void blacs_gridinit_nektar(int *BLACS_PARAMS, int *DESCA, int *DESCB){
int i,j,k;
/*
BLACS_PARAMS:
[0] = ictxt;
[1] = my_proc;
[2] = total_procs;
[3] = Nproc_row;
[4] = Nproc_col;
[5] = my_row;
[6] = my_col;
[7] = Global_rows;
[8] = Global_columns;
[9] = Block_Size_row;
[10] = Block_Size_col;
[11] = LOC_rows;
[12] = LOC_columns;
*/
blacs_pinfo_( i, j);
BLACS_PARAMS[1] = i;
BLACS_PARAMS[2] = j;
blacs_get_( -1, 0, k); // <- LG check the arguments of this call
BLACS_PARAMS[0] = k;
i = BLACS_PARAMS[3];
j = BLACS_PARAMS[4];
blacs_gridinit_( BLACS_PARAMS[0], "Row", i, j);
blacs_gridinfo_( BLACS_PARAMS[0] ,BLACS_PARAMS[3], BLACS_PARAMS[4], i, j);
BLACS_PARAMS[5] = i;
BLACS_PARAMS[6] = j;
i = 0;
BLACS_PARAMS[11] = numroc_(BLACS_PARAMS[7],BLACS_PARAMS[9], BLACS_PARAMS[5],i,BLACS_PARAMS[3]);
BLACS_PARAMS[12] = numroc_(BLACS_PARAMS[8],BLACS_PARAMS[10],BLACS_PARAMS[6],i,BLACS_PARAMS[4]);
i = 0;
j = 0;
descinit_(DESCA, BLACS_PARAMS[7], BLACS_PARAMS[8],
BLACS_PARAMS[9], BLACS_PARAMS[10],
i, j,
BLACS_PARAMS[0],BLACS_PARAMS[11],
k);
if (k != 0)
fprintf(stderr,"blacs_gridinit_nektar: ERROR, descinit(info) = %d \n",k);
descinit_(DESCB, BLACS_PARAMS[7], 1,
BLACS_PARAMS[9], 1,
i, j,
BLACS_PARAMS[0],BLACS_PARAMS[11],
k);
if (k != 0)
fprintf(stderr,"blacs_gridinit_nektar: ERROR, descinit(info) = %d \n",k);
}
int main(int argc, char **argv)
{
#define test_A(i,j) test_A[(size_t)(j)*N+(i)]
#define test_A2(i,j) test_A2[(size_t)(j)*N+(i)]
int N,NB,w,LDA,BB;
size_t memsize; //bytes
int iam, nprocs, mydevice;
int ICTXT, nprow, npcol, myprow, mypcol;
int i_one = 1, i_zero = 0, i_negone = -1;
double d_one = 1.0, d_zero = 0.0, d_negone = -1.0;
int IASEED = 100;
/* printf("N=?\n");
scanf("%ld",&N);
printf("NB=?\n");
scanf("%d", &NB);
printf("width of Y panel=?\n");
scanf("%ld",&w);
*/
if(argc < 4){
printf("invalid arguments N NB memsize(M)\n");
exit(1);
}
N = atoi(argv[1]);
NB = atoi(argv[2]);
memsize = (size_t)atoi(argv[3])*1024*1024;
BB = (N + NB - 1) / NB;
w = memsize/sizeof(double)/BB/NB/NB - 1;
assert(w > 0);
LDA = N + 0; //padding
int do_io = (N <= NSIZE);
double llttime;
double gflops;
nprow = npcol = 1;
blacs_pinfo_(&iam, &nprocs);
blacs_get_(&i_negone, &i_zero, &ICTXT);
blacs_gridinit_(&ICTXT, "R", &nprow, &npcol);
blacs_gridinfo_(&ICTXT, &nprow, &npcol, &myprow, &mypcol);
#ifdef USE_MIC
#ifdef __INTEL_OFFLOAD
printf("offload compilation enabled\ninitialize each MIC\n");
offload_init(&iam, &mydevice);
#pragma offload target(mic:0)
{
mkl_peak_mem_usage(MKL_PEAK_MEM_ENABLE);
}
#else
if(isroot)
printf("offload compilation not enabled\n");
exit(0);
#endif
#else
#ifdef USE_CUBLASV2
{
cublasStatus_t cuStatus;
for(int r = 0; r < OOC_NTHREADS; r++){
cuStatus = cublasCreate(&worker_handle[r]);
assert(cuStatus == CUBLAS_STATUS_SUCCESS);
}
}
#else
cublasInit();
#endif
#endif
double *test_A = (double*)memalign(64,(size_t)LDA*N*sizeof(double)); // for chol
#ifdef VERIFY
double *test_A2 = (double*)memalign(64,(size_t)LDA*N*sizeof(double)); // for verify
#endif
/*Initialize A */
int i,j;
printf("Initialize A ... "); fflush(stdout);
llttime = MPI_Wtime();
pdmatgen(&ICTXT, "Symm", "Diag", &N,
&N, &NB, &NB,
test_A, &LDA, &i_zero, &i_zero,
&IASEED, &i_zero, &N, &i_zero, &N,
&myprow, &mypcol, &nprow, &npcol);
llttime = MPI_Wtime() - llttime;
printf("time %lf\n", llttime);
/*print test_A*/
if(do_io){
printf("Original A=\n\n");
matprint(test_A, N, LDA, 'A');
}
/*Use directed unblocked Cholesky factorization*/
/*
t1 = clock();
Test_dpotrf(test_A2,N);
t2 = clock();
printf ("time for unblocked Cholesky factorization on host %f \n",
((float) (t2 - t1)) / CLOCKS_PER_SEC);
*/
/*print test_A*/
/*
if(do_io){
printf("Unblocked result:\n\n");
matprint(test_A2,N,'L');
}
*/
/*Use tile algorithm*/
Quark *quark = QUARK_New(OOC_NTHREADS);
QUARK_DOT_DAG_Enable(quark, 0);
#ifdef USE_MIC
// mklmem(NB);
printf("QUARK MIC affinity binding\n");
QUARK_bind(quark);
printf("offload warm up\n");
warmup(quark);
#endif
QUARK_DOT_DAG_Enable(quark, quark_getenv_int("QUARK_DOT_DAG_ENABLE", 0));
printf("LLT start %lf\n", MPI_Wtime());
llttime = Cholesky(quark,test_A,N,NB,LDA,memsize);
printf("LLT end %lf\n", MPI_Wtime());
QUARK_Delete(quark);
#ifdef USE_MIC
offload_destroy();
#else
#ifdef USE_CUBLASV2
{
cublasStatus_t cuStatus;
for(int r = 0; r < OOC_NTHREADS; r++){
cuStatus = cublasDestroy(worker_handle[r]);
assert(cuStatus == CUBLAS_STATUS_SUCCESS);
}
}
#else
cublasShutdown();
#endif
#endif
gflops = (double) N;
gflops = gflops/3.0 + 0.5;
gflops = gflops*(double)(N)*(double)(N);
gflops = gflops/llttime/1024.0/1024.0/1024.0;
printf ("N NB memsize(MB) quark_pthreads time Gflops\n%d %d %lf %d %lf %lf\n",
N, NB, (double)memsize/1024/1024, OOC_NTHREADS, llttime, gflops);
#ifdef USE_MIC
#pragma offload target(mic:0)
{
memsize = mkl_peak_mem_usage(MKL_PEAK_MEM_RESET);
}
printf("mkl_peak_mem_usage %lf MB\n", (double)memsize/1024.0/1024.0);
#endif
/*Update and print L*/
if(do_io){
printf("L:\n\n");
matprint(test_A,N,LDA,'L');
}
#ifdef VERIFY
printf("Verify... ");
llttime = MPI_Wtime();
/*
* ------------------------
* check difference betwen
* test_A and test_A2
* ------------------------
*/
/*
{
double maxerr = 0;
double maxerr2 = 0;
for (j = 0; j < N; j++)
{
for (i = j; i < N; i++)
{
double err = (test_A (i, j) - test_A2 (i, j));
err = ABS (err);
maxerr = MAX (err, maxerr);
maxerr2 = maxerr2 + err * err;
};
};
maxerr2 = sqrt (ABS (maxerr2));
printf ("max difference between test_A and test_A2 %lf \n", maxerr);
printf ("L2 difference between test_A and test_A2 %lf \n", maxerr2);
};
*/
/*
* ------------------
* over-write test_A2
* ------------------
*/
pdmatgen(&ICTXT, "Symm", "Diag", &N,
&N, &NB, &NB,
test_A2, &LDA, &i_zero,
&i_zero, &IASEED, &i_zero, &N, &i_zero, &N,
&myprow, &mypcol, &nprow, &npcol);
/*
* ---------------------------------------
* after solve, test_A2 should be identity
* ---------------------------------------
*/
// test_A = chol(B) = L;
// test_A2 = B
// solve L*L'*X = B
// if L is correct, X is identity */
{
int uplo = 'L';
const char *uplo_char = ((uplo == (int) 'U')
|| (uplo == (int) 'u')) ? "U" : "L";
int info = 0;
int nrhs = N;
int LDA = N;
int ldb = N;
dpotrs(uplo_char, &N, &nrhs, test_A, &LDA, test_A2, &ldb, &info);
assert (info == 0);
}
{
double maxerr = 0;
double maxerr2 = 0;
for (j = 0; j < N; j++)
{
for (i = 0; i < N; i++)
{
double eyeij = (i == j) ? 1.0 : 0.0;
double err = (test_A2 (i, j) - eyeij);
err = ABS (err);
maxerr = MAX (maxerr, err);
maxerr2 = maxerr2 + err * err;
};
};
maxerr2 = sqrt (ABS (maxerr2));
printf("time %lf\n", MPI_Wtime() - llttime);
printf ("max error %lf \n", maxerr);
printf ("max L2 error %lf \n", maxerr2);
}
#endif
free(test_A);test_A=NULL;
#ifdef VERIFY
free(test_A2);test_A2=NULL;
#endif
blacs_gridexit_(&ICTXT);
blacs_exit_(&i_zero);
return 0;
#undef test_A
#undef test_A2
}
int main(int argc, char **argv) {
int info, i, j, pcol, Adim;
double *D;
int *DESCD;
CSRdouble BT_i, B_j, Xsparse, Zsparse, Btsparse;
/*BT_i.allocate(0,0,0);
B_j.allocate(0,0,0);
Xsparse.allocate(0,0,0);
Zsparse.allocate(0,0,0);
Btsparse.allocate(0,0,0);*/
//Initialise MPI and some MPI-variables
info = MPI_Init ( &argc, &argv );
if ( info != 0 ) {
printf ( "Error in MPI initialisation: %d\n",info );
return info;
}
position= ( int* ) calloc ( 2,sizeof ( int ) );
if ( position==NULL ) {
printf ( "unable to allocate memory for processor position coordinate\n" );
return EXIT_FAILURE;
}
dims= ( int* ) calloc ( 2,sizeof ( int ) );
if ( dims==NULL ) {
printf ( "unable to allocate memory for grid dimensions coordinate\n" );
return EXIT_FAILURE;
}
//BLACS is the interface used by PBLAS and ScaLAPACK on top of MPI
blacs_pinfo_ ( &iam,&size ); //determine the number of processes involved
info=MPI_Dims_create ( size, 2, dims ); //determine the best 2D cartesian grid with the number of processes
if ( info != 0 ) {
printf ( "Error in MPI creation of dimensions: %d\n",info );
return info;
}
//Until now the code can only work with square process grids
//So we try to get the biggest square grid possible with the number of processes involved
if (*dims != *(dims+1)) {
while (*dims * *dims > size)
*dims -=1;
*(dims+1)= *dims;
if (iam==0)
printf("WARNING: %d processor(s) unused due to reformatting to a square process grid\n", size - (*dims * *dims));
size = *dims * *dims;
//cout << "New size of process grid: " << size << endl;
}
blacs_get_ ( &i_negone,&i_zero,&ICTXT2D );
//Initialisation of the BLACS process grid, which is referenced as ICTXT2D
blacs_gridinit_ ( &ICTXT2D,"R",dims, dims+1 );
if (iam < size) {
//The rank (iam) of the process is mapped to a 2D grid: position= (process row, process column)
blacs_pcoord_ ( &ICTXT2D,&iam,position, position+1 );
if ( *position ==-1 ) {
printf ( "Error in proces grid\n" );
return -1;
}
//Filenames, dimensions of all matrices and other important variables are read in as global variables (see src/readinput.cpp)
info=read_input ( *++argv );
if ( info!=0 ) {
printf ( "Something went wrong when reading input file for processor %d\n",iam );
return -1;
}
//blacs_barrier is used to stop any process of going beyond this point before all processes have made it up to this point.
blacs_barrier_ ( &ICTXT2D,"ALL" );
if ( * ( position+1 ) ==0 && *position==0 )
printf ( "Reading of input-file succesful\n" );
if ( * ( position+1 ) ==0 && *position==0 ) {
printf("\nA linear mixed model with %d observations, %d genotypes, %d random effects and %d fixed effects\n", n,k,m,l);
printf("was analyzed using %d (%d x %d) processors\n",size,*dims,*(dims+1));
}
//Dimension of A (sparse matrix) is the number of fixed effects(m) + the sparse random effects (l)
Adim=m+l;
//Dimension of D (dense matrix) is the number of dense effects (k)
Ddim=k;
pcol= * ( position+1 );
//Define number of blocks needed to store a complete column/row of D
Dblocks= Ddim%blocksize==0 ? Ddim/blocksize : Ddim/blocksize +1;
//Define the number of rowblocks needed by the current process to store its part of the dense matrix D
Drows= ( Dblocks - *position ) % *dims == 0 ? ( Dblocks- *position ) / *dims : ( Dblocks- *position ) / *dims +1;
Drows= Drows<1? 1 : Drows;
//Define the number of columnblocks needed by the current process to store its part of the dense matrix D
Dcols= ( Dblocks - pcol ) % * ( dims+1 ) == 0 ? ( Dblocks- pcol ) / * ( dims+1 ) : ( Dblocks- pcol ) / * ( dims+1 ) +1;
Dcols=Dcols<1? 1 : Dcols;
//Define the local leading dimension of D (keeping in mind that matrices are always stored column-wise)
lld_D=Drows*blocksize;
//Initialise the descriptor of the dense distributed matrix
DESCD= ( int* ) malloc ( DLEN_ * sizeof ( int ) );
if ( DESCD==NULL ) {
printf ( "unable to allocate memory for descriptor for C\n" );
return -1;
}
//D with dimensions (Ddim,Ddim) is distributed over all processes in ICTXT2D, with the first element in process (0,0)
//D is distributed into blocks of size (blocksize,blocksize), having a local leading dimension lld_D in this specific process
descinit_ ( DESCD, &Ddim, &Ddim, &blocksize, &blocksize, &i_zero, &i_zero, &ICTXT2D, &lld_D, &info );
if ( info!=0 ) {
printf ( "Descriptor of matrix C returns info: %d\n",info );
return info;
}
//Allocate the space necessary to store the part of D that is held into memory of this process.
D = ( double* ) calloc ( Drows * blocksize * Dcols * blocksize,sizeof ( double ) );
if ( D==NULL ) {
printf ( "unable to allocate memory for Matrix D (required: %ld bytes)\n", Drows * blocksize * Dcols * blocksize * sizeof ( double ) );
return EXIT_FAILURE;
}
blacs_barrier_ ( &ICTXT2D,"ALL" );
if (iam==0)
printf ( "Start set up of B & D\n" );
blacs_barrier_ ( &ICTXT2D,"ALL" );
//set_up_BD is declared in readdist.cpp and constructs the parts of matrices B & D in each processor
//which are necessary to create the distributed Schur complement of D
info = set_up_BD ( DESCD, D, BT_i, B_j, Btsparse );
//printdense(Drows*blocksize, Dcols * blocksize,D,"matrix_D.txt");
blacs_barrier_ ( &ICTXT2D,"ALL" );
if (iam==0)
printf ( "Matrices B & D set up\n" );
if(printD_bool) {
int array_of_gsizes[2], array_of_distribs[2], array_of_dargs[2], array_of_psize[2] ;
int buffersize;
MPI_Datatype file_type;
MPI_File fh;
MPI_Status status;
array_of_gsizes[0]=Dblocks * blocksize;
array_of_gsizes[1]=Dblocks * blocksize;
array_of_distribs[0]=MPI_DISTRIBUTE_CYCLIC;
array_of_distribs[1]=MPI_DISTRIBUTE_CYCLIC;
array_of_dargs[0]=blocksize;
array_of_dargs[1]=blocksize;
array_of_psize[0]=*dims;
array_of_psize[1]=*(dims + 1);
MPI_Type_create_darray(size,iam,2,array_of_gsizes, array_of_distribs,
array_of_dargs, array_of_psize, MPI_ORDER_FORTRAN,
MPI_DOUBLE, &file_type);
MPI_Type_commit(&file_type);
info = MPI_File_open(MPI_COMM_WORLD, filenameD,
MPI_MODE_CREATE | MPI_MODE_WRONLY,
MPI_INFO_NULL, &fh);
/*if ( ( Drows-1 ) % *(dims+1) == *position && ( Dcols-1 ) % *(dims) == pcol && Ddim%blocksize !=0 )
buffersize=((Drows-1) * blocksize + Ddim % blocksize) * ((Dcols-1) * blocksize + Ddim % blocksize);
else if ( ( Drows-1 ) % *(dims+1) == *position && Ddim%blocksize !=0 )
buffersize=((Drows-1) * blocksize + Ddim % blocksize) * Dcols * blocksize;
else if ( ( Dcols-1 ) % *(dims) == *position && Ddim%blocksize !=0 )
buffersize=((Dcols-1) * blocksize + Ddim % blocksize) * Drows * blocksize;
else*/
buffersize= Dcols * Drows * blocksize * blocksize;
MPI_File_set_view(fh, 0, MPI_DOUBLE, file_type, "native", MPI_INFO_NULL);
info =MPI_File_write_all(fh, D,buffersize, MPI_DOUBLE,
&status);
MPI_File_close(&fh);
if(iam==0) {
printf("Matrix D (dimension %d) is printed in file %s\n", Dblocks*blocksize,filenameD);
}
if(filenameD != NULL)
free(filenameD);
filenameD=NULL;
//delete[] array_of_gsizes, delete[] array_of_distribs, delete[] array_of_dargs, delete[] array_of_psize;
}
//Now every matrix has to set up the sparse matrix A, consisting of X'X, X'Z, Z'X and Z'Z + lambda*I
Xsparse.loadFromFile ( filenameX );
Zsparse.loadFromFile ( filenameZ );
if(filenameX != NULL)
free(filenameX);
filenameX=NULL;
if(filenameZ != NULL)
free(filenameZ);
filenameZ=NULL;
smat_t *X_smat, *Z_smat;
X_smat= (smat_t *) calloc(1,sizeof(smat_t));
Z_smat= (smat_t *) calloc(1,sizeof(smat_t));
X_smat = smat_new_from ( Xsparse.nrows,Xsparse.ncols,Xsparse.pRows,Xsparse.pCols,Xsparse.pData,0,0 );
Z_smat = smat_new_from ( Zsparse.nrows,Zsparse.ncols,Zsparse.pRows,Zsparse.pCols,Zsparse.pData,0,0 );
smat_t *Xt_smat, *Zt_smat;
Xt_smat= (smat_t *) calloc(1,sizeof(smat_t));
Zt_smat= (smat_t *) calloc(1,sizeof(smat_t));
Xt_smat = smat_copy_trans ( X_smat );
Zt_smat = smat_copy_trans ( Z_smat );
CSRdouble Asparse;
smat_t *XtX_smat, *XtZ_smat, *ZtZ_smat, *lambda_smat, *ZtZlambda_smat;
XtX_smat= (smat_t *) calloc(1,sizeof(smat_t));
XtZ_smat= (smat_t *) calloc(1,sizeof(smat_t));
ZtZ_smat= (smat_t *) calloc(1,sizeof(smat_t));
XtX_smat = smat_matmul ( Xt_smat, X_smat );
XtZ_smat = smat_matmul ( Xt_smat, Z_smat );
ZtZ_smat = smat_matmul ( Zt_smat,Z_smat );
Xsparse.clear();
Zsparse.clear();
smat_free(Xt_smat);
smat_free(Zt_smat);
/*smat_free(X_smat);
smat_free(Z_smat);*/
CSRdouble Imat;
makeIdentity ( l, Imat );
lambda_smat= (smat_t *) calloc(1,sizeof(smat_t));
lambda_smat = smat_new_from ( Imat.nrows,Imat.ncols,Imat.pRows,Imat.pCols,Imat.pData,0,0 );
smat_scale_diag ( lambda_smat, -lambda );
ZtZlambda_smat= (smat_t *) calloc(1,sizeof(smat_t));
ZtZlambda_smat = smat_add ( lambda_smat, ZtZ_smat );
smat_free(ZtZ_smat);
//smat_free(lambda_smat);
smat_to_symmetric_structure ( XtX_smat );
smat_to_symmetric_structure ( ZtZlambda_smat );
CSRdouble XtX_sparse, XtZ_sparse, ZtZ_sparse;
XtX_sparse.make2 ( XtX_smat->m,XtX_smat->n,XtX_smat->nnz,XtX_smat->ia,XtX_smat->ja,XtX_smat->a );
XtZ_sparse.make2 ( XtZ_smat->m,XtZ_smat->n,XtZ_smat->nnz,XtZ_smat->ia,XtZ_smat->ja,XtZ_smat->a );
ZtZ_sparse.make2 ( ZtZlambda_smat->m,ZtZlambda_smat->n,ZtZlambda_smat->nnz,ZtZlambda_smat->ia,ZtZlambda_smat->ja,ZtZlambda_smat->a );
/*smat_free(XtX_smat);
smat_free(XtZ_smat);
smat_free(ZtZlambda_smat);*/
Imat.clear();
if (iam==0) {
cout << "*** [ t t ] *** " << endl;
cout << "*** [ X X X Z ] *** " << endl;
cout << "*** [ ] *** " << endl;
cout << "*** G e n e r a t i n g m a t r i x A = [ ] *** " << endl;
cout << "*** [ t t ] *** " << endl;
cout << "*** [ Z X Z Z ] *** " << endl;
}
//Sparse matrix A only contains the upper triangular part of A
create2x2SymBlockMatrix ( XtX_sparse, XtZ_sparse, ZtZ_sparse, Asparse );
//Asparse.writeToFile("A_sparse.csr");
smat_free(XtX_smat);
smat_free(XtZ_smat);
smat_free(ZtZlambda_smat);
XtX_sparse.clear();
XtZ_sparse.clear();
ZtZ_sparse.clear();
blacs_barrier_ ( &ICTXT2D,"ALL" );
if(printsparseC_bool) {
CSRdouble Dmat, Dblock, Csparse;
Dblock.nrows=Dblocks * blocksize;
Dblock.ncols=Dblocks * blocksize;
Dblock.allocate(Dblocks * blocksize, Dblocks * blocksize, 0);
Dmat.allocate(0,0,0);
for (i=0; i<Drows; ++i) {
for(j=0; j<Dcols; ++j) {
dense2CSR_sub(D + i * blocksize + j * lld_D * blocksize,blocksize,blocksize,lld_D,Dblock,( * ( dims) * i + *position ) *blocksize,
( * ( dims+1 ) * j + pcol ) *blocksize);
if ( Dblock.nonzeros>0 ) {
if ( Dmat.nonzeros==0 ) {
Dmat.make2 ( Dblock.nrows,Dblock.ncols,Dblock.nonzeros,Dblock.pRows,Dblock.pCols,Dblock.pData );
}
else {
Dmat.addBCSR ( Dblock );
}
}
Dblock.clear();
}
}
blacs_barrier_(&ICTXT2D,"A");
if ( iam!=0 ) {
//Each process other than root sends its Dmat to the root process.
MPI_Send ( & ( Dmat.nonzeros ),1, MPI_INT,0,iam,MPI_COMM_WORLD );
MPI_Send ( & ( Dmat.pRows[0] ),Dmat.nrows + 1, MPI_INT,0,iam+size,MPI_COMM_WORLD );
MPI_Send ( & ( Dmat.pCols[0] ),Dmat.nonzeros, MPI_INT,0,iam+2*size,MPI_COMM_WORLD );
MPI_Send ( & ( Dmat.pData[0] ),Dmat.nonzeros, MPI_DOUBLE,0,iam+3*size,MPI_COMM_WORLD );
Dmat.clear();
}
else {
for ( i=1; i<size; ++i ) {
// The root process receives parts of Dmat sequentially from all processes and directly adds them together.
int nonzeroes, count;
MPI_Recv ( &nonzeroes,1,MPI_INT,i,i,MPI_COMM_WORLD,&status );
/*MPI_Get_count(&status, MPI_INT, &count);
printf("Process 0 received %d elements of process %d\n",count,i);*/
if(nonzeroes>0) {
printf("Nonzeroes : %d\n ",nonzeroes);
Dblock.allocate ( Dblocks * blocksize,Dblocks * blocksize,nonzeroes );
MPI_Recv ( & ( Dblock.pRows[0] ), Dblocks * blocksize + 1, MPI_INT,i,i+size,MPI_COMM_WORLD,&status );
/*MPI_Get_count(&status, MPI_INT, &count);
printf("Process 0 received %d elements of process %d\n",count,i);*/
MPI_Recv ( & ( Dblock.pCols[0] ),nonzeroes, MPI_INT,i,i+2*size,MPI_COMM_WORLD,&status );
/*MPI_Get_count(&status, MPI_INT, &count);
printf("Process 0 received %d elements of process %d\n",count,i);*/
MPI_Recv ( & ( Dblock.pData[0] ),nonzeroes, MPI_DOUBLE,i,i+3*size,MPI_COMM_WORLD,&status );
/*MPI_Get_count(&status, MPI_DOUBLE, &count);
printf("Process 0 received %d elements of process %d\n",count,i);*/
Dmat.addBCSR ( Dblock );
}
}
//Dmat.writeToFile("D_sparse.csr");
Dmat.reduceSymmetric();
Btsparse.transposeIt(1);
create2x2SymBlockMatrix(Asparse,Btsparse, Dmat, Csparse);
Btsparse.clear();
Dmat.clear();
Csparse.writeToFile(filenameC);
Csparse.clear();
if(filenameC != NULL)
free(filenameC);
filenameC=NULL;
}
}
Btsparse.clear();
blacs_barrier_(&ICTXT2D,"A");
//AB_sol will contain the solution of A*X=B, distributed across the process rows. Processes in the same process row possess the same part of AB_sol
double * AB_sol;
int * DESCAB_sol;
DESCAB_sol= ( int* ) malloc ( DLEN_ * sizeof ( int ) );
if ( DESCAB_sol==NULL ) {
printf ( "unable to allocate memory for descriptor for AB_sol\n" );
return -1;
}
//AB_sol (Adim, Ddim) is distributed across all processes in ICTXT2D starting from process (0,0) into blocks of size (Adim, blocksize)
descinit_ ( DESCAB_sol, &Adim, &Ddim, &Adim, &blocksize, &i_zero, &i_zero, &ICTXT2D, &Adim, &info );
if ( info!=0 ) {
printf ( "Descriptor of matrix C returns info: %d\n",info );
return info;
}
AB_sol=(double *) calloc(Adim * Dcols*blocksize,sizeof(double));
// Each process calculates the Schur complement of the part of D at its disposal. (see src/schur.cpp)
// The solution of A * Y = B_j is stored in AB_sol (= A^-1 * B_j)
blacs_barrier_(&ICTXT2D,"A");
make_Sij_parallel_denseB ( Asparse, BT_i, B_j, D, lld_D, AB_sol );
BT_i.clear();
B_j.clear();
//From here on the Schur complement S of D is stored in D
blacs_barrier_ ( &ICTXT2D,"ALL" );
//The Schur complement is factorised (by ScaLAPACK)
pdpotrf_ ( "U",&k,D,&i_one,&i_one,DESCD,&info );
if ( info != 0 ) {
printf ( "Cholesky decomposition of D was unsuccessful, error returned: %d\n",info );
return -1;
}
//From here on the factorization of the Schur complement S is stored in D
blacs_barrier_ ( &ICTXT2D,"ALL" );
//The Schur complement is inverted (by ScaLAPACK)
pdpotri_ ( "U",&k,D,&i_one,&i_one,DESCD,&info );
if ( info != 0 ) {
printf ( "Inverse of D was unsuccessful, error returned: %d\n",info );
return -1;
}
//From here on the inverse of the Schur complement S is stored in D
blacs_barrier_(&ICTXT2D,"A");
double* InvD_T_Block = ( double* ) calloc ( Dblocks * blocksize + Adim ,sizeof ( double ) );
//Diagonal elements of the (1,1) block of C^-1 are still distributed and here they are gathered in InvD_T_Block in the root process.
if(*position == pcol) {
for (i=0; i<Ddim; ++i) {
if (pcol == (i/blocksize) % *dims) {
int Dpos = i%blocksize + ((i/blocksize) / *dims) * blocksize ;
*(InvD_T_Block + Adim +i) = *( D + Dpos + lld_D * Dpos);
}
}
for ( i=0,j=0; i<Dblocks; ++i,++j ) {
if ( j==*dims )
j=0;
if ( *position==j ) {
dgesd2d_ ( &ICTXT2D,&blocksize,&i_one,InvD_T_Block + Adim + i * blocksize,&blocksize,&i_zero,&i_zero );
}
if ( *position==0 ) {
dgerv2d_ ( &ICTXT2D,&blocksize,&i_one,InvD_T_Block + Adim + blocksize*i,&blocksize,&j,&j );
}
}
}
blacs_barrier_(&ICTXT2D,"A");
//Only the root process performs a selected inversion of A.
if (iam==0) {
int pardiso_message_level = 1;
int pardiso_mtype=-2;
ParDiSO pardiso ( pardiso_mtype, pardiso_message_level );
int number_of_processors = 1;
char* var = getenv("OMP_NUM_THREADS");
if(var != NULL) {
sscanf( var, "%d", &number_of_processors );
}
else {
printf("Set environment OMP_NUM_THREADS to 1");
exit(1);
}
pardiso.iparm[2] = 2;
pardiso.iparm[3] = number_of_processors;
pardiso.iparm[8] = 0;
pardiso.iparm[11] = 1;
pardiso.iparm[13] = 0;
pardiso.iparm[28] = 0;
//This function calculates the factorisation of A once again so this might be optimized.
pardiso.findInverseOfA ( Asparse );
printf("Processor %d inverted matrix A\n",iam);
}
blacs_barrier_(&ICTXT2D,"A");
// To minimize memory usage, and because only the diagonal elements of the inverse are needed, Y' * S is calculated row by rowblocks
// the diagonal element is calculates as the dot product of this row and the corresponding column of Y. (Y is solution of AY=B)
double* YSrow= ( double* ) calloc ( Dcols * blocksize,sizeof ( double ) );
int * DESCYSROW;
DESCYSROW= ( int* ) malloc ( DLEN_ * sizeof ( int ) );
if ( DESCYSROW==NULL ) {
printf ( "unable to allocate memory for descriptor for AB_sol\n" );
return -1;
}
//YSrow (1,Ddim) is distributed across processes of ICTXT2D starting from process (0,0) into blocks of size (1,blocksize)
descinit_ ( DESCYSROW, &i_one, &Ddim, &i_one,&blocksize, &i_zero, &i_zero, &ICTXT2D, &i_one, &info );
if ( info!=0 ) {
printf ( "Descriptor of matrix C returns info: %d\n",info );
return info;
}
blacs_barrier_(&ICTXT2D,"A");
//Calculating diagonal elements 1 by 1 of the (0,0)-block of C^-1.
for (i=1; i<=Adim; ++i) {
pdsymm_ ("R","U",&i_one,&Ddim,&d_one,D,&i_one,&i_one,DESCD,AB_sol,&i,&i_one,DESCAB_sol,&d_zero,YSrow,&i_one,&i_one,DESCYSROW);
pddot_(&Ddim,InvD_T_Block+i-1,AB_sol,&i,&i_one,DESCAB_sol,&Adim,YSrow,&i_one,&i_one,DESCYSROW,&i_one);
/*if(*position==1 && pcol==1)
printf("Dot product in process (1,1) is: %g\n", *(InvD_T_Block+i-1));
if(*position==0 && pcol==1)
printf("Dot product in process (0,1) is: %g\n",*(InvD_T_Block+i-1));*/
}
blacs_barrier_(&ICTXT2D,"A");
if(YSrow != NULL)
free(YSrow);
YSrow = NULL;
if(DESCYSROW != NULL)
free(DESCYSROW);
DESCYSROW = NULL;
if(AB_sol != NULL)
free(AB_sol);
AB_sol = NULL;
if(DESCAB_sol != NULL)
free(DESCAB_sol);
DESCAB_sol = NULL;
if(D != NULL)
free(D);
D = NULL;
if(DESCD != NULL)
free(DESCD);
DESCD = NULL;
//Only in the root process we add the diagonal elements of A^-1
if (iam ==0) {
for(i=0; i<Adim; ++i) {
j=Asparse.pRows[i];
*(InvD_T_Block+i) += Asparse.pData[j];
}
Asparse.clear();
printdense ( Adim+k,1,InvD_T_Block,"diag_inverse_C_parallel.txt" );
}
if(InvD_T_Block != NULL)
free(InvD_T_Block);
InvD_T_Block = NULL;
blacs_gridexit_(&ICTXT2D);
}
//cout << iam << " reached end before MPI_Barrier" << endl;
MPI_Barrier(MPI_COMM_WORLD);
//MPI_Finalize();
return 0;
}
int main()
{
const MKL_INT m = 1000;
const MKL_INT k = 100000;
const MKL_INT n = 1000;
const MKL_INT nb = 100;
const MKL_INT nprow = 2;
const MKL_INT npcol = 2;
MKL_INT iam, nprocs, ictxt, myrow, mycol;
MDESC descA, descB, descC, descA_local, descB_local, descC_local;
MKL_INT info;
MKL_INT a_m_local, a_n_local, b_m_local, b_n_local, c_m_local, c_n_local;
MKL_INT a_lld, b_lld, c_lld;
blacs_pinfo_( &iam, &nprocs );
blacs_get_( &i_negone, &i_zero, &ictxt );
blacs_gridinit_( &ictxt, "R", &nprow, &npcol );
blacs_gridinfo_( &ictxt, &nprow, &npcol, &myrow, &mycol );
double *a = 0;
double *b = 0;
double *c = 0;
if (iam==0)
{
a = gen_a(m, k);
b = gen_b(k, n);
c = (double*)calloc(m*n, sizeof(double));
puts("a=");
print(a, m, k);
puts("b=");
print(b, k, n);
}
a_m_local = numroc_( &m, &nb, &myrow, &i_zero, &nprow );
a_n_local = numroc_( &k, &nb, &mycol, &i_zero, &npcol );
b_m_local = numroc_( &k, &nb, &myrow, &i_zero, &nprow );
b_n_local = numroc_( &n, &nb, &mycol, &i_zero, &npcol );
c_m_local = numroc_( &m, &nb, &myrow, &i_zero, &nprow );
c_n_local = numroc_( &n, &nb, &mycol, &i_zero, &npcol );
double *A = (double*) calloc( a_m_local * a_n_local, sizeof( double ) );
double *B = (double*) calloc( b_m_local * b_n_local, sizeof( double ) );
double *C = (double*) calloc( c_m_local * c_n_local, sizeof( double ) );
a_lld = MAX( a_m_local, 1 );
b_lld = MAX( b_m_local, 1 );
c_lld = MAX( c_m_local, 1 );
if (iam==0)
{
printf("a_m_local = %d\ta_n_local = %d\tb_m_local = %d\tb_n_local = %d\tc_m_local = %d\tc_n_local = %d\n", a_m_local, a_n_local, b_m_local, b_n_local,
c_m_local, c_n_local);
printf("a_lld = %d\tb_lld = %d\tc_lld = %d\n", a_lld, b_lld, c_lld);
}
descinit_( descA_local, &m, &k, &m, &k, &i_zero, &i_zero, &ictxt, &m, &info );
descinit_( descB_local, &k, &n, &k, &n, &i_zero, &i_zero, &ictxt, &k, &info );
descinit_( descC_local, &m, &n, &m, &n, &i_zero, &i_zero, &ictxt, &m, &info );
descinit_( descA, &m, &k, &nb, &nb, &i_zero, &i_zero, &ictxt, &a_lld, &info );
descinit_( descB, &k, &n, &nb, &nb, &i_zero, &i_zero, &ictxt, &b_lld, &info );
descinit_( descC, &m, &n, &nb, &nb, &i_zero, &i_zero, &ictxt, &c_lld, &info );
printf("Rank %d: start distribute data\n", iam);
pdgeadd_( &trans, &m, &k, &one, a, &i_one, &i_one, descA_local, &zero, A, &i_one, &i_one, descA );
pdgeadd_( &trans, &k, &n, &one, b, &i_one, &i_one, descB_local, &zero, B, &i_one, &i_one, descB );
printf("Rank %d: finished distribute data\n", iam);
if (iam==0)
{
puts("a");
print(A, a_m_local, a_n_local);
puts("b");
print(B, b_m_local, b_n_local);
}
pdgemm_( "N", "N", &m, &n, &k, &one, A, &i_one, &i_one, descA, B, &i_one, &i_one, descB,
&zero, C, &i_one, &i_one, descC );
printf("Rank %d: finished dgemm\n", iam);
if (iam == 0)
{
puts("c");
print(C, c_m_local, c_n_local);
}
pdgeadd_( &trans, &m, &n, &one, C, &i_one, &i_one, descC, &zero, c, &i_one, &i_one, descC_local);
if (iam==0)
{
puts("global c");
print(c, m, n);
}
free(A);
free(B);
free(C);
if (iam==0)
{
free(a);
free(b);
free(c);
}
blacs_gridexit_( &ictxt );
blacs_exit_( &i_zero );
}
int main ( int argc, char **argv ) {
int info, i, j, pcol;
double *D, *AB_sol, *InvD_T_Block, *XSrow;
int *DESCD, *DESCAB_sol, *DESCXSROW;
bool readAFromFile = false;
//CSRdouble BT_i, B_j;
double* BT_i;
double* B_j;
int s_BT_i = 0;
int s_B_j = 0; // size of BT_i (#rows) and B_j (#cols)
int nx, ny, nz;
CSRdouble Asparse, Btsparse;
if (argc < 6)
{
// needed args: nx, ny, nz, Ddim, blocksize;
// optional: C.csr - if provided, the output file is written.
cout << "Too few arguments." << endl;
cout << "Usage: " << argv[0] << " nx ny nz Ddim blocksize [C.csr]" << endl;
cout << "Usage: " << argv[0] << " -fileA filename Adim Ddim blocksize [C.csr]" << endl;
exit(-1);
}
if (strcmp(argv[1], "-fileA") == 0) // if (argv[1] == "-fileA")
{
readAFromFile = true;
filenameA = new char[250];
strcpy(filenameA, argv[2]);
Adim = atoi(argv[3]);
}
else
{
nx = atoi(argv[1]);
ny = atoi(argv[2]);
nz = atoi(argv[3]);
Adim = nx * ny * nz;
}
Ddim = atoi(argv[4]);
blocksize = atoi(argv[5]);
//printf("Adim=%d, Ddim=%d, blocksize=%d *** %s", Adim, Ddim, blocksize, outputc);
//exit(-123);
//Initialise MPI and some MPI-variables
info = MPI_Init ( &argc, &argv );
if ( info != 0 ) {
printf ( "Error in MPI initialisation: %d\n",info );
return info;
}
position= ( int* ) calloc ( 2,sizeof ( int ) );
if ( position==NULL ) {
printf ( "unable to allocate memory for processor position coordinate\n" );
return EXIT_FAILURE;
}
dims= ( int* ) calloc ( 2,sizeof ( int ) );
if ( dims==NULL ) {
printf ( "unable to allocate memory for grid dimensions coordinate\n" );
return EXIT_FAILURE;
}
//BLACS is the interface used by PBLAS and ScaLAPACK on top of MPI
blacs_pinfo_ ( &iam,&size ); //determine the number of processes involved
info=MPI_Dims_create ( size, 2, dims ); //determine the best 2D cartesian grid with the number of processes
if ( info != 0 ) {
printf ( "Error in MPI creation of dimensions: %d\n",info );
return info;
}
//Until now the code can only work with square process grids
//So we try to get the biggest square grid possible with the number of processes involved
if ( *dims != * ( dims+1 ) ) {
while ( *dims * *dims > size )
*dims -=1;
* ( dims+1 ) = *dims;
if ( iam==0 )
printf ( "WARNING: %d processor(s) unused due to reformatting to a square process grid\n", size - ( *dims * *dims ) );
size = *dims * *dims;
//cout << "New size of process grid: " << size << endl;
}
blacs_get_ ( &i_negone,&i_zero,&ICTXT2D );
//Initialisation of the BLACS process grid, which is referenced as ICTXT2D
blacs_gridinit_ ( &ICTXT2D,"R",dims, dims+1 );
if ( iam < size ) {
//The rank (iam) of the process is mapped to a 2D grid: position= (process row, process column)
blacs_pcoord_ ( &ICTXT2D,&iam,position, position+1 );
if ( *position ==-1 ) {
printf ( "Error in proces grid\n" );
return -1;
}
/*
//Filenames, dimensions of all matrices and other important variables are read in as global variables (see src/readinput.cpp)
info=read_input ( *++argv );
if ( info!=0 )
{
printf ( "Something went wrong when reading input file for processor %d\n",iam );
return -1;
}
*/
//blacs_barrier is used to stop any process of going beyond this point before all processes have made it up to this point.
blacs_barrier_ ( &ICTXT2D,"ALL" );
if ( * ( position+1 ) ==0 && *position==0 )
printf ( "Reading of input-file succesful\n" );
if ( * ( position+1 ) ==0 && *position==0 ) {
printf ( "\nA sparse square matrix of dimension %d with a dense square submatrix with dimension %d \n", Adim+Ddim,Ddim );
printf ( "was analyzed using %d (%d x %d) processors\n",size,*dims,* ( dims+1 ) );
}
pcol= * ( position+1 );
//Define number of blocks needed to store a complete column/row of D
Dblocks= Ddim%blocksize==0 ? Ddim/blocksize : Ddim/blocksize +1;
//Define the number of rowblocks needed by the current process to store its part of the dense matrix D
Drows= ( Dblocks - *position ) % *dims == 0 ? ( Dblocks- *position ) / *dims : ( Dblocks- *position ) / *dims +1;
Drows= Drows<1? 1 : Drows;
//Define the number of columnblocks needed by the current process to store its part of the dense matrix D
Dcols= ( Dblocks - pcol ) % * ( dims+1 ) == 0 ? ( Dblocks- pcol ) / * ( dims+1 ) : ( Dblocks- pcol ) / * ( dims+1 ) +1;
Dcols=Dcols<1? 1 : Dcols;
//Define the local leading dimension of D (keeping in mind that matrices are always stored column-wise)
lld_D=Drows*blocksize;
// cout << "Hi! I am " << iam << ". My position is ( " << *position << "," << *(position+1) << ") and I have... Dblocks: " << Dblocks << "; Drows: " << Drows << "; Dcols: " << Dcols << "; blocksize: " << blocksize << endl;
//Initialise the descriptor of the dense distributed matrix
DESCD= ( int* ) malloc ( DLEN_ * sizeof ( int ) );
if ( DESCD==NULL ) {
printf ( "unable to allocate memory for descriptor for C\n" );
return -1;
}
//D with dimensions (Ddim,Ddim) is distributed over all processes in ICTXT2D, with the first element in process (0,0)
//D is distributed into blocks of size (blocksize,blocksize), having a local leading dimension lld_D in this specific process
descinit_ ( DESCD, &Ddim, &Ddim, &blocksize, &blocksize, &i_zero, &i_zero, &ICTXT2D, &lld_D, &info );
if ( info!=0 ) {
printf ( "Descriptor of matrix C returns info: %d\n",info );
return info;
}
//Allocate the space necessary to store the part of D that is held into memory of this process.
D = ( double* ) calloc ( Drows * blocksize * Dcols * blocksize,sizeof ( double ) );
if ( D==NULL ) {
printf ( "unable to allocate memory for Matrix D (required: %ld bytes)\n", Drows * blocksize * Dcols * blocksize * sizeof ( double ) );
return EXIT_FAILURE;
}
blacs_barrier_ ( &ICTXT2D,"ALL" ); //added
B_j = new double[Adim * Dcols * blocksize];
BT_i = new double[Adim * Drows * blocksize];
//read_in_BD ( DESCD,D, BT_i, B_j, Btsparse ) ;
if ( iam == 0 )
cout << "Generating A, B and D... \n" << endl;
generate_BD(D, BT_i, B_j, &s_BT_i, &s_B_j);
cout << "- B, D generated." << endl;
//Now every process has to read in the sparse matrix A
//makeDiagonalPerturbD(Adim, 1000.0, 1e-10, Asparse); cout << "A is a pert. diag." << endl;
//makeRandCSRUpper(Adim, 0.001, Asparse);
//cout << "nnz(A) = " << Asparse.nonzeros << endl;
//Asparse.loadFromFileSym("/users/drosos/simple/matrices/NornePrimaryJacobian.csr");
if (readAFromFile)
{
Asparse.loadFromFile(filenameA);
cout << "A loaded from file" << endl;
//Asparse.reduceSymmetric();
}
else
{
make3DLaplace(nx, ny, nz, Asparse);
cout << "A is Laplacian" << endl;
shiftIndices(Asparse, -1);
}
cout << "- A generated." << endl;
Asparse.matrixType = SYMMETRIC;
assert(Asparse.nrows == Adim);
assert(Asparse.ncols == Adim);
//if (iam == 0) Asparse.writeToFile("A_debug.csr"); exit(-1234);
if (argc == 7) // if the name of the output file for C is given as parameter
{
filenameC = new char[250];
//strcpy(filenameC, argv[6]);
sprintf(filenameC, "/scratch/daint/verbof/sparsedense/C_%d_%d.csr", Adim, Ddim);
CSRdouble Dmat, Dblock, Csparse, Bblock;
Dblock.nrows=Dblocks * blocksize;
Dblock.ncols=Dblocks * blocksize;
Dblock.allocate ( Dblocks * blocksize, Dblocks * blocksize, 0 );
Dmat.allocate ( 0,0,0 );
for ( i=0; i<Drows; ++i ) {
for ( j=0; j<Dcols; ++j ) {
dense2CSR_sub ( D + i * blocksize + j * lld_D * blocksize,blocksize,blocksize,lld_D,Dblock, ( * ( dims ) * i + *position ) *blocksize,
( * ( dims+1 ) * j + pcol ) *blocksize );
if ( Dblock.nonzeros>0 ) {
if ( Dmat.nonzeros==0 ) {
Dmat.make2 ( Dblock.nrows,Dblock.ncols,Dblock.nonzeros,Dblock.pRows,Dblock.pCols,Dblock.pData );
} else {
Dmat.addBCSR ( Dblock );
}
}
Dblock.clear();
}
}
if ( *position==0 ) {
Bblock.nrows=Adim;
Bblock.ncols=Dblocks * blocksize;
Bblock.allocate ( Adim, Dblocks * blocksize, 0 );
Btsparse.allocate ( 0,0,0 );
for ( j=0; j<Dcols; ++j ) {
dense2CSR_sub ( B_j + j * Adim * blocksize,Adim,blocksize,Adim,Bblock,0, ( * ( dims+1 ) * j + pcol ) *blocksize );
if ( Bblock.nonzeros>0 ) {
if ( Btsparse.nonzeros==0 ) {
Btsparse.make2 ( Bblock.nrows,Bblock.ncols,Bblock.nonzeros,Bblock.pRows,Bblock.pCols,Bblock.pData );
} else {
Btsparse.addBCSR ( Bblock );
}
}
Bblock.clear();
}
}
blacs_barrier_ ( &ICTXT2D,"A" );
if ( iam!=0 ) {
//Each process other than root sends its Dmat to the root process.
MPI_Send ( & ( Dmat.nonzeros ),1, MPI_INT,0,iam,MPI_COMM_WORLD );
MPI_Send ( & ( Dmat.pRows[0] ),Dmat.nrows + 1, MPI_INT,0,iam+size,MPI_COMM_WORLD );
MPI_Send ( & ( Dmat.pCols[0] ),Dmat.nonzeros, MPI_INT,0,iam+2*size,MPI_COMM_WORLD );
MPI_Send ( & ( Dmat.pData[0] ),Dmat.nonzeros, MPI_DOUBLE,0,iam+3*size,MPI_COMM_WORLD );
Dmat.clear();
if ( *position==0 ) {
MPI_Send ( & ( Btsparse.nonzeros ),1, MPI_INT,0,iam+4*size,MPI_COMM_WORLD );
MPI_Send ( & ( Btsparse.pRows[0] ),Btsparse.nrows + 1, MPI_INT,0,iam+5*size,MPI_COMM_WORLD );
MPI_Send ( & ( Btsparse.pCols[0] ),Btsparse.nonzeros, MPI_INT,0,iam+6*size,MPI_COMM_WORLD );
MPI_Send ( & ( Btsparse.pData[0] ),Btsparse.nonzeros, MPI_DOUBLE,0,iam+7*size,MPI_COMM_WORLD );
Btsparse.clear();
}
} else {
//Btsparse.writeToFile("Btsparse_pre.csr");
for ( i=1; i<size; ++i ) {
// The root process receives parts of Dmat sequentially from all processes and directly adds them together.
int nonzeroes, count;
MPI_Recv ( &nonzeroes,1,MPI_INT,i,i,MPI_COMM_WORLD,&status );
/*MPI_Get_count(&status, MPI_INT, &count);
printf("Process 0 received %d elements of process %d\n",count,i);*/
if ( nonzeroes>0 ) {
printf ( "Nonzeroes : %d\n ",nonzeroes );
Dblock.allocate ( Dblocks * blocksize,Dblocks * blocksize,nonzeroes );
MPI_Recv ( & ( Dblock.pRows[0] ), Dblocks * blocksize + 1, MPI_INT,i,i+size,MPI_COMM_WORLD,&status );
/*MPI_Get_count(&status, MPI_INT, &count);
printf("Process 0 received %d elements of process %d\n",count,i);*/
MPI_Recv ( & ( Dblock.pCols[0] ),nonzeroes, MPI_INT,i,i+2*size,MPI_COMM_WORLD,&status );
/*MPI_Get_count(&status, MPI_INT, &count);
printf("Process 0 received %d elements of process %d\n",count,i);*/
MPI_Recv ( & ( Dblock.pData[0] ),nonzeroes, MPI_DOUBLE,i,i+3*size,MPI_COMM_WORLD,&status );
/*MPI_Get_count(&status, MPI_DOUBLE, &count);
printf("Process 0 received %d elements of process %d\n",count,i);*/
Dmat.addBCSR ( Dblock );
Dblock.clear();
}
if ( i / *dims == 0 ) {
MPI_Recv ( &nonzeroes,1,MPI_INT,i,i+4*size,MPI_COMM_WORLD,&status );
/*MPI_Get_count(&status, MPI_INT, &count);
printf("Process 0 received %d elements of process %d\n",count,i);*/
if ( nonzeroes>0 ) {
printf ( "Nonzeroes : %d\n ",nonzeroes );
Bblock.allocate ( Adim,Dblocks * blocksize,nonzeroes );
MPI_Recv ( & ( Bblock.pRows[0] ), Adim + 1, MPI_INT,i,i+5*size,MPI_COMM_WORLD,&status );
/*MPI_Get_count(&status, MPI_INT, &count);
printf("Process 0 received %d elements of process %d\n",count,i);*/
MPI_Recv ( & ( Bblock.pCols[0] ),nonzeroes, MPI_INT,i,i+6*size,MPI_COMM_WORLD,&status );
/*MPI_Get_count(&status, MPI_INT, &count);
printf("Process 0 received %d elements of process %d\n",count,i);*/
MPI_Recv ( & ( Bblock.pData[0] ),nonzeroes, MPI_DOUBLE,i,i+7*size,MPI_COMM_WORLD,&status );
/*MPI_Get_count(&status, MPI_DOUBLE, &count);
printf("Process 0 received %d elements of process %d\n",count,i);*/
Btsparse.addBCSR ( Bblock );
Bblock.clear();
}
}
}
//Dmat.writeToFile("D_sparse.csr");
printf ( "Number of nonzeroes in D: %d\n",Dmat.nonzeros );
Dmat.reduceSymmetric();
//Dmat.writeToFile("D_sparse_symm.csr");
//Btsparse.writeToFile("Btsparse.csr");
Dmat.changeCols(Ddim);
Dmat.changeRows(Ddim);
//Dmat.writeToFile("Dsparse_red.csr");
Btsparse.changeCols(Ddim);
create2x2SymBlockMatrix ( Asparse,Btsparse, Dmat, Csparse );
Btsparse.clear();
Dmat.clear();
ParDiSO p(-2,0);
p.init(Csparse, 1);
p.factorize(Csparse);
//Csparse.fillSymmetric();
//Csparse.writeToFilePSelInv(filenameC);
//Csparse.writeToFile(filenameC);
Csparse.clear();
//double* Cdense = new double[Csparse.nrows * Csparse.ncols];
//CSR2dense(Csparse, Cdense);
//printdense(Adim+Ddim, Adim+Ddim, Cdense, "C.txt");
if ( filenameC != NULL )
free ( filenameC );
filenameC=NULL;
}
if (iam == 0)
{
cout << "\n - C saved in file " << filenameC << "! Exiting... \n\n" << endl;
exit(-12345);
}
}
//AB_sol will contain the solution of A*X=B, distributed across the process rows. Processes in the same process row possess the same part of AB_sol
DESCAB_sol= ( int* ) malloc ( DLEN_ * sizeof ( int ) );
if ( DESCAB_sol==NULL ) {
printf ( "unable to allocate memory for descriptor for AB_sol\n" );
return -1;
}
//AB_sol (Adim, Ddim) is distributed across all processes in ICTXT2D starting from process (0,0) into blocks of size (Adim, blocksize)
descinit_ ( DESCAB_sol, &Adim, &Ddim, &Adim, &blocksize, &i_zero, &i_zero, &ICTXT2D, &Adim, &info );
if ( info!=0 ) {
printf ( "Descriptor of matrix C returns info: %d\n",info );
return info;
}
AB_sol= ( double * ) calloc ( Adim * s_B_j,sizeof ( double ) );
blacs_barrier_ ( &ICTXT2D,"A" );
/********************** TIMING **********************/
if ( iam == 0 )
watch.tick ( totaltime );
if ( iam == 0 )
watch.tick ( cresctime );
// Each process calculates the Schur complement of the part of D at its disposal. (see src/schur.cpp)
// The solution of A * X = B_j is stored in AB_sol (= A^-1 * B_j)
/*
char * BT_i_debugFile = new char[100];
char * B_j_debugFile = new char[100];
sprintf(BT_i_debugFile, "BT_i_debug_%d.txt", iam);
sprintf(B_j_debugFile, "B_j_debug_%d.txt", iam);
BT_i.writeToFile(BT_i_debugFile);
B_j.writeToFile(B_j_debugFile);
*/
make_Sij_denseB ( Asparse, BT_i, B_j, s_BT_i, s_B_j, D, lld_D, AB_sol );
/*
char * AB_sol_debugFile = new char[100];
char * D_debugFile = new char[100];
sprintf(AB_sol_debugFile, "AB_sol_debug_%d.txt", iam);
sprintf(D_debugFile, "D_debug_%d.txt", iam);
printDenseDouble(AB_sol_debugFile, ios::out, Drows*blocksize, Dcols*blocksize, AB_sol);
printDenseDouble(D_debugFile, ios::out, Ddim, Ddim, D);
cout << iam << " just wrote debug stuff... " << endl;
*/
blacs_barrier_ ( &ICTXT2D,"ALL" );
if ( iam == 0 )
watch.tack ( cresctime );
if ( iam !=0 ) {
Asparse.clear();
pardiso_var.clear();
}
//BT_i.clear();
//B_j.clear();
delete[] BT_i;
delete[] B_j;
blacs_barrier_ ( &ICTXT2D,"ALL" );
/********************** TIMING **********************/
if ( iam == 0 )
watch.tick ( facsctime );
//The Schur complement is factorised (by ScaLAPACK)
pdpotrf_ ( "U",&Ddim,D,&i_one,&i_one,DESCD,&info );
if ( info != 0 ) {
printf ( "Cholesky decomposition of D was unsuccessful, error returned: %d\n",info );
return -1;
}
blacs_barrier_ ( &ICTXT2D,"ALL" );
/********************** TIMING **********************/
if ( iam == 0 )
watch.tack ( facsctime );
if ( iam == 0 )
watch.tick ( invsctime );
//The Schur complement is inverteded (by ScaLAPACK)
pdpotri_ ( "U",&Ddim,D,&i_one,&i_one,DESCD,&info );
if ( info != 0 ) {
printf ( "Inverse of D was unsuccessful, error returned: %d\n",info );
return -1;
}
blacs_barrier_ ( &ICTXT2D,"A" );
/********************** TIMING **********************/
if ( iam == 0 )
watch.tack ( invsctime );
InvD_T_Block = ( double* ) calloc ( Dblocks * blocksize + Adim ,sizeof ( double ) );
if ( iam == 0 )
watch.tick ( gathrtime );
blacs_barrier_ ( &ICTXT2D,"A" );
/********************** TIMING **********************/
if ( iam == 0 )
watch.tick ( sndrctime );
//Diagonal elements of the (1,1) block of C^-1 are still distributed and here they are gathered in InvD_T_Block in the root process.
if ( *position == pcol ) {
for ( i=0; i<Ddim; ++i ) {
if ( pcol == ( i/blocksize ) % *dims ) {
int Dpos = i%blocksize + ( ( i/blocksize ) / *dims ) * blocksize ;
* ( InvD_T_Block + Adim +i ) = * ( D + Dpos + lld_D * Dpos );
}
}
for ( i=0,j=0; i<Dblocks; ++i,++j ) {
if ( j==*dims )
j=0;
if ( *position==j ) {
dgesd2d_ ( &ICTXT2D,&blocksize,&i_one,InvD_T_Block + Adim + i * blocksize,&blocksize,&i_zero,&i_zero );
}
if ( *position==0 ) {
dgerv2d_ ( &ICTXT2D,&blocksize,&i_one,InvD_T_Block + Adim + blocksize*i,&blocksize,&j,&j );
}
}
}
blacs_barrier_ ( &ICTXT2D,"A" );
/********************** TIMING **********************/
if ( iam == 0 )
watch.tack ( sndrctime );
if ( position != NULL ) {
free ( position );
position=NULL;
}
if ( dims != NULL ) {
free ( dims );
dims=NULL;
}
//Only the root process performs a selected inversion of A.
if ( iam==0 ) {
watch.tick ( invrAtime );
/*int pardiso_message_level = 1;
int pardiso_mtype=-2;
ParDiSO pardiso ( pardiso_mtype, pardiso_message_level );*/
int number_of_processors = 1;
char* var = getenv ( "OMP_NUM_THREADS" );
if ( var != NULL )
sscanf ( var, "%d", &number_of_processors );
else {
printf ( "Set environment OMP_NUM_THREADS to 1" );
exit ( 1 );
}
pardiso_var.iparm[2] = 2;
pardiso_var.iparm[3] = number_of_processors;
pardiso_var.iparm[8] = 0;
pardiso_var.iparm[11] = 1;
pardiso_var.iparm[13] = 0;
pardiso_var.iparm[28] = 0;
//This function calculates the factorisation of A once again so this might be optimized.
pardiso_var.findInverseOfA ( Asparse );
cout << "Memory allocated by pardiso: " << pardiso_var.memoryAllocated() << endl;
printf ( "Processor %d inverted matrix A\n",iam );
watch.tack ( invrAtime );
}
blacs_barrier_ ( &ICTXT2D,"A" );
// To minimize memory usage, and because only the diagonal elements of the inverse are needed, X' * S is calculated row by row
// the diagonal element is calculated as the dot product of this row and the corresponding column of X. (X is solution of AX=B)
XSrow= ( double* ) calloc ( Dcols * blocksize,sizeof ( double ) );
DESCXSROW= ( int* ) malloc ( DLEN_ * sizeof ( int ) );
if ( DESCXSROW==NULL ) {
printf ( "unable to allocate memory for descriptor for AB_sol\n" );
return -1;
}
//XSrow (1,Ddim) is distributed acrros processes of ICTXT2D starting from process (0,0) into blocks of size (1,blocksize)
descinit_ ( DESCXSROW, &i_one, &Ddim, &i_one,&blocksize, &i_zero, &i_zero, &ICTXT2D, &i_one, &info );
if ( info!=0 ) {
printf ( "Descriptor of matrix C returns info: %d\n",info );
return info;
}
blacs_barrier_ ( &ICTXT2D,"A" );
if ( iam == 0 )
cout << "Calculating diagonal elements of the first block of the inverse... \n" << endl;
blacs_barrier_ ( &ICTXT2D,"A" );
/********************** TIMING **********************/
if ( iam == 0 )
watch.tick ( dotprtime );
//Calculating diagonal elements 1 by 1 of the (0,0)-block of C^-1.
for ( i=1; i<=Adim; ++i ) {
pdsymm_ ( "R","U",&i_one,&Ddim,&d_one,D,&i_one,&i_one,DESCD,AB_sol,&i,&i_one,DESCAB_sol,&d_zero,XSrow,&i_one,&i_one,DESCXSROW );
pddot_ ( &Ddim,InvD_T_Block+i-1,AB_sol,&i,&i_one,DESCAB_sol,&Adim,XSrow,&i_one,&i_one,DESCXSROW,&i_one );
}
blacs_barrier_ ( &ICTXT2D,"A" );
/********************** TIMING **********************/
if ( iam == 0 )
watch.tack ( dotprtime );
if ( D!=NULL ) {
free ( D );
D=NULL;
}
if ( AB_sol!=NULL ) {
free ( AB_sol );
AB_sol=NULL;
}
if ( XSrow !=NULL ) {
free ( XSrow );
XSrow=NULL;
}
if ( DESCD!=NULL ) {
free ( DESCD );
DESCD=NULL;
}
if ( DESCAB_sol!=NULL ) {
free ( DESCAB_sol );
DESCAB_sol=NULL;
}
if ( DESCXSROW!=NULL ) {
free ( DESCXSROW );
DESCXSROW=NULL;
}
//Only in the root process we add the diagonal elements of A^-1
if ( iam ==0 ) {
for ( i = 0; i < Adim; i++ ) {
j = Asparse.pRows[i];
* ( InvD_T_Block+i ) += Asparse.pData[j];
}
/********************** TIMING **********************/
watch.tack ( gathrtime );
watch.tack ( totaltime );
/*
//cout << "Extraction completed by ";
for (i = 0; i < Ddim; i++)
{
cout << "Extracting row " << i << "/" << Ddim << endl;
//cout << setw(3) << std::setfill('0') << int(i*100.0 / (Ddim-1)) << "%" << "\b\b\b\b";
diagonal[Asparse.nrows + i] = InvD_T_Block[i*Ddim + i];
}
cout << endl;
*/
Asparse.clear();
/*
cout << "Extracting diagonal... \n" << endl;
cout << "Saving diagonal... \n" << endl;
char* diagOutFile = new char[50];
sprintf ( diagOutFile, "diag_inverse_C_parallel_%d.txt", size );
printdense ( Adim+Ddim, 1, InvD_T_Block, diagOutFile );
delete[] diagOutFile;
*/
}
if ( InvD_T_Block !=NULL ) {
free ( InvD_T_Block );
InvD_T_Block=NULL;
}
if ( iam == 0 ) {
// Conversion milliseconds -> seconds
cresctime /= 1000.0;
facsctime /= 1000.0;
invsctime /= 1000.0;
gathrtime /= 1000.0;
invrAtime /= 1000.0;
totaltime /= 1000.0;
cout << "********************************* TIME REPORT ********************************** \n" << endl;
cout << " SCHUR COMPLEMENT BUILDING: " << cresctime << " seconds" << endl;
cout << " SCHUR COMPLEMENT FACTORIZATION: " << facsctime << " seconds" << endl;
cout << " SCHUR COMPLEMENT INVERSION: " << invsctime << " seconds" << endl;
cout << " " << endl;
cout << " FINAL OPERATIONS (INVERSION OF A INCLUDED): " << gathrtime << " seconds" << endl;
cout << " INVERSION OF A: " << invrAtime << " seconds" << endl;
cout << " TOTAL TIME: " << totaltime << " seconds" << endl;
cout << "******************************************************************************** \n" << endl;
/*
* double totaltime = 0.0; // Total execution time
* double cresctime = 0.0; // Schur-complement (total)
* double facsctime = 0.0; // Schur-complement factorization
* double invsctime = 0.0; // Schur-complement inversion
* double gathrtime = 0.0; // Last operationsdouble invrAtime = 0.0; // Inversion of A
* */
char* timingFile = new char[50];
sprintf ( timingFile, "weak_tests.csv" );
std::fstream timeF;
timeF.open ( timingFile, std::fstream::out | std::fstream::app );
timeF.setf ( ios::scientific, ios::floatfield );
//timeF << "PROBLEM SIZE: " << Adim/1000 << "k + " << Ddim/1000 << "k" << endl;
//timeF <<
//"#PROCS,SCHUR_BUILD,SCHUR_FACT,SCHUR_INV,INV(A),FINAL_OPS,
//SEND_RECV, DOT_PROD,TOTAL" << endl;
timeF << size << "," << cresctime << "," << facsctime << "," << invsctime << "," << invrAtime << "," << gathrtime << "," << sndrctime << "," << dotprtime << "," << totaltime << endl;
timeF.close();
}
blacs_barrier_ ( &ICTXT2D,"A" );
blacs_gridexit_ ( &ICTXT2D );
}
//cout << iam << " reached end before MPI_Barrier" << endl;
MPI_Barrier ( MPI_COMM_WORLD );
MPI_Finalize();
return 0;
}
/*==== MAIN FUNCTION =================================================*/
int main( int argc, char *argv[] ){
/* ==== Declarations =================================================== */
/* File variables */
FILE *fin;
/* Matrix descriptors */
MDESC descA, descB, descC, descA_local, descB_local;
/* Local scalars */
MKL_INT iam, nprocs, ictxt, myrow, mycol, nprow, npcol;
MKL_INT n, nb, mp, nq, lld, lld_local;
MKL_INT i, j, info;
int n_int, nb_int, nprow_int, npcol_int;
double thresh, diffnorm, anorm, bnorm, residual, eps;
/* Local arrays */
double *A_local, *B_local, *A, *B, *C, *work;
MKL_INT iwork[ 4 ];
/* ==== Executable statements ========================================== */
/* Get information about how many processes are used for program execution
and number of current process */
blacs_pinfo_( &iam, &nprocs );
/* Init temporary 1D process grid */
blacs_get_( &i_negone, &i_zero, &ictxt );
blacs_gridinit_( &ictxt, "C", &nprocs, &i_one );
/* Open input file */
if ( iam == 0 ) {
fin = fopen( "../in/pblas3ex.in", "r" );
if ( fin == NULL ) {
printf( "Error while open input file." );
return 2;
}
}
/* Read data and send it to all processes */
if ( iam == 0 ) {
/* Read parameters */
fscanf( fin, "%d n, dimension of vectors, must be > 0 ", &n_int );
fscanf( fin, "%d nb, size of blocks, must be > 0 ", &nb_int );
fscanf( fin, "%d p, number of rows in the process grid, must be > 0", &nprow_int );
fscanf( fin, "%d q, number of columns in the process grid, must be > 0, p*q = number of processes", &npcol_int );
fscanf( fin, "%lf threshold for residual check (to switch off check set it < 0.0) ", &thresh );
n = (MKL_INT) n_int;
nb = (MKL_INT) nb_int;
nprow = (MKL_INT) nprow_int;
npcol = (MKL_INT) npcol_int;
/* Check if all parameters are correct */
if( ( n<=0 )||( nb<=0 )||( nprow<=0 )||( npcol<=0 )||( nprow*npcol != nprocs ) ) {
printf( "One or several input parameters has incorrect value. Limitations:\n" );
printf( "n > 0, nb > 0, p > 0, q > 0 - integer\n" );
printf( "p*q = number of processes\n" );
printf( "threshold - double (set to negative to swicth off check)\n");
return 2;
}
/* Pack data into array and send it to other processes */
iwork[ 0 ] = n;
iwork[ 1 ] = nb;
iwork[ 2 ] = nprow;
iwork[ 3 ] = npcol;
igebs2d_( &ictxt, "All", " ", &i_four, &i_one, iwork, &i_four );
dgebs2d_( &ictxt, "All", " ", &i_one, &i_one, &thresh, &i_one );
} else {
/* Recieve and unpack data */
igebr2d_( &ictxt, "All", " ", &i_four, &i_one, iwork, &i_four, &i_zero, &i_zero );
dgebr2d_( &ictxt, "All", " ", &i_one, &i_one, &thresh, &i_one, &i_zero, &i_zero );
n = iwork[ 0 ];
nb = iwork[ 1 ];
nprow = iwork[ 2 ];
npcol = iwork[ 3 ];
}
if ( iam == 0 ) { fclose( fin ); }
/* Destroy temporary process grid */
blacs_gridexit_( &ictxt );
/* Init workind 2D process grid */
blacs_get_( &i_negone, &i_zero, &ictxt );
blacs_gridinit_( &ictxt, "R", &nprow, &npcol );
blacs_gridinfo_( &ictxt, &nprow, &npcol, &myrow, &mycol );
/* Create on process 0 two matrices: A - orthonormal, B -random */
if ( ( myrow == 0 ) && ( mycol == 0 ) ){
/* Allocate arrays */
A_local = (double*) calloc( n*n, sizeof( double ) );
B_local = (double*) calloc( n*n, sizeof( double ) );
/* Set arrays */
for ( i=0; i<n; i++ ){
for ( j=0; j<n; j++ ){
B_local[ i+n*j ] = one*rand()/RAND_MAX;
}
B_local[ i+n*i ] += two;
}
for ( j=0; j<n; j++ ){
for ( i=0; i<n; i++ ){
if ( j < n-1 ){
if ( i <= j ){
A_local[ i+n*j ] = one / sqrt( ( double )( (j+1)*(j+2) ) );
} else if ( i == j+1 ) {
A_local[ i+n*j ] = -one / sqrt( one + one/( double )(j+1) );
} else {
A_local[ i+n*j ] = zero;
}
} else {
A_local[ i+n*(n-1) ] = one / sqrt( ( double )n );
}
}
}
/* Print information of task */
printf( "=== START OF EXAMPLE ===================\n" );
printf( "Matrix-matrix multiplication: A*B = C\n\n" );
printf( "/ 1/q_1 ........ 1/q_n-1 1/q_n \\ \n" );
printf( "| . | \n" );
printf( "| `. : : | \n" );
printf( "| -1/q_1 `. : : | \n" );
printf( "| . `. : : | = A \n" );
printf( "| 0 `. ` | \n" );
printf( "| : `. `. 1/q_n-1 1/q_n | \n" );
printf( "| : `. `. | \n" );
printf( "\\ 0 .... 0 -(n-1)/q_n-1 1/q_n / \n\n" );
printf( "q_i = sqrt( i^2 + i ), i=1..n-1, q_n = sqrt( n )\n\n" );
printf( "A - n*n real matrix (orthonormal) \n" );
printf( "B - random n*n real matrix\n\n" );
printf( "n = %d, nb = %d; %dx%d - process grid\n\n", n, nb, nprow, npcol );
printf( "=== PROGRESS ===========================\n" );
} else {
/* Other processes don't contain parts of initial arrays */
A_local = NULL;
B_local = NULL;
}
/* Compute precise length of local pieces and allocate array on
each process for parts of distributed vectors */
mp = numroc_( &n, &nb, &myrow, &i_zero, &nprow );
nq = numroc_( &n, &nb, &mycol, &i_zero, &npcol );
A = (double*) calloc( mp*nq, sizeof( double ) );
B = (double*) calloc( mp*nq, sizeof( double ) );
C = (double*) calloc( mp*nq, sizeof( double ) );
/* Compute leading dimensions */
lld_local = MAX( numroc_( &n, &n, &myrow, &i_zero, &nprow ), 1 );
lld = MAX( mp, 1 );
/* Initialize descriptors for initial arrays located on 0 process */
descinit_( descA_local, &n, &n, &n, &n, &i_zero, &i_zero, &ictxt, &lld_local, &info );
descinit_( descB_local, &n, &n, &n, &n, &i_zero, &i_zero, &ictxt, &lld_local, &info );
/* Initialize descriptors for distributed arrays */
descinit_( descA, &n, &n, &nb, &nb, &i_zero, &i_zero, &ictxt, &lld, &info );
descinit_( descB, &n, &n, &nb, &nb, &i_zero, &i_zero, &ictxt, &lld, &info );
descinit_( descC, &n, &n, &nb, &nb, &i_zero, &i_zero, &ictxt, &lld, &info );
/* Distribute matrices from 0 process over process grid */
pdgeadd_( &trans, &n, &n, &one, A_local, &i_one, &i_one, descA_local, &zero, A, &i_one, &i_one, descA );
pdgeadd_( &trans, &n, &n, &one, B_local, &i_one, &i_one, descB_local, &zero, B, &i_one, &i_one, descB );
if( iam == 0 ){ printf( ".. Arrays are distributed ( p?geadd ) ..\n" ); }
/* Destroy arrays on 0 process - they are not necessary anymore */
if( ( myrow == 0 ) && ( mycol == 0 ) ){
free( A_local );
free( B_local );
}
/* Compute norm of A and B */
work = (double*) calloc( mp, sizeof( double ) );
anorm = pdlange_( "I", &n, &n, A, &i_one, &i_one, descA, work );
bnorm = pdlange_( "I", &n, &n, B, &i_one, &i_one, descB, work );
if( iam == 0 ){ printf( ".. Norms of A and B are computed ( p?lange ) ..\n" ); }
/* Compute product C = A*B */
pdgemm_( "N", "N", &n, &n, &n, &one, A, &i_one, &i_one, descA, B, &i_one, &i_one, descB,
&zero, C, &i_one, &i_one, descC );
if( iam == 0 ){ printf( ".. Multiplication A*B=C is done ( p?gemm ) ..\n" ); }
/* Compute difference B - inv_A*C (inv_A = transpose(A) because A is orthonormal) */
pdgemm_( "T", "N", &n, &n, &n, &one, A, &i_one, &i_one, descA, C, &i_one, &i_one, descC,
&negone, B, &i_one, &i_one, descB );
if( iam == 0 ){ printf( ".. Difference is computed ( p?gemm ) ..\n" ); }
/* Compute norm of B - inv_A*C (which is contained in B) */
diffnorm = pdlange_( "I", &n, &n, B, &i_one, &i_one, descB, work );
free( work );
if( iam == 0 ){ printf( ".. Norms of the difference B-inv_A*C is computed ( p?lange ) ..\n" ); }
/* Print results */
if( iam == 0 ){
printf( ".. Solutions are compared ..\n" );
printf( "== Results ==\n" );
printf( "||A|| = %03.11f\n", anorm );
printf( "||B|| = %03.11f\n", bnorm );
printf( "=== END OF EXAMPLE =====================\n" );
}
/* Compute machine epsilon */
eps = pdlamch_( &ictxt, "e" );
/* Compute residual */
residual = diffnorm /( two*anorm*bnorm*eps );
/* Destroy arrays */
free( A );
free( B );
free( C );
/* Destroy process grid */
blacs_gridexit_( &ictxt );
blacs_exit_( &i_zero );
/* Check if residual passed or failed the threshold */
if ( ( iam == 0 ) && ( thresh >= zero ) && !( residual <= thresh ) ){
printf( "FAILED. Residual = %05.16f\n", residual );
return 1;
} else {
return 0;
}
/*========================================================================
====== End of PBLAS Level 3 example ====================================
======================================================================*/
}
int main (int argc, char *argv[]) {
myscalar *A=NULL, *X=NULL, *B=NULL, *Y=NULL, *Xtrue=NULL;
myscalar elem;
int descA[BLACSCTXTSIZE], descVec[BLACSCTXTSIZE], descelem[BLACSCTXTSIZE];
int n;
int nrhs;
int nb;
int locr, locc;
int i, j, ii, jj;
int ierr;
int dummy;
int myid, np;
int myrow, mycol, nprow, npcol;
int ctxt;
myreal rdummy, res;
n=1024; /* Size of the problem */
nrhs=3; /* Number of RHS */
nb=16; /* Blocksize for the 2D block-cyclic distribution */
/* Initialize MPI */
if((ierr=MPI_Init(&argc,&argv)))
return 1;
myid=-1;
if((ierr=MPI_Comm_rank(MPI_COMM_WORLD,&myid)))
return 1;
np=-1;
if((ierr=MPI_Comm_size(MPI_COMM_WORLD,&np)))
return 1;
/* Initialize the BLACS grid */
nprow=floor(sqrt((float)np));
npcol=np/nprow;
blacs_get_(&IZERO,&IZERO,&ctxt);
blacs_gridinit_(&ctxt,"R",&nprow,&npcol);
blacs_gridinfo_(&ctxt,&nprow,&npcol,&myrow,&mycol);
/* A is a dense n x n distributed Toeplitz matrix */
if(myid<nprow*npcol) {
locr=numroc_(&n,&nb,&myrow,&IZERO,&nprow);
locc=numroc_(&n,&nb,&mycol,&IZERO,&npcol);
A=new myscalar[locr*locc];
dummy=std::max(1,locr);
descinit_(descA,&n,&n,&nb,&nb,&IZERO,&IZERO,&ctxt,&dummy,&ierr);
myreal pi=3.1416, d=0.1;
for(i=1;i<=locr;i++) {
for(j=1;j<=locc;j++) {
ii=indxl2g_(&i,&nb,&myrow,&IZERO,&nprow);
jj=indxl2g_(&j,&nb,&mycol,&IZERO,&npcol);
// Toeplitz matrix from Quantum Chemistry.
A[locr*(j-1)+(i-1)]=ii==jj?std::pow(pi,2)/6.0/std::pow(d,2):std::pow(-1.0,ii-jj)/std::pow((myreal)ii-jj,2)/std::pow(d,2);
}
}
} else {
descset_(descA,&n,&n,&nb,&nb,&IZERO,&IZERO,&INONE,&IONE);
}
/* Initializing solution */
if(myid<nprow*npcol) {
locr=numroc_(&n,&nb,&myrow,&IZERO,&nprow);
locc=numroc_(&nrhs,&nb,&mycol,&IZERO,&npcol);
dummy=std::max(1,locr);
descinit_(descVec,&n,&nrhs,&nb,&nb,&IZERO,&IZERO,&ctxt,&dummy,&ierr);
Xtrue=new myscalar[locr*locc]();
for(i=0;i<locr*locc;i++)
Xtrue[i]=static_cast<myscalar>(rand())/(static_cast<myscalar>(RAND_MAX));
} else {
descset_(descVec,&n,&nrhs,&nb,&nb,&IZERO,&IZERO,&INONE,&IONE);
}
/* Initializing solution and intermediate vector space */
if(myid<nprow*npcol) {
X=new myscalar[locr*locc]();
Y=new myscalar[locr*locc]();
}
/* Initializing RHS as A*Xtrue */
if(myid<nprow*npcol) {
B=new myscalar[locr*locc]();
pgemm('N','N',n,nrhs,n,ONE,A,IONE,IONE,descA,Xtrue,IONE,IONE,descVec,ZERO,B,IONE,IONE,descVec);
}
/* Initialize the solver and set parameters */
StrumpackDensePackage<myscalar,myreal> sdp(MPI_COMM_WORLD);
sdp.use_HSS=true;
sdp.levels_HSS=4;
sdp.min_rand_HSS=64;
sdp.lim_rand_HSS=0;
sdp.tol_HSS=1e-12;
sdp.split_HSS=768; /* Size of A11 */
/* Compression */
sdp.compress(A,descA);
/* Accuracy checking */
sdp.check_compression(A,descA);
/* Factorization */
sdp.partially_factor(A,descA,sdp.split_HSS);
/* Schur complement update */
sdp.compute_schur();
/* Extracting a random element from the Schur complement */
if(myid<nprow*npcol) {
descinit_(descelem,&IONE,&IONE,&nb,&nb,&IZERO,&IZERO,&ctxt,&dummy,&ierr);
} else {
descset_(descelem,&IONE,&IONE,&nb,&nb,&IZERO,&IZERO,&INONE,&IONE);
}
i=1+rand()%(n-sdp.split_HSS);
j=1+rand()%(n-sdp.split_HSS);
MPI_Bcast((void *)&i,IONE,MPI_INTEGER,IZERO,MPI_COMM_WORLD);
MPI_Bcast((void *)&j,IONE,MPI_INTEGER,IZERO,MPI_COMM_WORLD);
sdp.extract_schur(&elem,descelem,&i,IONE,&j,IONE);
if(!myid)
std::cout << "Element (" << i << "," << j << ") of Schur complement = " << elem << std::endl << std::endl;
/* Condensation */
sdp.reduce_RHS(Y,descVec,B,descVec);
/* Solve the Schur complement system (touches only the bottom part of X)*/
sdp.verbose=false;
if(!myid)
std::cout << "Solving Schur complement system with Conjugate Gradient..." << std::endl << std::endl;
CG(&sdp,X,Y,descVec,n,nrhs,3000,1e-14);
sdp.verbose=true;
/* Expansion (touches only the top part of X) */
sdp.expand_solution(X,descVec,Y,descVec);
/* Accuracy checking */
sdp.check_solution(A,descA,X,descVec,B,descVec);
/* Forward error */
if(myid<nprow*npcol) {
for(i=0;i<locr*locc;i++)
Y[i]=X[i]-Xtrue[i];
res=plange('F',n,nrhs,Y,IONE,IONE,descVec,&rdummy);
res/=plange('F',n,nrhs,Xtrue,IONE,IONE,descVec,&rdummy);
if(!myid)
std::cout << "Forward error = " << res << std::endl;
}
/* Statistics */
sdp.print_statistics();
/* Clean-up */
delete[] A;
delete[] B;
delete[] X;
delete[] Y;
delete[] Xtrue;
/* The end */
MPI_Finalize();
return 0;
}
int main (int argc, char *argv[]) {
myscalar *A=NULL, *B=NULL, *Btrue=NULL;
int descA[BLACSCTXTSIZE], descB[BLACSCTXTSIZE];
int n;
int nb;
int locr, locc;
int i, j, ii, jj;
int *I, *J;
int nI, nJ;
int ierr;
int dummy;
int myid, np;
int myrow, mycol, nprow, npcol;
int ctxt;
myreal err;
n=1024; /* Size of the problem */
nb=16; /* Blocksize for the 2D block-cyclic distribution */
/* Initialize MPI */
if((ierr=MPI_Init(&argc,&argv)))
return 1;
myid=-1;
if((ierr=MPI_Comm_rank(MPI_COMM_WORLD,&myid)))
return 1;
np=-1;
if((ierr=MPI_Comm_size(MPI_COMM_WORLD,&np)))
return 1;
/* Initialize the BLACS grid */
nprow=floor(sqrt((float)np));
npcol=np/nprow;
blacs_get_(&IZERO,&IZERO,&ctxt);
blacs_gridinit_(&ctxt,"R",&nprow,&npcol);
blacs_gridinfo_(&ctxt,&nprow,&npcol,&myrow,&mycol);
/* A is a dense n x n distributed Toeplitz matrix */
if(myid<nprow*npcol) {
locr=numroc_(&n,&nb,&myrow,&IZERO,&nprow);
locc=numroc_(&n,&nb,&mycol,&IZERO,&npcol);
A=new myscalar[locr*locc];
dummy=std::max(1,locr);
descinit_(descA,&n,&n,&nb,&nb,&IZERO,&IZERO,&ctxt,&dummy,&ierr);
for(i=1;i<=locr;i++)
for(j=1;j<=locc;j++) {
ii=indxl2g_(&i,&nb,&myrow,&IZERO,&nprow);
jj=indxl2g_(&j,&nb,&mycol,&IZERO,&npcol);
// Toeplitz matrix from Quantum Chemistry.
myreal pi=3.1416, d=0.1;
A[locr*(j-1)+(i-1)]=ii==jj?std::pow(pi,2)/6.0/std::pow(d,2):std::pow(-1.0,ii-jj)/std::pow((myreal)ii-jj,2)/std::pow(d,2);
}
} else {
descset_(descA,&n,&n,&nb,&nb,&IZERO,&IZERO,&INONE,&IONE);
}
/* Initialize the solver and set parameters */
StrumpackDensePackage<myscalar,myreal> sdp(MPI_COMM_WORLD);
sdp.use_HSS=true;
sdp.levels_HSS=4;
sdp.min_rand_HSS=64;
sdp.lim_rand_HSS=0;
sdp.tol_HSS=1e-6;
/* Compression */
sdp.compress(A,descA);
/* Accuracy checking */
sdp.check_compression(A,descA);
/* Element extraction: a bunch of random indices.
* Not that duplicates do not matter (the code works).
*/
nI=1+rand()%n;
MPI_Bcast((void*)&nI,IONE,MPI_INTEGER,IZERO,MPI_COMM_WORLD);
I=new int[nI];
if(!myid)
for(i=0;i<nI;i++)
I[i]=1+rand()%n;
MPI_Bcast((void*)I,nI,MPI_INTEGER,IZERO,MPI_COMM_WORLD);
nJ=1+rand()%n;
MPI_Bcast((void*)&nJ,IONE,MPI_INTEGER,IZERO,MPI_COMM_WORLD);
J=new int[nJ];
if(!myid)
for(j=0;j<nJ;j++)
J[j]=1+rand()%n;
MPI_Bcast((void*)J,nJ,MPI_INTEGER,IZERO,MPI_COMM_WORLD);
/* Extraction for the HSS form */
if(myid<nprow*npcol) {
locr=numroc_(&nI,&nb,&myrow,&IZERO,&nprow);
locc=numroc_(&nJ,&nb,&mycol,&IZERO,&npcol);
B=new myscalar[locr*locc]();
dummy=std::max(1,locr);
descinit_(descB,&nI,&nJ,&nb,&nb,&IZERO,&IZERO,&ctxt,&dummy,&ierr);
} else
descset_(descB,&nI,&nJ,&nb,&nb,&IZERO,&IZERO,&INONE,&IONE);
sdp.extract(A,descA,B,descB,I,nI,J,nJ);
/* Extraction from the original matrix just to compare */
sdp.use_HSS=false;
if(myid<nprow*npcol)
Btrue=new myscalar[locr*locc];
sdp.extract(A,descA,Btrue,descB,I,nI,J,nJ);
/* Comparison with elements of input matrix */
if(myid<nprow*npcol){
err=plange('M',nI,nJ,Btrue,IONE,IONE,descB,(myreal*)NULL);
for(i=0;i<locr*locc;i++)
Btrue[i]-=B[i];
err=plange('M',nI,nJ,Btrue,IONE,IONE,descB,(myreal*)NULL)/err;
}
if(!myid)
std::cout << "Element extraction (" << nI << "x" << nJ << " submatrix): maximum relative error max ||A(I,J)-HSS(I,J)||//||A(I,J)|| = " << err << std::endl << std::endl;
/* Statistics */
sdp.print_statistics();
/* Clean-up */
delete[] A;
delete[] B;
delete[] Btrue;
delete[] I;
delete[] J;
/* The end */
MPI_Finalize();
return 0;
}
