr[*][]");
}
mybufmax[0] = SUPERLU_MAX( mybufmax[0], len1 );
mybufmax[1] = SUPERLU_MAX( mybufmax[1], len*nsupc );
mybufmax[4] = SUPERLU_MAX( mybufmax[4], len );
index[0] = nrbl; /* Number of row blocks */
index[1] = len; /* LDA of the nzval[] */
next_lind = BC_HEADER;
next_lval = 0;
for (k = 0; k < nrbl; ++k) {
gb = Lrb_number[k];
lb = LBi( gb, grid );
len = Lrb_length[lb];
Lrb_length[lb] = 0; /* Reset vector of block length */
index[next_lind++] = gb; /* Descriptor */
index[next_lind++] = len;
Lrb_indptr[lb] = next_lind;
Lrb_valptr[lb] = next_lval;
next_lind += len;
next_lval += len;
}
/* Propagate the compressed row subscripts to Lindex[], and
the initial values of A from SPA into Lnzval[]. */
lusup = Lnzval_bc_ptr[ljb];
len = index[1]; /* LDA of lusup[] */
for (i = istart; i < xlsub[fsupc+1]; ++i) {
irow = lsub[i];
gb = BlockNum( irow );
if ( myrow == PROW( gb, grid ) ) {
lb = LBi( gb, grid );
k = Lrb_indptr[lb]++; /* Random access a block */
index[k] = irow;
k = Lrb_valptr[lb]++;
irow = ilsum[lb] + irow - FstBlockC( gb );
for (j = 0, dense_col = dense; j < nsupc; ++j) {
lusup[k] = dense_col[irow];
dense_col[irow] = 0.0;
k += len;
dense_col += ldaspa;
}
}
} /* for i ... */
} else {
Lrowind_bc_ptr[ljb] = NULL;
Lnzval_bc_ptr[ljb] = NULL;
} /* if nrbl ... */
#if ( PROFlevel>=1 )
t_l += SuperLU_timer_() - t;
#endif
} /* if mycol == pc */
} /* for jb ... */
Llu->Lrowind_bc_ptr = Lrowind_bc_ptr;
Llu->Lnzval_bc_ptr = Lnzval_bc_ptr;
Llu->Ufstnz_br_ptr = Ufstnz_br_ptr;
Llu->Unzval_br_ptr = Unzval_br_ptr;
Llu->ToRecv = ToRecv;
Llu->ToSendD = ToSendD;
Llu->ToSendR = ToSendR;
Llu->fmod = fmod;
Llu->fsendx_plist = fsendx_plist;
Llu->nfrecvx = nfrecvx;
Llu->nfsendx = nfsendx;
Llu->bmod = bmod;
Llu->bsendx_plist = bsendx_plist;
Llu->nbrecvx = nbrecvx;
Llu->nbsendx = nbsendx;
Llu->ilsum = ilsum;
Llu->ldalsum = ldaspa;
#if ( PRNTlevel>=1 )
if ( !iam ) printf(".. # L blocks " IFMT "\t# U blocks " IFMT "\n",
nLblocks, nUblocks);
#endif
SUPERLU_FREE(rb_marker);
SUPERLU_FREE(Urb_fstnz);
SUPERLU_FREE(Urb_length);
SUPERLU_FREE(Urb_indptr);
SUPERLU_FREE(Lrb_length);
SUPERLU_FREE(Lrb_number);
SUPERLU_FREE(Lrb_indptr);
SUPERLU_FREE(Lrb_valptr);
SUPERLU_FREE(dense);
k = CEILING( nsupers, grid->nprow );/* Number of local block rows */
if ( !(Llu->mod_bit = intMalloc_dist(k)) )
ABORT("Malloc fails for mod_bit[].");
/* Find the maximum buffer size. */
MPI_Allreduce(mybufmax, Llu->bufmax, NBUFFERS, mpi_int_t,
MPI_MAX, grid->comm);
#if ( PROFlevel>=1 )
if ( !iam ) printf(".. 1st distribute time:\n "
"\tL\t%.2f\n\tU\t%.2f\n"
"\tu_blks %d\tnrbu %d\n--------\n",
t_l, t_u, u_blks, nrbu);
#endif
} /* else fact != SamePattern_SameRowPerm */
#if ( DEBUGlevel>=1 )
/* Memory allocated but not freed:
ilsum, fmod, fsendx_plist, bmod, bsendx_plist */
CHECK_MALLOC(iam, "Exit ddistribute()");
#endif
return (mem_use);
} /* DDISTRIBUTE */
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 */
static void pdgstrf2
/************************************************************************/
(
superlu_options_t *options,
int_t k, double thresh, Glu_persist_t *Glu_persist, gridinfo_t *grid,
LocalLU_t *Llu, SuperLUStat_t *stat, int* info
)
/*
* Purpose
* =======
* Factor diagonal and subdiagonal blocks and test for exact singularity.
* Only the process column that owns block column *k* participates
* in the work.
*
* Arguments
* =========
*
* k (input) int (global)
* The column number of the block column to be factorized.
*
* thresh (input) double (global)
* The threshold value = s_eps * anorm.
*
* Glu_persist (input) Glu_persist_t*
* Global data structures (xsup, supno) replicated on all processes.
*
* grid (input) gridinfo_t*
* The 2D process mesh.
*
* Llu (input/output) LocalLU_t*
* Local data structures to store distributed L and U matrices.
*
* stat (output) SuperLUStat_t*
* Record the statistics about the factorization.
* See SuperLUStat_t structure defined in util.h.
*
* info (output) int*
* = 0: successful exit
* < 0: if info = -i, the i-th argument had an illegal value
* > 0: if info = i, U(i,i) is exactly zero. The factorization has
* been completed, but the factor U is exactly singular,
* and division by zero will occur if it is used to solve a
* system of equations.
*
*/
{
int c, iam, l, pkk;
int incx = 1, incy = 1;
int nsupr; /* number of rows in the block (LDA) */
int luptr;
int_t i, krow, j, jfst, jlst;
int_t nsupc; /* number of columns in the block */
int_t *xsup = Glu_persist->xsup;
double *lusup, temp;
double *ujrow;
double alpha = -1;
*info = 0;
/* Quick return. */
/* Initialization. */
iam = grid->iam;
krow = PROW( k, grid );
pkk = PNUM( PROW(k, grid), PCOL(k, grid), grid );
j = LBj( k, grid ); /* Local block number */
jfst = FstBlockC( k );
jlst = FstBlockC( k+1 );
lusup = Llu->Lnzval_bc_ptr[j];
nsupc = SuperSize( k );
if ( Llu->Lrowind_bc_ptr[j] ) nsupr = Llu->Lrowind_bc_ptr[j][1];
ujrow = Llu->ujrow;
luptr = 0; /* Point to the diagonal entries. */
c = nsupc;
for (j = 0; j < jlst - jfst; ++j) {
/* Broadcast the j-th row (nsupc - j) elements to
the process column. */
if ( iam == pkk ) { /* Diagonal process. */
i = luptr;
if ( options->ReplaceTinyPivot == YES || lusup[i] == 0.0 ) {
if ( fabs(lusup[i]) < thresh ) { /* Diagonal */
#if ( PRNTlevel>=2 )
printf("(%d) .. col %d, tiny pivot %e ",
iam, jfst+j, lusup[i]);
#endif
/* Keep the replaced diagonal with the same sign. */
if ( lusup[i] < 0 ) lusup[i] = -thresh;
else lusup[i] = thresh;
#if ( PRNTlevel>=2 )
printf("replaced by %e\n", lusup[i]);
#endif
++(stat->TinyPivots);
}
}
for (l = 0; l < c; ++l, i += nsupr) ujrow[l] = lusup[i];
}
#if 0
dbcast_col(ujrow, c, pkk, UjROW, grid, &c);
#else
MPI_Bcast(ujrow, c, MPI_DOUBLE, krow, (grid->cscp).comm);
/*bcast_tree(ujrow, c, MPI_DOUBLE, krow, (24*k+j)%NTAGS,
grid, COMM_COLUMN, &c);*/
#endif
#if ( DEBUGlevel>=2 )
if ( k == 3329 && j == 2 ) {
if ( iam == pkk ) {
printf("..(%d) k %d, j %d: Send ujrow[0] %e\n",iam,k,j,ujrow[0]);
} else {
printf("..(%d) k %d, j %d: Recv ujrow[0] %e\n",iam,k,j,ujrow[0]);
}
}
#endif
if ( !lusup ) { /* Empty block column. */
--c;
if ( ujrow[0] == 0.0 ) *info = j+jfst+1;
continue;
}
/* Test for singularity. */
if ( ujrow[0] == 0.0 ) {
*info = j+jfst+1;
} else {
/* Scale the j-th column of the matrix. */
temp = 1.0 / ujrow[0];
if ( iam == pkk ) {
for (i = luptr+1; i < luptr-j+nsupr; ++i) lusup[i] *= temp;
stat->ops[FACT] += nsupr-j-1;
} else {
for (i = luptr; i < luptr+nsupr; ++i) lusup[i] *= temp;
stat->ops[FACT] += nsupr;
}
}
/* Rank-1 update of the trailing submatrix. */
if ( --c ) {
if ( iam == pkk ) {
l = nsupr - j - 1;
#ifdef _CRAY
SGER(&l, &c, &alpha, &lusup[luptr+1], &incx,
&ujrow[1], &incy, &lusup[luptr+nsupr+1], &nsupr);
#elif defined (USE_VENDOR_BLAS)
dger_(&l, &c, &alpha, &lusup[luptr+1], &incx,
&ujrow[1], &incy, &lusup[luptr+nsupr+1], &nsupr);
#else
hypre_F90_NAME_BLAS(dger,DGER)(&l, &c, &alpha,
&lusup[luptr+1], &incx,
&ujrow[1], &incy, &lusup[luptr+nsupr+1], &nsupr);
#endif
stat->ops[FACT] += 2 * l * c;
} else {
#ifdef _CRAY
SGER(&nsupr, &c, &alpha, &lusup[luptr], &incx,
&ujrow[1], &incy, &lusup[luptr+nsupr], &nsupr);
#elif defined (USE_VENDOR_BLAS)
dger_(&nsupr, &c, &alpha, &lusup[luptr], &incx,
&ujrow[1], &incy, &lusup[luptr+nsupr], &nsupr);
#else
hypre_F90_NAME_BLAS(dger,DGER)(&nsupr, &c, &alpha,
&lusup[luptr], &incx,
&ujrow[1], &incy, &lusup[luptr+nsupr], &nsupr);
#endif
stat->ops[FACT] += 2 * nsupr * c;
}
}
/* Move to the next column. */
if ( iam == pkk ) luptr += nsupr + 1;
else luptr += nsupr;
} /* for j ... */
} /* PDGSTRF2 */
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 */
/*! \brief
*
* <pre>
* Purpose
* =======
* Set up the communication pattern for the triangular solution.
*
* Arguments
* =========
*
* n (input) int (global)
* The dimension of the linear system.
*
* m_loc (input) int (local)
* The local row dimension of the distributed input matrix.
*
* nrhs (input) int (global)
* Number of right-hand sides.
*
* fst_row (input) int (global)
* The row number of matrix B's first row in the global matrix.
*
* perm_r (input) int* (global)
* The row permutation vector.
*
* perm_c (input) int* (global)
* The column permutation vector.
*
* grid (input) gridinfo_t*
* The 2D process mesh.
* </pre>
*/
int_t
pxgstrs_init(int_t n, int_t m_loc, int_t nrhs, int_t fst_row,
int_t perm_r[], int_t perm_c[], gridinfo_t *grid,
Glu_persist_t *Glu_persist, SOLVEstruct_t *SOLVEstruct)
{
int *SendCnt, *SendCnt_nrhs, *RecvCnt, *RecvCnt_nrhs;
int *sdispls, *sdispls_nrhs, *rdispls, *rdispls_nrhs;
int *itemp, *ptr_to_ibuf, *ptr_to_dbuf;
int_t *row_to_proc;
int_t i, gbi, k, l, num_diag_procs, *diag_procs;
int_t irow, lk, q, knsupc, nsupers, *xsup, *supno;
int iam, p, pkk, procs;
pxgstrs_comm_t *gstrs_comm;
procs = grid->nprow * grid->npcol;
iam = grid->iam;
gstrs_comm = SOLVEstruct->gstrs_comm;
xsup = Glu_persist->xsup;
supno = Glu_persist->supno;
nsupers = Glu_persist->supno[n-1] + 1;
row_to_proc = SOLVEstruct->row_to_proc;
/* ------------------------------------------------------------
SET UP COMMUNICATION PATTERN FOR ReDistribute_B_to_X.
------------------------------------------------------------*/
if ( !(itemp = SUPERLU_MALLOC(8*procs * sizeof(int))) )
ABORT("Malloc fails for B_to_X_itemp[].");
SendCnt = itemp;
SendCnt_nrhs = itemp + procs;
RecvCnt = itemp + 2*procs;
RecvCnt_nrhs = itemp + 3*procs;
sdispls = itemp + 4*procs;
sdispls_nrhs = itemp + 5*procs;
rdispls = itemp + 6*procs;
rdispls_nrhs = itemp + 7*procs;
/* Count the number of elements to be sent to each diagonal process.*/
for (p = 0; p < procs; ++p) SendCnt[p] = 0;
for (i = 0, l = fst_row; i < m_loc; ++i, ++l) {
irow = perm_c[perm_r[l]]; /* Row number in Pc*Pr*B */
gbi = BlockNum( irow );
p = PNUM( PROW(gbi,grid), PCOL(gbi,grid), grid ); /* Diagonal process */
++SendCnt[p];
}
/* Set up the displacements for alltoall. */
MPI_Alltoall(SendCnt, 1, MPI_INT, RecvCnt, 1, MPI_INT, grid->comm);
sdispls[0] = rdispls[0] = 0;
for (p = 1; p < procs; ++p) {
sdispls[p] = sdispls[p-1] + SendCnt[p-1];
rdispls[p] = rdispls[p-1] + RecvCnt[p-1];
}
for (p = 0; p < procs; ++p) {
SendCnt_nrhs[p] = SendCnt[p] * nrhs;
sdispls_nrhs[p] = sdispls[p] * nrhs;
RecvCnt_nrhs[p] = RecvCnt[p] * nrhs;
rdispls_nrhs[p] = rdispls[p] * nrhs;
}
/* This is saved for repeated solves, and is freed in pxgstrs_finalize().*/
gstrs_comm->B_to_X_SendCnt = SendCnt;
/* ------------------------------------------------------------
SET UP COMMUNICATION PATTERN FOR ReDistribute_X_to_B.
------------------------------------------------------------*/
/* This is freed in pxgstrs_finalize(). */
if ( !(itemp = SUPERLU_MALLOC(8*procs * sizeof(int))) )
ABORT("Malloc fails for X_to_B_itemp[].");
SendCnt = itemp;
SendCnt_nrhs = itemp + procs;
RecvCnt = itemp + 2*procs;
RecvCnt_nrhs = itemp + 3*procs;
sdispls = itemp + 4*procs;
sdispls_nrhs = itemp + 5*procs;
rdispls = itemp + 6*procs;
rdispls_nrhs = itemp + 7*procs;
/* Count the number of X entries to be sent to each process.*/
for (p = 0; p < procs; ++p) SendCnt[p] = 0;
num_diag_procs = SOLVEstruct->num_diag_procs;
diag_procs = SOLVEstruct->diag_procs;
for (p = 0; p < num_diag_procs; ++p) { /* for all diagonal processes */
pkk = diag_procs[p];
if ( iam == pkk ) {
for (k = p; k < nsupers; k += num_diag_procs) {
knsupc = SuperSize( k );
lk = LBi( k, grid ); /* Local block number */
irow = FstBlockC( k );
for (i = 0; i < knsupc; ++i) {
#if 0
q = row_to_proc[inv_perm_c[irow]];
#else
q = row_to_proc[irow];
#endif
++SendCnt[q];
++irow;
}
}
}
}
MPI_Alltoall(SendCnt, 1, MPI_INT, RecvCnt, 1, MPI_INT, grid->comm);
sdispls[0] = rdispls[0] = 0;
sdispls_nrhs[0] = rdispls_nrhs[0] = 0;
SendCnt_nrhs[0] = SendCnt[0] * nrhs;
RecvCnt_nrhs[0] = RecvCnt[0] * nrhs;
for (p = 1; p < procs; ++p) {
sdispls[p] = sdispls[p-1] + SendCnt[p-1];
rdispls[p] = rdispls[p-1] + RecvCnt[p-1];
sdispls_nrhs[p] = sdispls[p] * nrhs;
rdispls_nrhs[p] = rdispls[p] * nrhs;
SendCnt_nrhs[p] = SendCnt[p] * nrhs;
RecvCnt_nrhs[p] = RecvCnt[p] * nrhs;
}
/* This is saved for repeated solves, and is freed in pxgstrs_finalize().*/
gstrs_comm->X_to_B_SendCnt = SendCnt;
if ( !(ptr_to_ibuf = SUPERLU_MALLOC(2*procs * sizeof(int))) )
ABORT("Malloc fails for ptr_to_ibuf[].");
gstrs_comm->ptr_to_ibuf = ptr_to_ibuf;
gstrs_comm->ptr_to_dbuf = ptr_to_ibuf + procs;
} /* PXGSTRS_INIT */
void
pdgsrfs_ABXglobal(int_t n, SuperMatrix *A, double anorm, LUstruct_t *LUstruct,
gridinfo_t *grid, double *B, int_t ldb, double *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;
double *val;
int_t *mv_sup_to_proc; /* Supernode to process mapping in
matrix-vector multiply. */
/*-- end data structures for matrix-vector multiply --*/
double *b, *ax, *R, *B_col, *temp, *work, *X_col,
*x_trs, *dx_trs;
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 pdgstrs1(int_t, LUstruct_t *, gridinfo_t *,
double *, int, SuperLUStat_t *, int *);
/* 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_D || 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);
pxerr_dist("pdgsrfs_ABXglobal", grid, 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;
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(iam, "Enter pdgsrfs_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 = " IFMT "\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[]");
pdgsmv_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 = doubleMalloc_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 ( DEBUGlevel>=2 )
{
double *dwork = doubleMalloc_dist(n);
for (i = 0; i < n; ++i) {
if ( i & 1 ) dwork[i] = 1.;
else dwork[i] = 2.;
}
/* Check correctness of matrix-vector multiply. */
pdgsmv_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 = dmach_dist("Epsilon");
safmin = dmach_dist("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] = 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. */
pdgsmv_AXglobal(N_update, update, val, bindx, X_col, ax);
/* Compute residual. */
for (i = 0; i < N_update; ++i) R[i] = b[i] - ax[i];
/* Compute abs(op(A))*abs(X) + abs(B). */
pdgsmv_AXglobal_abs(N_update, update, val, bindx, X_col, temp);
for (i = 0; i < N_update; ++i) temp[i] += fabs(b[i]);
s = 0.0;
for (i = 0; i < N_update; ++i) {
if ( temp[i] > safe2 ) {
s = SUPERLU_MAX(s, fabs(R[i]) / temp[i]);
} else if ( temp[i] != 0.0 ) {
/* Adding SAFE1 to the numerator guards against
spuriously zero residuals (underflow). */
s = SUPERLU_MAX(s, (safe1 + fabs(R[i])) / temp[i]);
}
/* If temp[i] is exactly 0.0 (computed by PxGSMV), then
we know the true residual also must be exactly 0.0. */
}
MPI_Allreduce( &s, &berr[j], 1, MPI_DOUBLE, MPI_MAX, grid->comm );
#if ( PRNTlevel>= 1 )
if ( !iam )
printf("(%2d) .. Step " IFMT ": berr[j] = %e\n", iam, count, berr[j]);
#endif
if ( berr[j] > eps && berr[j] * 2 <= lstres && count < ITMAX ) {
/* Compute new dx. */
redist_all_to_diag(n, R, Glu_persist, Llu, grid,
mv_sup_to_proc, dx_trs);
pdgstrs1(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)
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);
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(iam, "Exit pdgsrfs_ABXglobal()");
#endif
} /* PDGSRFS_ABXGLOBAL */
int_t
pzReDistribute_B_to_X(doublecomplex *B, int_t m_loc, int nrhs, int_t ldb,
int_t fst_row, int_t *ilsum, doublecomplex *x,
ScalePermstruct_t *ScalePermstruct,
Glu_persist_t *Glu_persist,
gridinfo_t *grid, SOLVEstruct_t *SOLVEstruct)
{
int *SendCnt, *SendCnt_nrhs, *RecvCnt, *RecvCnt_nrhs;
int *sdispls, *sdispls_nrhs, *rdispls, *rdispls_nrhs;
int *ptr_to_ibuf, *ptr_to_dbuf;
int_t *perm_r, *perm_c; /* row and column permutation vectors */
int_t *send_ibuf, *recv_ibuf;
doublecomplex *send_dbuf, *recv_dbuf;
int_t *xsup, *supno;
int_t i, ii, irow, gbi, j, jj, k, knsupc, l, lk;
int p, procs;
pxgstrs_comm_t *gstrs_comm = SOLVEstruct->gstrs_comm;
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(grid->iam, "Enter pzReDistribute_B_to_X()");
#endif
/* ------------------------------------------------------------
INITIALIZATION.
------------------------------------------------------------*/
perm_r = ScalePermstruct->perm_r;
perm_c = ScalePermstruct->perm_c;
procs = grid->nprow * grid->npcol;
xsup = Glu_persist->xsup;
supno = Glu_persist->supno;
SendCnt = gstrs_comm->B_to_X_SendCnt;
SendCnt_nrhs = gstrs_comm->B_to_X_SendCnt + procs;
RecvCnt = gstrs_comm->B_to_X_SendCnt + 2*procs;
RecvCnt_nrhs = gstrs_comm->B_to_X_SendCnt + 3*procs;
sdispls = gstrs_comm->B_to_X_SendCnt + 4*procs;
sdispls_nrhs = gstrs_comm->B_to_X_SendCnt + 5*procs;
rdispls = gstrs_comm->B_to_X_SendCnt + 6*procs;
rdispls_nrhs = gstrs_comm->B_to_X_SendCnt + 7*procs;
ptr_to_ibuf = gstrs_comm->ptr_to_ibuf;
ptr_to_dbuf = gstrs_comm->ptr_to_dbuf;
/* ------------------------------------------------------------
NOW COMMUNICATE THE ACTUAL DATA.
------------------------------------------------------------*/
k = sdispls[procs-1] + SendCnt[procs-1]; /* Total number of sends */
l = rdispls[procs-1] + RecvCnt[procs-1]; /* Total number of receives */
if ( !(send_ibuf = intMalloc_dist(k + l)) )
ABORT("Malloc fails for send_ibuf[].");
recv_ibuf = send_ibuf + k;
if ( !(send_dbuf = doublecomplexMalloc_dist((k + l)* (size_t)nrhs)) )
ABORT("Malloc fails for send_dbuf[].");
recv_dbuf = send_dbuf + k * nrhs;
for (p = 0; p < procs; ++p) {
ptr_to_ibuf[p] = sdispls[p];
ptr_to_dbuf[p] = sdispls[p] * nrhs;
}
/* Copy the row indices and values to the send buffer. */
for (i = 0, l = fst_row; i < m_loc; ++i, ++l) {
irow = perm_c[perm_r[l]]; /* Row number in Pc*Pr*B */
gbi = BlockNum( irow );
p = PNUM( PROW(gbi,grid), PCOL(gbi,grid), grid ); /* Diagonal process */
k = ptr_to_ibuf[p];
send_ibuf[k] = irow;
k = ptr_to_dbuf[p];
RHS_ITERATE(j) { /* RHS is stored in row major in the buffer. */
send_dbuf[k++] = B[i + j*ldb];
}
++ptr_to_ibuf[p];
ptr_to_dbuf[p] += nrhs;
}
/* Communicate the (permuted) row indices. */
MPI_Alltoallv(send_ibuf, SendCnt, sdispls, mpi_int_t,
recv_ibuf, RecvCnt, rdispls, mpi_int_t, grid->comm);
/* Communicate the numerical values. */
MPI_Alltoallv(send_dbuf, SendCnt_nrhs, sdispls_nrhs, SuperLU_MPI_DOUBLE_COMPLEX,
recv_dbuf, RecvCnt_nrhs, rdispls_nrhs, SuperLU_MPI_DOUBLE_COMPLEX,
grid->comm);
/* ------------------------------------------------------------
Copy buffer into X on the diagonal processes.
------------------------------------------------------------*/
ii = 0;
for (p = 0; p < procs; ++p) {
jj = rdispls_nrhs[p];
for (i = 0; i < RecvCnt[p]; ++i) {
/* Only the diagonal processes do this; the off-diagonal processes
have 0 RecvCnt. */
irow = recv_ibuf[ii]; /* The permuted row index. */
k = BlockNum( irow );
knsupc = SuperSize( k );
lk = LBi( k, grid ); /* Local block number. */
l = X_BLK( lk );
x[l - XK_H].r = k; /* Block number prepended in the header. */
x[l - XK_H].i = 0;
irow = irow - FstBlockC(k); /* Relative row number in X-block */
RHS_ITERATE(j) {
x[l + irow + j*knsupc] = recv_dbuf[jj++];
}
++ii;
}
}
SUPERLU_FREE(send_ibuf);
SUPERLU_FREE(send_dbuf);
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(grid->iam, "Exit pzReDistribute_B_to_X()");
#endif
return 0;
} /* pzReDistribute_B_to_X */
/*! \brief
*
* <pre>
* Purpose
* =======
* Perform parallel triangular solves
* U(k,:) := A(k,:) \ L(k,k).
* Only the process column that owns block column *k* participates
* in the work.
*
* Arguments
* =========
*
* m (input) int (global)
* Number of rows in the matrix.
*
* k (input) int (global)
* The row number of the block row to be factorized.
*
* Glu_persist (input) Glu_persist_t*
* Global data structures (xsup, supno) replicated on all processes.
*
* grid (input) gridinfo_t*
* The 2D process mesh.
*
* Llu (input/output) LocalLU_t*
* Local data structures to store distributed L and U matrices.
*
* stat (output) SuperLUStat_t*
* Record the statistics about the factorization;
* See SuperLUStat_t structure defined in util.h.
* </pre>
*/
static void pdgstrs2
/************************************************************************/
#ifdef _CRAY
(
int_t m, int_t k, Glu_persist_t *Glu_persist, gridinfo_t *grid,
LocalLU_t *Llu, SuperLUStat_t *stat, _fcd ftcs1, _fcd ftcs2, _fcd ftcs3
)
#else
(
int_t m, int_t k, Glu_persist_t *Glu_persist, gridinfo_t *grid,
LocalLU_t *Llu, SuperLUStat_t *stat
)
#endif
{
int iam, pkk;
int incx = 1;
int nsupr; /* number of rows in the block L(:,k) (LDA) */
int segsize;
int_t nsupc; /* number of columns in the block */
int_t luptr, iukp, rukp;
int_t b, gb, j, klst, knsupc, lk, nb;
int_t *xsup = Glu_persist->xsup;
int_t *usub;
double *lusup, *uval;
/* Quick return. */
lk = LBi( k, grid ); /* Local block number */
if ( !Llu->Unzval_br_ptr[lk] ) return;
/* Initialization. */
iam = grid->iam;
pkk = PNUM( PROW(k, grid), PCOL(k, grid), grid );
klst = FstBlockC( k+1 );
knsupc = SuperSize( k );
usub = Llu->Ufstnz_br_ptr[lk]; /* index[] of block row U(k,:) */
uval = Llu->Unzval_br_ptr[lk];
nb = usub[0];
iukp = BR_HEADER;
rukp = 0;
if ( iam == pkk ) {
lk = LBj( k, grid );
nsupr = Llu->Lrowind_bc_ptr[lk][1]; /* LDA of lusup[] */
lusup = Llu->Lnzval_bc_ptr[lk];
} else {
nsupr = Llu->Lsub_buf_2[k%2][1]; /* LDA of lusup[] */
lusup = Llu->Lval_buf_2[k%2];
}
/* Loop through all the row blocks. */
for (b = 0; b < nb; ++b) {
gb = usub[iukp];
nsupc = SuperSize( gb );
iukp += UB_DESCRIPTOR;
/* Loop through all the segments in the block. */
for (j = 0; j < nsupc; ++j) {
segsize = klst - usub[iukp++];
if ( segsize ) { /* Nonzero segment. */
luptr = (knsupc - segsize) * (nsupr + 1);
#ifdef _CRAY
STRSV(ftcs1, ftcs2, ftcs3, &segsize, &lusup[luptr], &nsupr,
&uval[rukp], &incx);
#else
dtrsv_("L", "N", "U", &segsize, &lusup[luptr], &nsupr,
&uval[rukp], &incx);
#endif
stat->ops[FACT] += segsize * (segsize + 1);
rukp += segsize;
}
}
} /* for b ... */
} /* PDGSTRS2 */
/*! \brief
*
* <pre>
* Purpose
* =======
* Factor diagonal and subdiagonal blocks and test for exact singularity.
* Only the process column that owns block column *k* participates
* in the work.
*
* Arguments
* =========
*
* k (input) int (global)
* The column number of the block column to be factorized.
*
* thresh (input) double (global)
* The threshold value = s_eps * anorm.
*
* Glu_persist (input) Glu_persist_t*
* Global data structures (xsup, supno) replicated on all processes.
*
* grid (input) gridinfo_t*
* The 2D process mesh.
*
* Llu (input/output) LocalLU_t*
* Local data structures to store distributed L and U matrices.
*
* stat (output) SuperLUStat_t*
* Record the statistics about the factorization.
* See SuperLUStat_t structure defined in util.h.
*
* info (output) int*
* = 0: successful exit
* < 0: if info = -i, the i-th argument had an illegal value
* > 0: if info = i, U(i,i) is exactly zero. The factorization has
* been completed, but the factor U is exactly singular,
* and division by zero will occur if it is used to solve a
* system of equations.
* </pre>
*/
static void pdgstrf2
/************************************************************************/
(
superlu_options_t *options,
int_t k, double thresh, Glu_persist_t *Glu_persist, gridinfo_t *grid,
LocalLU_t *Llu, SuperLUStat_t *stat, int* info
)
{
int c, iam, l, pkk;
int incx = 1, incy = 1;
int nsupr; /* number of rows in the block (LDA) */
int luptr;
int_t i, krow, j, jfst, jlst;
int_t nsupc; /* number of columns in the block */
int_t *xsup = Glu_persist->xsup;
double *lusup, temp;
double *ujrow;
double alpha = -1;
*info = 0;
/* Quick return. */
/* Initialization. */
iam = grid->iam;
krow = PROW( k, grid );
pkk = PNUM( PROW(k, grid), PCOL(k, grid), grid );
j = LBj( k, grid ); /* Local block number */
jfst = FstBlockC( k );
jlst = FstBlockC( k+1 );
lusup = Llu->Lnzval_bc_ptr[j];
nsupc = SuperSize( k );
if ( Llu->Lrowind_bc_ptr[j] ) nsupr = Llu->Lrowind_bc_ptr[j][1];
ujrow = Llu->ujrow;
luptr = 0; /* Point to the diagonal entries. */
c = nsupc;
for (j = 0; j < jlst - jfst; ++j) {
/* Broadcast the j-th row (nsupc - j) elements to
the process column. */
if ( iam == pkk ) { /* Diagonal process. */
i = luptr;
if ( options->ReplaceTinyPivot == YES || lusup[i] == 0.0 ) {
if ( fabs(lusup[i]) < thresh ) { /* Diagonal */
#if ( PRNTlevel>=2 )
printf("(%d) .. col %d, tiny pivot %e ",
iam, jfst+j, lusup[i]);
#endif
/* Keep the replaced diagonal with the same sign. */
if ( lusup[i] < 0 ) lusup[i] = -thresh;
else lusup[i] = thresh;
#if ( PRNTlevel>=2 )
printf("replaced by %e\n", lusup[i]);
#endif
++(stat->TinyPivots);
}
}
for (l = 0; l < c; ++l, i += nsupr) ujrow[l] = lusup[i];
}
#if 0
dbcast_col(ujrow, c, pkk, UjROW, grid, &c);
#else
MPI_Bcast(ujrow, c, MPI_DOUBLE, krow, (grid->cscp).comm);
/*bcast_tree(ujrow, c, MPI_DOUBLE, krow, (24*k+j)%NTAGS,
grid, COMM_COLUMN, &c);*/
#endif
#if ( DEBUGlevel>=2 )
if ( k == 3329 && j == 2 ) {
if ( iam == pkk ) {
printf("..(%d) k %d, j %d: Send ujrow[0] %e\n",iam,k,j,ujrow[0]);
} else {
printf("..(%d) k %d, j %d: Recv ujrow[0] %e\n",iam,k,j,ujrow[0]);
}
}
#endif
if ( !lusup ) { /* Empty block column. */
--c;
if ( ujrow[0] == 0.0 ) *info = j+jfst+1;
continue;
}
/* Test for singularity. */
if ( ujrow[0] == 0.0 ) {
*info = j+jfst+1;
} else {
/* Scale the j-th column of the matrix. */
temp = 1.0 / ujrow[0];
if ( iam == pkk ) {
for (i = luptr+1; i < luptr-j+nsupr; ++i) lusup[i] *= temp;
stat->ops[FACT] += nsupr-j-1;
} else {
for (i = luptr; i < luptr+nsupr; ++i) lusup[i] *= temp;
stat->ops[FACT] += nsupr;
}
}
/* Rank-1 update of the trailing submatrix. */
if ( --c ) {
if ( iam == pkk ) {
l = nsupr - j - 1;
#ifdef _CRAY
SGER(&l, &c, &alpha, &lusup[luptr+1], &incx,
&ujrow[1], &incy, &lusup[luptr+nsupr+1], &nsupr);
#else
dger_(&l, &c, &alpha, &lusup[luptr+1], &incx,
&ujrow[1], &incy, &lusup[luptr+nsupr+1], &nsupr);
#endif
stat->ops[FACT] += 2 * l * c;
} else {
#ifdef _CRAY
SGER(&nsupr, &c, &alpha, &lusup[luptr], &incx,
&ujrow[1], &incy, &lusup[luptr+nsupr], &nsupr);
#else
dger_(&nsupr, &c, &alpha, &lusup[luptr], &incx,
&ujrow[1], &incy, &lusup[luptr+nsupr], &nsupr);
#endif
stat->ops[FACT] += 2 * nsupr * c;
}
}
/* Move to the next column. */
if ( iam == pkk ) luptr += nsupr + 1;
else luptr += nsupr;
} /* for j ... */
} /* PDGSTRF2 */
int_t
pddistribute(fact_t fact, int_t n, SuperMatrix *A,
ScalePermstruct_t *ScalePermstruct,
Glu_freeable_t *Glu_freeable, LUstruct_t *LUstruct,
gridinfo_t *grid)
/*
* -- Distributed SuperLU routine (version 2.0) --
* Lawrence Berkeley National Lab, Univ. of California Berkeley.
* March 15, 2003
*
*
* Purpose
* =======
* Distribute the matrix onto the 2D process mesh.
*
* Arguments
* =========
*
* fact (input) fact_t
* Specifies whether or not the L and U structures will be re-used.
* = SamePattern_SameRowPerm: L and U structures are input, and
* unchanged on exit.
* = DOFACT or SamePattern: L and U structures are computed and output.
*
* n (input) int
* Dimension of the matrix.
*
* A (input) SuperMatrix*
* The distributed input matrix A of dimension (A->nrow, A->ncol).
* A may be overwritten by diag(R)*A*diag(C)*Pc^T.
* The type of A can be: Stype = NR; Dtype = SLU_D; Mtype = GE.
*
* ScalePermstruct (input) ScalePermstruct_t*
* The data structure to store the scaling and permutation vectors
* describing the transformations performed to the original matrix A.
*
* Glu_freeable (input) *Glu_freeable_t
* The global structure describing the graph of L and U.
*
* LUstruct (input) LUstruct_t*
* Data structures for L and U factors.
*
* grid (input) gridinfo_t*
* The 2D process mesh.
*
* Return value
* ============
* > 0, working storage required (in bytes).
*
*/
{
Glu_persist_t *Glu_persist = LUstruct->Glu_persist;
LocalLU_t *Llu = LUstruct->Llu;
int_t bnnz, fsupc, i, irow, istart, j, jb, jj, k, len, len1, nsupc;
int_t ljb; /* local block column number */
int_t nrbl; /* number of L blocks in current block column */
int_t nrbu; /* number of U blocks in current block column */
int_t gb; /* global block number; 0 < gb <= nsuper */
int_t lb; /* local block number; 0 < lb <= ceil(NSUPERS/Pr) */
int iam, jbrow, kcol, mycol, myrow, pc, pr;
int_t mybufmax[NBUFFERS];
#if 0
NCPformat *Astore;
#else /* XSL ==> */
NRformat_loc *Astore;
#endif
double *a;
int_t *asub, *xa;
#if 0
int_t *xa_begin, *xa_end;
#endif
int_t *xsup = Glu_persist->xsup; /* supernode and column mapping */
int_t *supno = Glu_persist->supno;
int_t *lsub, *xlsub, *usub, *xusub;
int_t nsupers;
int_t next_lind; /* next available position in index[*] */
int_t next_lval; /* next available position in nzval[*] */
int_t *index; /* indices consist of headers and row subscripts */
double *lusup, *uval; /* nonzero values in L and U */
double **Lnzval_bc_ptr; /* size ceil(NSUPERS/Pc) */
int_t **Lrowind_bc_ptr; /* size ceil(NSUPERS/Pc) */
double **Unzval_br_ptr; /* size ceil(NSUPERS/Pr) */
int_t **Ufstnz_br_ptr; /* size ceil(NSUPERS/Pr) */
/*-- Counts to be used in factorization. --*/
int_t *ToRecv, *ToSendD, **ToSendR;
/*-- Counts to be used in lower triangular solve. --*/
int_t *fmod; /* Modification count for L-solve. */
int_t **fsendx_plist; /* Column process list to send down Xk. */
int_t nfrecvx = 0; /* Number of Xk I will receive. */
int_t kseen;
/*-- Counts to be used in upper triangular solve. --*/
int_t *bmod; /* Modification count for U-solve. */
int_t **bsendx_plist; /* Column process list to send down Xk. */
int_t nbrecvx = 0; /* Number of Xk I will receive. */
int_t *ilsum; /* starting position of each supernode in
the full array (local) */
/*-- Auxiliary arrays; freed on return --*/
int_t *rb_marker; /* block hit marker; size ceil(NSUPERS/Pr) */
int_t *Urb_length; /* U block length; size ceil(NSUPERS/Pr) */
int_t *Urb_indptr; /* pointers to U index[]; size ceil(NSUPERS/Pr) */
int_t *Urb_fstnz; /* # of fstnz in a block row; size ceil(NSUPERS/Pr) */
int_t *Ucbs; /* number of column blocks in a block row */
int_t *Lrb_length; /* L block length; size ceil(NSUPERS/Pr) */
int_t *Lrb_number; /* global block number; size ceil(NSUPERS/Pr) */
int_t *Lrb_indptr; /* pointers to L index[]; size ceil(NSUPERS/Pr) */
int_t *Lrb_valptr; /* pointers to L nzval[]; size ceil(NSUPERS/Pr) */
double *dense, *dense_col; /* SPA */
double zero = 0.0;
int_t ldaspa; /* LDA of SPA */
int_t mem_use = 0, iword, dword;
#if ( PRNTlevel>=1 )
int_t nLblocks = 0, nUblocks = 0;
#endif
#if ( PROFlevel>=1 )
double t, t_u, t_l;
int_t u_blks;
#endif
/* Initialization. */
iam = grid->iam;
myrow = MYROW( iam, grid );
mycol = MYCOL( iam, grid );
for (i = 0; i < NBUFFERS; ++i) mybufmax[i] = 0;
nsupers = supno[n-1] + 1;
Astore = (NRformat_loc *) A->Store;
#if ( PRNTlevel>=1 )
iword = sizeof(int_t);
dword = sizeof(double);
#endif
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(iam, "Enter pddistribute()");
#endif
dReDistribute_A(A, ScalePermstruct, Glu_freeable, xsup, supno,
grid, &xa, &asub, &a);
if ( fact == SamePattern_SameRowPerm ) {
#if ( PROFlevel>=1 )
t_l = t_u = 0; u_blks = 0;
#endif
/* We can propagate the new values of A into the existing
L and U data structures. */
ilsum = Llu->ilsum;
ldaspa = Llu->ldalsum;
if ( !(dense = doubleCalloc_dist(ldaspa * sp_ienv_dist(3))) )
ABORT("Calloc fails for SPA dense[].");
nrbu = CEILING( nsupers, grid->nprow ); /* Number of local block rows */
if ( !(Urb_length = intCalloc_dist(nrbu)) )
ABORT("Calloc fails for Urb_length[].");
if ( !(Urb_indptr = intMalloc_dist(nrbu)) )
ABORT("Malloc fails for Urb_indptr[].");
for (lb = 0; lb < nrbu; ++lb)
Urb_indptr[lb] = BR_HEADER; /* Skip header in U index[]. */
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;
#if ( PRNTlevel>=1 )
mem_use += 2*nrbu*iword + ldaspa*sp_ienv_dist(3)*dword;
#endif
for (jb = 0; jb < nsupers; ++jb) { /* Loop through each block column */
pc = PCOL( jb, grid );
if ( mycol == pc ) { /* Block column jb in my process column */
fsupc = FstBlockC( jb );
nsupc = SuperSize( jb );
/* Scatter A into SPA. */
for (j = fsupc, dense_col = dense; j < FstBlockC(jb+1); ++j) {
for (i = xa[j]; i < xa[j+1]; ++i) {
irow = asub[i];
gb = BlockNum( irow );
if ( myrow == PROW( gb, grid ) ) {
lb = LBi( gb, grid );
irow = ilsum[lb] + irow - FstBlockC( gb );
dense_col[irow] = a[i];
}
}
dense_col += ldaspa;
}
#if ( PROFlevel>=1 )
t = SuperLU_timer_();
#endif
/* Gather the values of A from SPA into Unzval[]. */
for (lb = 0; lb < nrbu; ++lb) {
index = Ufstnz_br_ptr[lb];
if ( index && index[Urb_indptr[lb]] == jb ) {
uval = Unzval_br_ptr[lb];
len = Urb_indptr[lb] + UB_DESCRIPTOR;
gb = lb * grid->nprow + myrow;/* Global block number */
k = FstBlockC( gb+1 );
irow = ilsum[lb] - FstBlockC( gb );
for (jj = 0, dense_col = dense; jj < nsupc; ++jj) {
j = index[len+jj];
for (i = j; i < k; ++i) {
uval[Urb_length[lb]++] = dense_col[irow+i];
dense_col[irow+i] = zero;
}
dense_col += ldaspa;
}
Urb_indptr[lb] += UB_DESCRIPTOR + nsupc;
} /* if index != NULL */
} /* for lb ... */
#if ( PROFlevel>=1 )
t_u += SuperLU_timer_() - t;
t = SuperLU_timer_();
#endif
/* Gather the values of A from SPA into Lnzval[]. */
ljb = LBj( jb, grid ); /* Local block number */
index = Lrowind_bc_ptr[ljb];
if ( index ) {
nrbl = index[0]; /* Number of row blocks. */
len = index[1]; /* LDA of lusup[]. */
lusup = Lnzval_bc_ptr[ljb];
next_lind = BC_HEADER;
next_lval = 0;
for (jj = 0; jj < nrbl; ++jj) {
gb = index[next_lind++];
len1 = index[next_lind++]; /* Rows in the block. */
lb = LBi( gb, grid );
for (bnnz = 0; bnnz < len1; ++bnnz) {
irow = index[next_lind++]; /* Global index. */
irow = ilsum[lb] + irow - FstBlockC( gb );
k = next_lval++;
for (j = 0, dense_col = dense; j < nsupc; ++j) {
lusup[k] = dense_col[irow];
dense_col[irow] = zero;
k += len;
dense_col += ldaspa;
}
} /* for bnnz ... */
} /* for jj ... */
} /* if index ... */
#if ( PROFlevel>=1 )
t_l += SuperLU_timer_() - t;
#endif
} /* if mycol == pc */
} /* for jb ... */
SUPERLU_FREE(dense);
SUPERLU_FREE(Urb_length);
SUPERLU_FREE(Urb_indptr);
#if ( PROFlevel>=1 )
if ( !iam ) printf(".. 2nd distribute time: L %.2f\tU %.2f\tu_blks %d\tnrbu %d\n",
t_l, t_u, u_blks, nrbu);
#endif
} else {
/* ------------------------------------------------------------
FIRST TIME CREATING THE L AND U DATA STRUCTURES.
------------------------------------------------------------*/
#if ( PROFlevel>=1 )
t_l = t_u = 0; u_blks = 0;
#endif
/* We first need to set up the L and U data structures and then
* propagate the values of A into them.
*/
lsub = Glu_freeable->lsub; /* compressed L subscripts */
xlsub = Glu_freeable->xlsub;
usub = Glu_freeable->usub; /* compressed U subscripts */
xusub = Glu_freeable->xusub;
if ( !(ToRecv = intCalloc_dist(nsupers)) )
ABORT("Calloc fails for ToRecv[].");
k = CEILING( nsupers, grid->npcol );/* Number of local column blocks */
if ( !(ToSendR = (int_t **) SUPERLU_MALLOC(k*sizeof(int_t*))) )
ABORT("Malloc fails for ToSendR[].");
j = k * grid->npcol;
if ( !(index = intMalloc_dist(j)) )
ABORT("Malloc fails for index[].");
#if ( PRNTlevel>=1 )
mem_use = k*sizeof(int_t*) + (j + nsupers)*iword;
#endif
for (i = 0; i < j; ++i) index[i] = EMPTY;
for (i = 0,j = 0; i < k; ++i, j += grid->npcol) ToSendR[i] = &index[j];
k = CEILING( nsupers, grid->nprow ); /* Number of local block rows */
/* Pointers to the beginning of each block row of U. */
if ( !(Unzval_br_ptr =
(double**)SUPERLU_MALLOC(k * sizeof(double*))) )
ABORT("Malloc fails for Unzval_br_ptr[].");
if ( !(Ufstnz_br_ptr = (int_t**)SUPERLU_MALLOC(k * sizeof(int_t*))) )
ABORT("Malloc fails for Ufstnz_br_ptr[].");
if ( !(ToSendD = intCalloc_dist(k)) )
ABORT("Malloc fails for ToSendD[].");
if ( !(ilsum = intMalloc_dist(k+1)) )
ABORT("Malloc fails for ilsum[].");
/* Auxiliary arrays used to set up U block data structures.
They are freed on return. */
if ( !(rb_marker = intCalloc_dist(k)) )
ABORT("Calloc fails for rb_marker[].");
if ( !(Urb_length = intCalloc_dist(k)) )
ABORT("Calloc fails for Urb_length[].");
if ( !(Urb_indptr = intMalloc_dist(k)) )
ABORT("Malloc fails for Urb_indptr[].");
if ( !(Urb_fstnz = intCalloc_dist(k)) )
ABORT("Calloc fails for Urb_fstnz[].");
if ( !(Ucbs = intCalloc_dist(k)) )
ABORT("Calloc fails for Ucbs[].");
#if ( PRNTlevel>=1 )
mem_use = 2*k*sizeof(int_t*) + (7*k+1)*iword;
#endif
/* Compute ldaspa and ilsum[]. */
ldaspa = 0;
ilsum[0] = 0;
for (gb = 0; gb < nsupers; ++gb) {
if ( myrow == PROW( gb, grid ) ) {
i = SuperSize( gb );
ldaspa += i;
lb = LBi( gb, grid );
ilsum[lb + 1] = ilsum[lb] + i;
}
}
/* ------------------------------------------------------------
COUNT NUMBER OF ROW BLOCKS AND THE LENGTH OF EACH BLOCK IN U.
THIS ACCOUNTS FOR ONE-PASS PROCESSING OF G(U).
------------------------------------------------------------*/
/* Loop through each supernode column. */
for (jb = 0; jb < nsupers; ++jb) {
pc = PCOL( jb, grid );
fsupc = FstBlockC( jb );
nsupc = SuperSize( jb );
/* Loop through each column in the block. */
for (j = fsupc; j < fsupc + nsupc; ++j) {
/* usub[*] contains only "first nonzero" in each segment. */
for (i = xusub[j]; i < xusub[j+1]; ++i) {
irow = usub[i]; /* First nonzero of the segment. */
gb = BlockNum( irow );
kcol = PCOL( gb, grid );
ljb = LBj( gb, grid );
if ( mycol == kcol && mycol != pc ) ToSendR[ljb][pc] = YES;
pr = PROW( gb, grid );
lb = LBi( gb, grid );
if ( mycol == pc ) {
if ( myrow == pr ) {
ToSendD[lb] = YES;
/* Count nonzeros in entire block row. */
Urb_length[lb] += FstBlockC( gb+1 ) - irow;
if (rb_marker[lb] <= jb) {/* First see the block */
rb_marker[lb] = jb + 1;
Urb_fstnz[lb] += nsupc;
++Ucbs[lb]; /* Number of column blocks
in block row lb. */
#if ( PRNTlevel>=1 )
++nUblocks;
#endif
}
ToRecv[gb] = 1;
} else ToRecv[gb] = 2; /* Do I need 0, 1, 2 ? */
}
} /* for i ... */
} /* for j ... */
} /* for jb ... */
/* Set up the initial pointers for each block row in U. */
nrbu = CEILING( nsupers, grid->nprow );/* Number of local block rows */
for (lb = 0; lb < nrbu; ++lb) {
len = Urb_length[lb];
rb_marker[lb] = 0; /* Reset block marker. */
if ( len ) {
/* Add room for descriptors */
len1 = Urb_fstnz[lb] + BR_HEADER + Ucbs[lb] * UB_DESCRIPTOR;
if ( !(index = intMalloc_dist(len1+1)) )
ABORT("Malloc fails for Uindex[].");
Ufstnz_br_ptr[lb] = index;
if ( !(Unzval_br_ptr[lb] = doubleMalloc_dist(len)) )
ABORT("Malloc fails for Unzval_br_ptr[*][].");
mybufmax[2] = SUPERLU_MAX( mybufmax[2], len1 );
mybufmax[3] = SUPERLU_MAX( mybufmax[3], len );
index[0] = Ucbs[lb]; /* Number of column blocks */
index[1] = len; /* Total length of nzval[] */
index[2] = len1; /* Total length of index[] */
index[len1] = -1; /* End marker */
} else {
Ufstnz_br_ptr[lb] = NULL;
Unzval_br_ptr[lb] = NULL;
}
Urb_length[lb] = 0; /* Reset block length. */
Urb_indptr[lb] = BR_HEADER; /* Skip header in U index[]. */
} /* for lb ... */
SUPERLU_FREE(Urb_fstnz);
SUPERLU_FREE(Ucbs);
#if ( PRNTlevel>=1 )
mem_use -= 2*k * iword;
#endif
/* Auxiliary arrays used to set up L block data structures.
They are freed on return.
k is the number of local row blocks. */
if ( !(Lrb_length = intCalloc_dist(k)) )
ABORT("Calloc fails for Lrb_length[].");
if ( !(Lrb_number = intMalloc_dist(k)) )
ABORT("Malloc fails for Lrb_number[].");
if ( !(Lrb_indptr = intMalloc_dist(k)) )
ABORT("Malloc fails for Lrb_indptr[].");
if ( !(Lrb_valptr = intMalloc_dist(k)) )
ABORT("Malloc fails for Lrb_valptr[].");
if ( !(dense = doubleCalloc_dist(ldaspa * sp_ienv_dist(3))) )
ABORT("Calloc fails for SPA dense[].");
/* These counts will be used for triangular solves. */
if ( !(fmod = intCalloc_dist(k)) )
ABORT("Calloc fails for fmod[].");
if ( !(bmod = intCalloc_dist(k)) )
ABORT("Calloc fails for bmod[].");
/* ------------------------------------------------ */
#if ( PRNTlevel>=1 )
mem_use += 6*k*iword + ldaspa*sp_ienv_dist(3)*dword;
#endif
k = CEILING( nsupers, grid->npcol );/* Number of local block columns */
/* Pointers to the beginning of each block column of L. */
if ( !(Lnzval_bc_ptr =
(double**)SUPERLU_MALLOC(k * sizeof(double*))) )
ABORT("Malloc fails for Lnzval_bc_ptr[].");
if ( !(Lrowind_bc_ptr = (int_t**)SUPERLU_MALLOC(k * sizeof(int_t*))) )
ABORT("Malloc fails for Lrowind_bc_ptr[].");
Lrowind_bc_ptr[k-1] = NULL;
/* These lists of processes will be used for triangular solves. */
if ( !(fsendx_plist = (int_t **) SUPERLU_MALLOC(k*sizeof(int_t*))) )
ABORT("Malloc fails for fsendx_plist[].");
len = k * grid->nprow;
if ( !(index = intMalloc_dist(len)) )
ABORT("Malloc fails for fsendx_plist[0]");
for (i = 0; i < len; ++i) index[i] = EMPTY;
for (i = 0, j = 0; i < k; ++i, j += grid->nprow)
fsendx_plist[i] = &index[j];
if ( !(bsendx_plist = (int_t **) SUPERLU_MALLOC(k*sizeof(int_t*))) )
ABORT("Malloc fails for bsendx_plist[].");
if ( !(index = intMalloc_dist(len)) )
ABORT("Malloc fails for bsendx_plist[0]");
for (i = 0; i < len; ++i) index[i] = EMPTY;
for (i = 0, j = 0; i < k; ++i, j += grid->nprow)
bsendx_plist[i] = &index[j];
/* -------------------------------------------------------------- */
#if ( PRNTlevel>=1 )
mem_use += 4*k*sizeof(int_t*) + 2*len*iword;
#endif
/*------------------------------------------------------------
PROPAGATE ROW SUBSCRIPTS AND VALUES OF A INTO L AND U BLOCKS.
THIS ACCOUNTS FOR ONE-PASS PROCESSING OF A, L AND U.
------------------------------------------------------------*/
for (jb = 0; jb < nsupers; ++jb) {
pc = PCOL( jb, grid );
if ( mycol == pc ) { /* Block column jb in my process column */
fsupc = FstBlockC( jb );
nsupc = SuperSize( jb );
ljb = LBj( jb, grid ); /* Local block number */
/* Scatter A into SPA. */
for (j = fsupc, dense_col = dense; j < FstBlockC(jb+1); ++j) {
for (i = xa[j]; i < xa[j+1]; ++i) {
irow = asub[i];
gb = BlockNum( irow );
if ( myrow == PROW( gb, grid ) ) {
lb = LBi( gb, grid );
irow = ilsum[lb] + irow - FstBlockC( gb );
dense_col[irow] = a[i];
}
}
dense_col += ldaspa;
}
jbrow = PROW( jb, grid );
#if ( PROFlevel>=1 )
t = SuperLU_timer_();
#endif
/*------------------------------------------------
* SET UP U BLOCKS.
*------------------------------------------------*/
kseen = 0;
/* Loop through each column in the block column. */
for (j = fsupc; j < FstBlockC( jb+1 ); ++j) {
istart = xusub[j];
for (i = istart; i < xusub[j+1]; ++i) {
irow = usub[i]; /* First nonzero in the segment. */
gb = BlockNum( irow );
pr = PROW( gb, grid );
if ( pr != jbrow )
bsendx_plist[ljb][pr] = YES;
if ( myrow == pr ) {
lb = LBi( gb, grid ); /* Local block number */
index = Ufstnz_br_ptr[lb];
if (rb_marker[lb] <= jb) {/* First see the block */
rb_marker[lb] = jb + 1;
index[Urb_indptr[lb]] = jb; /* Descriptor */
Urb_indptr[lb] += UB_DESCRIPTOR;
len = Urb_indptr[lb];
for (k = 0; k < nsupc; ++k)
index[len+k] = FstBlockC( gb+1 );
if ( gb != jb )/* Exclude diagonal block. */
++bmod[lb];/* Mod. count for back solve */
if ( kseen == 0 && myrow != jbrow ) {
++nbrecvx;
kseen = 1;
}
} else {
len = Urb_indptr[lb];/* Start fstnz in index */
}
jj = j - fsupc;
index[len+jj] = irow;
} /* if myrow == pr ... */
} /* for i ... */
} /* for j ... */
/* Figure out how many nonzeros in each block, and gather
the initial values of A from SPA into Uval. */
for (lb = 0; lb < nrbu; ++lb) {
if ( rb_marker[lb] == jb + 1 ) { /* Not an empty block. */
index = Ufstnz_br_ptr[lb];
uval = Unzval_br_ptr[lb];
len = Urb_indptr[lb];
gb = lb * grid->nprow + myrow;/* Global block number */
k = FstBlockC( gb+1 );
irow = ilsum[lb] - FstBlockC( gb );
for (jj=0, bnnz=0, dense_col=dense; jj < nsupc; ++jj) {
j = index[len+jj]; /* First nonzero in segment. */
bnnz += k - j;
for (i = j; i < k; ++i) {
uval[Urb_length[lb]++] = dense_col[irow + i];
dense_col[irow + i] = zero;
}
dense_col += ldaspa;
}
index[len-1] = bnnz; /* Set block length in Descriptor */
Urb_indptr[lb] += nsupc;
}
} /* for lb ... */
#if ( PROFlevel>=1 )
t_u += SuperLU_timer_() - t;
t = SuperLU_timer_();
#endif
/*------------------------------------------------
* SET UP L BLOCKS.
*------------------------------------------------*/
/* Count number of blocks and length of each block. */
nrbl = 0;
len = 0; /* Number of row subscripts I own. */
kseen = 0;
istart = xlsub[fsupc];
for (i = istart; i < xlsub[fsupc+1]; ++i) {
irow = lsub[i];
gb = BlockNum( irow ); /* Global block number */
pr = PROW( gb, grid ); /* Process row owning this block */
if ( pr != jbrow )
fsendx_plist[ljb][pr] = YES;
if ( myrow == pr ) {
lb = LBi( gb, grid ); /* Local block number */
if (rb_marker[lb] <= jb) { /* First see this block */
rb_marker[lb] = jb + 1;
Lrb_length[lb] = 1;
Lrb_number[nrbl++] = gb;
if ( gb != jb ) /* Exclude diagonal block. */
++fmod[lb]; /* Mod. count for forward solve */
if ( kseen == 0 && myrow != jbrow ) {
++nfrecvx;
kseen = 1;
}
#if ( PRNTlevel>=1 )
++nLblocks;
#endif
} else {
++Lrb_length[lb];
}
++len;
}
} /* for i ... */
if ( nrbl ) { /* Do not ensure the blocks are sorted! */
/* Set up the initial pointers for each block in
index[] and nzval[]. */
/* Add room for descriptors */
len1 = len + BC_HEADER + nrbl * LB_DESCRIPTOR;
if ( !(index = intMalloc_dist(len1)) )
ABORT("Malloc fails for index[]");
Lrowind_bc_ptr[ljb] = index;
if (!(Lnzval_bc_ptr[ljb] =
doubleMalloc_dist(len*nsupc))) {
fprintf(stderr, "col block %d ", jb);
ABORT("Malloc fails for Lnzval_bc_ptr[*][]");
}
mybufmax[0] = SUPERLU_MAX( mybufmax[0], len1 );
mybufmax[1] = SUPERLU_MAX( mybufmax[1], len*nsupc );
mybufmax[4] = SUPERLU_MAX( mybufmax[4], len );
index[0] = nrbl; /* Number of row blocks */
index[1] = len; /* LDA of the nzval[] */
next_lind = BC_HEADER;
next_lval = 0;
for (k = 0; k < nrbl; ++k) {
gb = Lrb_number[k];
lb = LBi( gb, grid );
len = Lrb_length[lb];
Lrb_length[lb] = 0; /* Reset vector of block length */
index[next_lind++] = gb; /* Descriptor */
index[next_lind++] = len;
Lrb_indptr[lb] = next_lind;
Lrb_valptr[lb] = next_lval;
next_lind += len;
next_lval += len;
}
/* Propagate the compressed row subscripts to Lindex[],
and the initial values of A from SPA into Lnzval[]. */
lusup = Lnzval_bc_ptr[ljb];
len = index[1]; /* LDA of lusup[] */
for (i = istart; i < xlsub[fsupc+1]; ++i) {
irow = lsub[i];
gb = BlockNum( irow );
if ( myrow == PROW( gb, grid ) ) {
lb = LBi( gb, grid );
k = Lrb_indptr[lb]++; /* Random access a block */
index[k] = irow;
k = Lrb_valptr[lb]++;
irow = ilsum[lb] + irow - FstBlockC( gb );
for (j = 0, dense_col = dense; j < nsupc; ++j) {
lusup[k] = dense_col[irow];
dense_col[irow] = zero;
k += len;
dense_col += ldaspa;
}
}
} /* for i ... */
} else {
Lrowind_bc_ptr[ljb] = NULL;
Lnzval_bc_ptr[ljb] = NULL;
} /* if nrbl ... */
#if ( PROFlevel>=1 )
t_l += SuperLU_timer_() - t;
#endif
} /* if mycol == pc */
} /* for jb ... */
Llu->Lrowind_bc_ptr = Lrowind_bc_ptr;
Llu->Lnzval_bc_ptr = Lnzval_bc_ptr;
Llu->Ufstnz_br_ptr = Ufstnz_br_ptr;
Llu->Unzval_br_ptr = Unzval_br_ptr;
Llu->ToRecv = ToRecv;
Llu->ToSendD = ToSendD;
Llu->ToSendR = ToSendR;
Llu->fmod = fmod;
Llu->fsendx_plist = fsendx_plist;
Llu->nfrecvx = nfrecvx;
Llu->bmod = bmod;
Llu->bsendx_plist = bsendx_plist;
Llu->nbrecvx = nbrecvx;
Llu->ilsum = ilsum;
Llu->ldalsum = ldaspa;
#if ( PRNTlevel>=1 )
if ( !iam ) printf(".. # L blocks %d\t# U blocks %d\n",
nLblocks, nUblocks);
#endif
SUPERLU_FREE(rb_marker);
SUPERLU_FREE(Urb_length);
SUPERLU_FREE(Urb_indptr);
SUPERLU_FREE(Lrb_length);
SUPERLU_FREE(Lrb_number);
SUPERLU_FREE(Lrb_indptr);
SUPERLU_FREE(Lrb_valptr);
SUPERLU_FREE(dense);
/* Find the maximum buffer size. */
MPI_Allreduce(mybufmax, Llu->bufmax, NBUFFERS, mpi_int_t,
MPI_MAX, grid->comm);
#if ( PROFlevel>=1 )
if ( !iam ) printf(".. 1st distribute time: L %.2f\tU %.2f\tu_blks %d\tnrbu %d\n",
t_l, t_u, u_blks, nrbu);
#endif
} /* else fact != SamePattern_SameRowPerm */
SUPERLU_FREE(xa);
SUPERLU_FREE(asub);
SUPERLU_FREE(a);
#if ( DEBUGlevel>=1 )
/* Memory allocated but not freed:
ilsum, fmod, fsendx_plist, bmod, bsendx_plist */
CHECK_MALLOC(iam, "Exit pddistribute()");
#endif
return (mem_use);
} /* PDDISTRIBUTE */
int_t pdgstrf
/************************************************************************/
(
superlu_options_t *options, int m, int n, double anorm,
LUstruct_t *LUstruct, gridinfo_t *grid, SuperLUStat_t *stat, int *info
)
/*
* Purpose
* =======
*
* PDGSTRF performs the LU factorization in parallel.
*
* Arguments
* =========
*
* options (input) superlu_options_t*
* 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_ddefs.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_ddefs.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
double alpha = 1.0, beta = 0.0;
int_t *xsup;
int_t *lsub, *lsub1, *usub, *Usub_buf,
*Lsub_buf_2[2]; /* Need 2 buffers to implement Irecv. */
double *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;
double **Unzval_br_ptr, **Lnzval_bc_ptr;
int_t *index;
double *nzval;
int_t *iuip, *ruip;/* Pointers to U index/nzval; size ceil(NSUPERS/Pr). */
double *ucol;
int_t *indirect;
double *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;
float s_eps;
double thresh;
double *tempU2d, *tempu;
int full, ldt, ldu, lead_zero, ncols;
MPI_Request recv_req[4], *send_req, *U_diag_blk_send_req = NULL;
MPI_Status status;
#if ( DEBUGlevel>=2 )
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), dword = sizeof(double);
#endif
/* Test the input parameters. */
*info = 0;
if ( m < 0 ) *info = -2;
else if ( n < 0 ) *info = -3;
if ( *info ) {
pxerbla("pdgstrf", grid, -*info);
return (-1);
}
/* Quick return if possible. */
if ( m == 0 || n == 0 ) return 0;
/*
* 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;
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(iam, "Enter pdgstrf()");
#endif
stat->ops[FACT] = 0.0;
if ( Pr*Pc > 1 ) {
i = Llu->bufmax[0];
if ( !(Llu->Lsub_buf_2[0] = intMalloc_dist(2 * ((size_t)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] = doubleMalloc_dist(2 * ((size_t)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 = doubleMalloc_dist(Llu->bufmax[3])) )
ABORT("Malloc fails for Uval_buf[].");
if ( !(U_diag_blk_send_req =
(MPI_Request *) SUPERLU_MALLOC(Pr*sizeof(MPI_Request))))
ABORT("Malloc fails for U_diag_blk_send_req[].");
U_diag_blk_send_req[myrow] = 0; /* flag no outstanding Isend */
if ( !(send_req =
(MPI_Request *) SUPERLU_MALLOC(2*Pc*sizeof(MPI_Request))))
ABORT("Malloc fails for send_req[].");
}
k = sp_ienv_dist(3); /* max supernode size */
if ( !(Llu->ujrow = doubleMalloc_dist(k*(k+1)/2)) )
ABORT("Malloc fails for ujrow[].");
#if ( PRNTlevel>=1 )
if ( !iam ) {
printf(".. thresh = s_eps %e * anorm %e = %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 = doubleCalloc_dist(2*((size_t)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[].");
#if ( VAMPIR>=1 )
VT_symdef(1, "Send-L", "Comm");
VT_symdef(2, "Recv-L", "Comm");
VT_symdef(3, "Send-U", "Comm");
VT_symdef(4, "Recv-U", "Comm");
VT_symdef(5, "TRF2", "Factor");
VT_symdef(100, "Factor", "Factor");
VT_begin(100);
VT_traceon();
#endif
/* ---------------------------------------------------------------
Handle the first block column separately to start the pipeline.
--------------------------------------------------------------- */
if ( mycol == 0 ) {
#if ( VAMPIR>=1 )
VT_begin(5);
#endif
pdgstrf2(options, 0, thresh, Glu_persist, grid, Llu,
U_diag_blk_send_req, stat, info);
#if ( VAMPIR>=1 )
VT_end(5);
#endif
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
#if ( VAMPIR>=1 )
VT_begin(1);
#endif
MPI_Isend( lsub, msgcnt[0], mpi_int_t, pj, 0, scp->comm,
&send_req[pj] );
MPI_Isend( lusup, msgcnt[1], MPI_DOUBLE, 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 ( VAMPIR>=1 )
VT_end(1);
#endif
#if ( PROFlevel>=1 )
TOC(t2, t1);
stat->utime[COMM] += t2;
msg_cnt += 2;
msg_vol += msgcnt[0]*iword + msgcnt[1]*dword;
#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], MPI_DOUBLE, 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
#if ( VAMPIR>=1 )
VT_begin(2);
#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], MPI_DOUBLE, kcol,
(4*k+1)%NTAGS, scp->comm, &status );*/
MPI_Wait( &recv_req[1], &status );
MPI_Get_count( &status, MPI_DOUBLE, &msgcnt[1] );
#if ( VAMPIR>=1 )
VT_end(2);
#endif
#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);
fflush(stdout);
#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
pdgstrs2(n, k, Glu_persist, grid, Llu, stat, ftcs1, ftcs2, ftcs3);
#else
pdgstrs2(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
#if ( VAMPIR>=1 )
VT_begin(3);
#endif
MPI_Send( usub, msgcnt[2], mpi_int_t, pi,
(4*k+2)%NTAGS, scp->comm);
MPI_Send( uval, msgcnt[3], MPI_DOUBLE, pi,
(4*k+3)%NTAGS, scp->comm);
#if ( VAMPIR>=1 )
VT_end(3);
#endif
#if ( PROFlevel>=1 )
TOC(t2, t1);
stat->utime[COMM] += t2;
msg_cnt += 2;
msg_vol += msgcnt[2]*iword + msgcnt[3]*dword;
#endif
#if ( DEBUGlevel>=2 )
printf("(%d) Send U(%4d,:) to Pr %2d\n", iam, k, pi);
#endif
} /* if pi ... */
} /* for pi ... */
} /* if ToSendD ... */
} else { /* myrow != krow */
if ( ToRecv[k] == 2 ) { /* Recv block row U(k,:). */
#if ( PROFlevel>=1 )
TIC(t1);
#endif
#if ( VAMPIR>=1 )
VT_begin(4);
#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, MPI_DOUBLE, scp->comm,
Llu->bufmax[3]);*/
MPI_Recv( Uval_buf, Llu->bufmax[3], MPI_DOUBLE, krow,
(4*k+3)%NTAGS, scp->comm, &status );
MPI_Get_count( &status, MPI_DOUBLE, &msgcnt[3] );
#if ( VAMPIR>=1 )
VT_end(4);
#endif
#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>=3 )
++num_update;
#endif
if ( full ) {
tempu = &uval[rukp];
} else { /* Copy block U(k,j) into tempU2d. */
#if ( DEBUGlevel>=3 )
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] = 0.0;
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
SGEMM(ftcs, ftcs, &nbrow, &ncols, &ldu, &alpha,
&lusup[luptr+(knsupc-ldu)*nsupr], &nsupr,
tempu, &ldu, &beta, tempv, &ldt);
#elif defined (USE_VENDOR_BLAS)
dgemm_("N", "N", &nbrow, &ncols, &ldu, &alpha,
&lusup[luptr+(knsupc-ldu)*nsupr], &nsupr,
tempu, &ldu, &beta, tempv, &ldt, 1, 1);
#else
dgemm_("N", "N", &nbrow, &ncols, &ldu, &alpha,
&lusup[luptr+(knsupc-ldu)*nsupr], &nsupr,
tempu, &ldu, &beta, tempv, &ldt);
#endif
stat->ops[FACT] += 2 * 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;
ucol[rel] -= tempv[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;
nzval[indirect[rel]] -= tempv[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 ) {
#if ( VAMPIR>=1 )
VT_begin(5);
#endif
/* Factor diagonal and subdiagonal blocks and test for exact
singularity. */
pdgstrf2(options, k+1, thresh, Glu_persist, grid, Llu,
U_diag_blk_send_req, stat, info);
#if ( VAMPIR>=1 )
VT_end(5);
#endif
/* 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
#if ( VAMPIR>=1 )
VT_begin(1);
#endif
MPI_Isend( lsub1, msgcnt[0], mpi_int_t, pj,
(4*(k+1))%NTAGS, scp->comm, &send_req[pj] );
MPI_Isend( lusup1, msgcnt[1], MPI_DOUBLE, pj,
(4*(k+1)+1)%NTAGS, scp->comm, &send_req[pj+Pc] );
#if ( VAMPIR>=1 )
VT_end(1);
#endif
#if ( PROFlevel>=1 )
TOC(t2, t1);
stat->utime[COMM] += t2;
msg_cnt += 2;
msg_vol += msgcnt[0]*iword + msgcnt[1]*dword;
#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], MPI_DOUBLE, kcol,
(4*(k+1)+1)%NTAGS, scp->comm, &recv_req[1]);
#if ( DEBUGlevel>=2 )
printf("(%d) Post Irecv L(:,%4d)\n", iam, k+1);
#endif
}
} /* 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>=3 )
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>=3 )
++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] = 0.0;
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
SGEMM(ftcs, ftcs, &nbrow, &ncols, &ldu, &alpha,
&lusup[luptr+(knsupc-ldu)*nsupr], &nsupr,
tempu, &ldu, &beta, tempv, &ldt);
#elif defined (USE_VENDOR_BLAS)
dgemm_("N", "N", &nbrow, &ncols, &ldu, &alpha,
&lusup[luptr+(knsupc-ldu)*nsupr], &nsupr,
tempu, &ldu, &beta, tempv, &ldt, 1, 1);
#else
dgemm_("N", "N", &nbrow, &ncols, &ldu, &alpha,
&lusup[luptr+(knsupc-ldu)*nsupr], &nsupr,
tempu, &ldu, &beta, tempv, &ldt);
#endif
stat->ops[FACT] += 2 * 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]];
}
/* Skip descriptor. Now point to fstnz index of
block U(i,j). */
iuip[lib] += UB_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 ; i < nbrow; ++i) {
rel = lsub[lptr + i] - fnz;
ucol[rel] -= tempv[i];
}
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 for the L blocks.
*/
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 (i = 0; i < nbrow; ++i) {
rel = lsub[lptr + i] - fnz;
nzval[indirect[rel]] -= tempv[i];
}
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 ( VAMPIR>=1 )
VT_end(100);
VT_traceoff();
#endif
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);
if ( U_diag_blk_send_req[myrow] ) {
/* wait for last Isend requests to complete, deallocate objects */
for (krow = 0; krow < Pr; ++krow)
if ( krow != myrow )
MPI_Wait(U_diag_blk_send_req + krow, &status);
}
SUPERLU_FREE(U_diag_blk_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("\tPDGSTRF 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 ( DEBUGlevel>=2 )
for (i = 0; i < Pr * Pc; ++i) {
if ( iam == i ) {
dPrintLblocks(iam, nsupers, grid, Glu_persist, Llu);
dPrintUblocks(iam, nsupers, grid, Glu_persist, Llu);
printf("(%d)\n", iam);
PrintInt10("Recv", nsupers, Llu->ToRecv);
}
MPI_Barrier( grid->comm );
}
#endif
#if ( DEBUGlevel>=3 )
printf("(%d) num_copy=%d, num_update=%d\n", iam, num_copy, num_update);
#endif
#if ( DEBUGlevel>=1 )
CHECK_MALLOC(iam, "Exit pdgstrf()");
#endif
} /* PDGSTRF */
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 */
static void pdgstrs2
/************************************************************************/
#ifdef _CRAY
(
int_t m, int_t k, Glu_persist_t *Glu_persist, gridinfo_t *grid,
LocalLU_t *Llu, SuperLUStat_t *stat, _fcd ftcs1, _fcd ftcs2, _fcd ftcs3
)
#else
(
int_t m, int_t k, Glu_persist_t *Glu_persist, gridinfo_t *grid,
LocalLU_t *Llu, SuperLUStat_t *stat
)
#endif
/*
* Purpose
* =======
* Perform parallel triangular solves
* U(k,:) := A(k,:) \ L(k,k).
* Only the process row that owns block row *k* participates
* in the work.
*
* Arguments
* =========
*
* m (input) int (global)
* Number of rows in the matrix.
*
* k (input) int (global)
* The row number of the block row to be factorized.
*
* Glu_persist (input) Glu_persist_t*
* Global data structures (xsup, supno) replicated on all processes.
*
* grid (input) gridinfo_t*
* The 2D process mesh.
*
* Llu (input/output) LocalLU_t*
* Local data structures to store distributed L and U matrices.
*
* stat (output) SuperLUStat_t*
* Record the statistics about the factorization;
* See SuperLUStat_t structure defined in util.h.
*
*/
{
int iam, pkk;
int incx = 1;
int nsupr; /* number of rows in the block L(:,k) (LDA) */
int segsize;
int_t nsupc; /* number of columns in the block */
int_t luptr, iukp, rukp;
int_t b, gb, j, klst, knsupc, lk, nb;
int_t *xsup = Glu_persist->xsup;
int_t *usub;
double *lusup, *uval;
/* Quick return. */
lk = LBi( k, grid ); /* Local block number */
if ( !Llu->Unzval_br_ptr[lk] ) return;
/* Initialization. */
iam = grid->iam;
pkk = PNUM( PROW(k, grid), PCOL(k, grid), grid );
klst = FstBlockC( k+1 );
knsupc = SuperSize( k );
usub = Llu->Ufstnz_br_ptr[lk]; /* index[] of block row U(k,:) */
uval = Llu->Unzval_br_ptr[lk];
nb = usub[0];
iukp = BR_HEADER;
rukp = 0;
if ( iam == pkk ) {
lk = LBj( k, grid );
nsupr = Llu->Lrowind_bc_ptr[lk][1]; /* LDA of lusup[] */
lusup = Llu->Lnzval_bc_ptr[lk];
} else {
nsupr = Llu->Lsub_buf_2[k%2][1]; /* LDA of lusup[] */
lusup = Llu->Lval_buf_2[k%2];
}
/* Loop through all the row blocks. */
for (b = 0; b < nb; ++b) {
gb = usub[iukp];
nsupc = SuperSize( gb );
iukp += UB_DESCRIPTOR;
/* Loop through all the segments in the block. */
for (j = 0; j < nsupc; ++j) {
segsize = klst - usub[iukp++];
if ( segsize ) { /* Nonzero segment. */
luptr = (knsupc - segsize) * (nsupr + 1);
#ifdef _CRAY
STRSV(ftcs1, ftcs2, ftcs3, &segsize, &lusup[luptr], &nsupr,
&uval[rukp], &incx);
#elif defined (USE_VENDOR_BLAS)
dtrsv_("L", "N", "U", &segsize, &lusup[luptr], &nsupr,
&uval[rukp], &incx, 1, 1, 1);
#else
dtrsv_("L", "N", "U", &segsize, &lusup[luptr], &nsupr,
&uval[rukp], &incx);
#endif
stat->ops[FACT] += segsize * (segsize + 1);
rukp += segsize;
}
}
} /* for b ... */
} /* PDGSTRS2 */
/*! \brief
*
* <pre>
* Purpose
* =======
* Panel factorization -- block column k
*
* Factor diagonal and subdiagonal blocks and test for exact singularity.
* Only the column processes that own block column *k* participate
* in the work.
*
* Arguments
* =========
*
* k (input) int (global)
* The column number of the block column to be factorized.
*
* thresh (input) double (global)
* The threshold value = s_eps * anorm.
*
* Glu_persist (input) Glu_persist_t*
* Global data structures (xsup, supno) replicated on all processes.
*
* grid (input) gridinfo_t*
* The 2D process mesh.
*
* Llu (input/output) LocalLU_t*
* Local data structures to store distributed L and U matrices.
*
* U_diag_blk_send_req (input/output) MPI_Request*
* List of send requests to send down the diagonal block of U.
*
* stat (output) SuperLUStat_t*
* Record the statistics about the factorization.
* See SuperLUStat_t structure defined in util.h.
*
* info (output) int*
* = 0: successful exit
* < 0: if info = -i, the i-th argument had an illegal value
* > 0: if info = i, U(i,i) is exactly zero. The factorization has
* been completed, but the factor U is exactly singular,
* and division by zero will occur if it is used to solve a
* system of equations.
* </pre>
*/
static void pdgstrf2
(
superlu_options_t *options,
int_t k, double thresh, Glu_persist_t *Glu_persist, gridinfo_t *grid,
LocalLU_t *Llu, MPI_Request *U_diag_blk_send_req,
SuperLUStat_t *stat, int* info
)
{
int cols_left, iam, l, pkk, pr;
int incx = 1, incy = 1;
int nsupr; /* number of rows in the block (LDA) */
int luptr;
int_t i, krow, j, jfst, jlst, u_diag_cnt;
int_t nsupc; /* number of columns in the block */
int_t *xsup = Glu_persist->xsup;
double *lusup, temp;
double *ujrow, *ublk_ptr; /* pointer to the U block */
double alpha = -1, zero = 0.0;
int_t Pr;
MPI_Status status;
MPI_Comm comm = (grid->cscp).comm;
/* Quick return. */
*info = 0;
/* Initialization. */
iam = grid->iam;
Pr = grid->nprow;
krow = PROW( k, grid );
pkk = PNUM( PROW(k, grid), PCOL(k, grid), grid );
j = LBj( k, grid ); /* Local block number */
jfst = FstBlockC( k );
jlst = FstBlockC( k+1 );
lusup = Llu->Lnzval_bc_ptr[j];
nsupc = SuperSize( k );
if ( Llu->Lrowind_bc_ptr[j] ) nsupr = Llu->Lrowind_bc_ptr[j][1];
ublk_ptr = ujrow = Llu->ujrow;
luptr = 0; /* Point to the diagonal entries. */
cols_left = nsupc; /* supernode size */
u_diag_cnt = 0;
if ( iam == pkk ) { /* diagonal process */
if ( U_diag_blk_send_req && U_diag_blk_send_req[krow] ) {
/* There are pending sends - wait for all Isend to complete */
for (pr = 0; pr < Pr; ++pr)
if (pr != krow)
MPI_Wait(U_diag_blk_send_req + pr, &status);
}
for (j = 0; j < jlst - jfst; ++j) { /* for each column in panel */
/* Diagonal pivot */
i = luptr;
if ( options->ReplaceTinyPivot == YES || lusup[i] == 0.0 ) {
if ( fabs(lusup[i]) < thresh ) { /* Diagonal */
#if ( PRNTlevel>=2 )
printf("(%d) .. col %d, tiny pivot %e ",
iam, jfst+j, lusup[i]);
#endif
/* Keep the new diagonal entry with the same sign. */
if ( lusup[i] < 0 ) lusup[i] = -thresh;
else lusup[i] = thresh;
#if ( PRNTlevel>=2 )
printf("replaced by %e\n", lusup[i]);
#endif
++(stat->TinyPivots);
}
}
for (l = 0; l < cols_left; ++l, i += nsupr, ++u_diag_cnt)
ublk_ptr[u_diag_cnt] = lusup[i]; /* copy one row of U */
if ( ujrow[0] == zero ) { /* Test for singularity. */
*info = j+jfst+1;
} else { /* Scale the j-th column. */
temp = 1.0 / ujrow[0];
for (i = luptr+1; i < luptr-j+nsupr; ++i) lusup[i] *= temp;
stat->ops[FACT] += nsupr-j-1;
}
/* Rank-1 update of the trailing submatrix. */
if ( --cols_left ) {
l = nsupr - j - 1;
#ifdef _CRAY
SGER(&l, &cols_left, &alpha, &lusup[luptr+1], &incx,
&ujrow[1], &incy, &lusup[luptr+nsupr+1], &nsupr);
#else
dger_(&l, &cols_left, &alpha, &lusup[luptr+1], &incx,
&ujrow[1], &incy, &lusup[luptr+nsupr+1], &nsupr);
#endif
stat->ops[FACT] += 2 * l * cols_left;
}
ujrow = ublk_ptr + u_diag_cnt; /* move to next row of U */
luptr += nsupr + 1; /* move to next column */
} /* for column j ... */
if ( U_diag_blk_send_req && iam == pkk ) { /* Send the U block */
/** ALWAYS SEND TO ALL OTHERS - TO FIX **/
for (pr = 0; pr < Pr; ++pr)
if (pr != krow)
MPI_Isend(ublk_ptr, u_diag_cnt, MPI_DOUBLE, pr,
((k<<2)+2)%NTAGS, comm, U_diag_blk_send_req + pr);
U_diag_blk_send_req[krow] = 1; /* flag outstanding Isend */
}
} else { /* non-diagonal process */
/* Receive the diagonal block of U */
MPI_Recv(ublk_ptr, (nsupc*(nsupc+1))>>1, MPI_DOUBLE,
krow, ((k<<2)+2)%NTAGS, comm, &status);
for (j = 0; j < jlst - jfst; ++j) { /* for each column in panel */
u_diag_cnt += cols_left;
if ( !lusup ) { /* empty block column */
--cols_left;
if ( ujrow[0] == zero ) *info = j+jfst+1;
continue;
}
/* Test for singularity. */
if ( ujrow[0] == zero ) {
*info = j+jfst+1;
} else {
/* Scale the j-th column. */
temp = 1.0 / ujrow[0];
for (i = luptr; i < luptr+nsupr; ++i) lusup[i] *= temp;
stat->ops[FACT] += nsupr;
}
/* Rank-1 update of the trailing submatrix. */
if ( --cols_left ) {
#ifdef _CRAY
SGER(&nsupr, &cols_left, &alpha, &lusup[luptr], &incx,
&ujrow[1], &incy, &lusup[luptr+nsupr], &nsupr);
#else
dger_(&nsupr, &cols_left, &alpha, &lusup[luptr], &incx,
&ujrow[1], &incy, &lusup[luptr+nsupr], &nsupr);
#endif
stat->ops[FACT] += 2 * nsupr * cols_left;
}
ujrow = ublk_ptr + u_diag_cnt; /* move to next row of U */
luptr += nsupr; /* move to next column */
} /* for column j ... */
} /* end if pkk ... */
} /* PDGSTRF2 */
