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;
}
