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 main(int argc, char **argv) {
double sum_total_timer, total_timer = 0.0;
double sum_gather_timer, gather_timer = 0.0;
double sum_mpi_timer, mpi_timer = 0.0;
double curr_time;
double output_time;
double dt = 0.0;
double local_max_norm = 0.1;
double max_norm = 0;
int steps;
int* fish_off;
int* n_fish_split;
MPI_Init (&argc, &argv);
#ifdef TRACE_WITH_VAMPIR
VT_symdef(TRACE_LOCAL_COMP, "Local computation", "Computation");
VT_symdef(TRACE_FISH_GATHER, "Gathering to 0", "Communication");
VT_symdef(TRACE_MAX_NORM, "Collecting max norm", "Communication");
VT_symdef(TRACE_OUTPUT, "Output", "Output");
#endif
MPI_Comm_size (comm, &n_proc);
MPI_Comm_rank (comm, &rank);
make_fishtype (&fishtype);
get_options(argc, argv);
srand48(clock());
//MPI_Allreduce (&local_max_norm, &max_norm, 1, MPI_DOUBLE, MPI_MAX, comm);
//printf("local_max_norm = %g, max_norm = %g\n", local_max_norm, max_norm);
#ifdef TRACE_WITH_VAMPIR
VT_traceoff();
#endif
if (output_filename) {
outputp = 1;
if (0 == rank) {
output_fp = fopen(output_filename, "w");
if (output_fp == NULL) {
printf("Could not open %s for output\n", output_filename);
exit(1);
}
fprintf(output_fp, "n_fish: %d\n", n_fish);
}
}
fish_off = malloc ( (n_proc+1) * sizeof(int) );
n_fish_split = malloc ( (n_proc) * sizeof(int) );
//split each fish to different processors.
//fish_off: offset index of the fish in that processor
//n_fish_split is the # of fish in each processor
//ALL FUNCTIONALITY OF split_fish SHOULD BE DONE AFTER init_fish
//split_fish (n_proc, fish_off, n_fish_split);
//n_local_fish = n_fish_split[rank];
/*
All fish are generated on proc 0 to ensure same random numbers.
(Yes, the circle case could be parallelized. Feel free to
do it.)
*/
//split physical box sizes
row = (int)sqrt((double)n_proc);
column = n_proc/row;
double rowSep = WALL_SEP/row;
double columnSep = WALL_SEP/column;
int rowIndex = rank / column;
int columnIndex = rank % column;
topBound = rowSep * rowIndex;
bottomBound = topBound + rowSep;
leftBound = columnSep * columnIndex;
rightBound = leftBound + columnSep;
assert(n_proc % row == 0);
// Add n_proc # of arrays each holding ID of local fishes
fish_t fishProc[n_proc][n_fish];
int n_fish_proc[n_proc];
int k;
for (k = 0; k < n_proc; k++) n_fish_proc[k] = 0;
//////////////////////////////////
init_fish (rank, fish_off, n_fish_split, row, column, fishProc, n_fish_proc);
// distribute initial conditions to all processes
if (rank == 0) {
local_fish = fishProc[0];
n_local_fish = n_fish_proc[0];
// Functionality of MPI_Scatterv is done here with Isends
//MPI_Request request[n_proc-1];
int mesTag = 0;
MPI_Request *req;
for (k = 1; k < n_proc; ++k) {
//printf("n_fish_proc[%d], %d\n", k, n_fish_proc[k]);
MPI_Isend(fishProc[k], n_fish_proc[k], fishtype, k, mesTag, comm, req);
}
} else {
MPI_Status status;
// Processors of rank != 0 receives.
MPI_Recv( local_fish, n_fish, fishtype, 0, MPI_ANY_TAG, comm, &status);
MPI_Get_count(&status, fishtype, &n_local_fish);
}
printf("rank[%d], n_local_fish = %d\n", rank, n_local_fish);
///*
//MPI_Scatterv (fish, n_fish_split, fish_off, fishtype,
// local_fish, n_local_fish, fishtype,
// 0, comm);
//*/
#ifdef TRACE_WITH_VAMPIR
tracingp = 1;
VT_traceon();
#endif
start_mpi_timer(&total_timer);
for (output_time = 0.0, curr_time = 0.0, steps = 0;
curr_time <= end_time && steps < max_steps;
curr_time += dt, ++steps) {
#ifdef TRACE_WITH_VAMPIR
if (steps >= STEPS_TO_TRACE) {
tracingp = 0; VT_traceoff();
}
#endif
trace_begin(TRACE_FISH_GATHER);
start_mpi_timer (&gather_timer);
start_mpi_timer (&mpi_timer);
/*
Pull in all the fish. Obviously, this is not a good idea.
You will be greatly expanding this one line...
However, feel free to waste memory when producing output.
If you're dumping fish to a file, go ahead and do an
Allgatherv _in the output steps_ if you want. Or you could
pipeline dumping the fish.
MPI_Allgatherv (local_fish, n_local_fish, fishtype,
fish, n_fish_split, fish_off, fishtype, comm);
*/
//MPI_Request* sendReq, recvReq;
// Set aside buffer for fish received from other processes.
/*
for (j = 0; j < NUM_NEIGHBOR; ++j) {
//FIXME: which neighbors does not exist?
if (rankNeighbor[j] >= 0) {
MPI_Isend(local_fish, n_local_fish, fishtype, rankNeighbor[j], MPI_ANY_TAG, comm, &sendReqArray);
MPI_Irecv(impact_fish, n_fish, fishtype, rankNeighbor[NUM_NEIGHBOR - j], MPI_ANY_TAG, comm, &sendReqArray);
MPI_Wait(recvReq, MPI_STATUS_IGNORE);
interact_fish_mpi(local_fish, n_local_fish, impact_fish, sizeof(impact_fish));
}
}
*/
// get migrate fish
// send migrate fish
// receive migrate fish
// update local fish
// get impact fish
// send impact fish
// receive impact fish
// interact impact fish
// interact local fish
// move
MPI_Request sendReqArray[NUM_NEIGHBOR];
MPI_Request recvReqArray[NUM_NEIGHBOR];
fish_t receive_impact_fish[NUM_NEIGHBOR][n_fish];
int n_receive_impact_fish[NUM_NEIGHBOR];
fish_t receive_migrate_fish[NUM_NEIGHBOR][n_fish];
int n_receive_migrate_fish[NUM_NEIGHBOR];
int n_send_impact_fish[NUM_NEIGHBOR];
fish_t* send_impact_fish[NUM_NEIGHBOR];
int n_send_migrate_fish[NUM_NEIGHBOR];
fish_t* send_migrate_fish[NUM_NEIGHBOR];
get_interacting_fish( local_fish, n_local_fish, send_migrate_fish, n_send_migrate_fish, 1);
int tmp;
for (tmp = 0; tmp < NUM_NEIGHBOR; tmp++) {
printf("rank[%d], iter[%d] ------- get [%d] migrate fish for neig[%d]. \n", rank, iter, n_send_migrate_fish[tmp], tmp);
}
Isend_receive_fish(send_migrate_fish, n_send_migrate_fish, receive_migrate_fish, n_fish, sendReqArray, recvReqArray);
wait_for_fish(recvReqArray, n_receive_migrate_fish);
// FIXME: Have not implement update on local fish.
//update_local_fish();
get_interacting_fish(local_fish, n_local_fish, send_impact_fish, n_send_impact_fish, 0);
for (tmp = 0; tmp < NUM_NEIGHBOR; tmp++) {
printf("rank[%d], iter[%d] ------- get [%d] impact fish for neig[%d]. \n", rank, iter, n_send_impact_fish[tmp], tmp);
}
Isend_receive_fish(send_impact_fish, n_send_impact_fish, receive_impact_fish, n_fish, sendReqArray, recvReqArray);
wait_for_fish(recvReqArray, n_receive_impact_fish);
int index;
for (index = 0; index < NUM_NEIGHBOR; index++) {
if (n_receive_impact_fish[index] > 0) {
interact_fish_mpi(local_fish, n_local_fish, receive_impact_fish[index], n_receive_impact_fish[index]);
}
}
//*/
// make sure we are sending and receiving the same # msg.
//assert(dbg == 0);
// While waiting, interact with fish in its own pocket first
printf("rank[%d], iter[%d] ------- interact [%d] local fishes\n", rank, iter, n_local_fish);
interact_fish_mpi(local_fish, n_local_fish, local_fish, n_local_fish);
printf("rank[%d], iter[%d] ------- finished interact local fish\n", rank, iter);
stop_mpi_timer (&gather_timer);
stop_mpi_timer (&mpi_timer);
trace_end(TRACE_FISH_GATHER);
/*
We only output once every output_interval time unit, at most.
Without that restriction, we can easily create a huge output
file. Printing a record for ten fish takes about 300 bytes, so
for every 1000 steps, we could dump 300K of info. Now scale the
number of fish by 1000...
*/
trace_begin(TRACE_OUTPUT);
if (outputp && curr_time >= output_time) {
if (0 == rank)
output_fish (output_fp, curr_time, dt, fish, n_fish);
output_time = curr_time + output_interval;
}
trace_end(TRACE_OUTPUT);
trace_begin (TRACE_LOCAL_COMP);
//interact_fish (local_fish, n_local_fish, fish, n_fish);
local_max_norm = compute_norm (local_fish, n_local_fish);
trace_end (TRACE_LOCAL_COMP);
trace_begin (TRACE_MAX_NORM);
start_mpi_timer (&mpi_timer);
printf("rank[%d], iter[%d] ------- Allreduce max_norm, \n", rank, iter);
MPI_Allreduce (&local_max_norm, &max_norm, 1, MPI_DOUBLE, MPI_MAX, comm);
printf("rank[%d], iter[%d] ------- local_max_norm: %g, max_norm: %g\n", local_max_norm, max_norm);
stop_mpi_timer (&mpi_timer);
trace_end (TRACE_MAX_NORM);
trace_begin (TRACE_LOCAL_COMP);
dt = max_norm_change / max_norm;
dt = f_max(dt, min_dt);
dt = f_min(dt, max_dt);
printf("rank[%d], iter[%d] ------- moving [%d] local_fish, \n", rank, iter, n_local_fish);
move_fish(local_fish, n_local_fish, dt);
printf("rank[%d], iter[%d] ------- finished moving.\n", rank, iter);
trace_end (TRACE_LOCAL_COMP);
iter++;
}
stop_mpi_timer(&total_timer);
#ifdef TRACE_WITH_VAMPIR
VT_traceoff();
#endif
if (outputp) {
MPI_Allgatherv (local_fish, n_local_fish, fishtype,
fish, n_fish_split, fish_off, fishtype, comm);
if (0 == rank) {
output_fish (output_fp, curr_time, dt, fish, n_fish);
printf("\tEnded at %g (%g), %d (%d) steps\n",
curr_time, end_time, steps, max_steps);
}
}
printf("rank[%d], ------- 39, \n", rank);
MPI_Reduce (&total_timer, &sum_total_timer, 1, MPI_DOUBLE,
MPI_SUM, 0, comm);
printf("rank[%d], ------- 40, \n", rank);
MPI_Reduce (&gather_timer, &sum_gather_timer, 1, MPI_DOUBLE,
MPI_SUM, 0, comm);
printf("rank[%d], ------- 41, \n", rank);
MPI_Reduce (&mpi_timer, &sum_mpi_timer, 1, MPI_DOUBLE,
MPI_SUM, 0, comm);
printf("rank[%d], ------- 42, \n", rank);
if (0 == rank) {
printf("Number of PEs: %d\n"
"Time taken on 0: %g (avg. %g)\n"
"Time in gathers on 0: %g (avg %g)\n"
"Time in MPI on 0: %g (avg %g)\n",
n_proc,
total_timer, sum_total_timer / n_proc,
gather_timer, sum_gather_timer / n_proc,
mpi_timer, sum_mpi_timer / n_proc);
}
printf("rank[%d], ------- 43, \n", rank);
MPI_Barrier (comm);
printf("rank[%d], ------- 44, \n", rank);
MPI_Finalize ();
printf("rank[%d], ------- done!!, \n", rank);
return 0;
}
