bool ParDiSO::makeSchurComplement(CSRdouble& A, CSRdouble& S)
{
double ddum;
shiftIndices_(A, 1);
//shiftIndices_(S, 1);
// Check if this matrix is OK
PARDISOCHECK_D(&mtype,
&A.nrows,
A.pData,
A.pRows,
A.pCols,
&error);
error_();
phase = 12;
iparm[38] = S.nrows;
// Perform symbolic analysis and numerical factorization
PARDISOCALL_D(pt,
&maxfct,
&mnum,
&mtype,
&phase,
&A.nrows,
A.pData,
A.pRows,
A.pCols,
perm,
&nrhs,
&iparm[1],
&msglvl,
&ddum,
&ddum,
&error,
&dparm[1]);
S.nonzeros = int(iparm[39]);
S.allocate(S.nrows, S.ncols, S.nonzeros);
// calculate and store the Schur-complement
PARDISOSCHUR_D(pt,
&maxfct,
&mnum,
&mtype,
S.pData,
S.pRows,
S.pCols);
shiftIndices_(S, -1);
shiftIndices_(A, -1);
error_();
int nonzeros = S.pRows[S.nrows];
bool is_it_full = false;
if (nonzeros == S.nrows*S.ncols)
is_it_full = true;
return is_it_full;
}
int set_up_BD ( int * DESCD, double * Dmat, CSRdouble& BT_i, CSRdouble& B_j, CSRdouble& Btsparse ) {
// Read-in of matrices X, Z and T from file (filename[X,Z,T])
// X and Z are read in entrely by every process
// T is read in strip by strip (number of rows in each process is at maximum = blocksize)
// D is constructed directly in a distributed way
// B is first assembled sparse in root process and afterwards the necessary parts
// for constructing the distributed Schur complement are sent to each process
FILE *fT;
int ni, i,j, info;
int *DESCT;
double *Tblock, *temp;
int nTblocks, nstrips, pTblocks, stripcols, lld_T, pcol, colcur,rowcur;
CSRdouble Xtsparse, Ztsparse,XtT_sparse,ZtT_sparse,XtT_temp, ZtT_temp;
Xtsparse.loadFromFile ( filenameX );
Ztsparse.loadFromFile ( filenameZ );
Xtsparse.transposeIt ( 1 );
Ztsparse.transposeIt ( 1 );
XtT_sparse.allocate ( m,k,0 );
ZtT_sparse.allocate ( l,k,0 );
pcol= * ( position+1 );
// Matrix T is read in by strips of size (blocksize * *(dims+1), k)
// Strips of T are read in row-wise and thus it is as if we store strips of T' (transpose) column-wise with dimensions (k, blocksize * *(dims+1))
// However we must then also transpose the process grid to distribute T' correctly
// number of strips in which we divide matrix T'
nstrips= n % ( blocksize * * ( dims+1 ) ) ==0 ? n / ( blocksize * * ( dims+1 ) ) : ( n / ( blocksize * * ( dims+1 ) ) ) +1;
//the number of columns of T' included in each strip
stripcols= blocksize * * ( dims+1 );
//number of blocks necessary to store complete column of T'
nTblocks= k%blocksize==0 ? k/blocksize : k/blocksize +1;
//number of blocks necessary in this process to store complete column of T'
pTblocks= ( nTblocks - *position ) % *dims == 0 ? ( nTblocks- *position ) / *dims : ( nTblocks- *position ) / *dims +1;
pTblocks= pTblocks <1? 1:pTblocks;
//local leading dimension of the strip of T' (different from process to process)
lld_T=pTblocks*blocksize;
// Initialisation of descriptor of strips of matrix T'
DESCT= ( int* ) malloc ( DLEN_ * sizeof ( int ) );
if ( DESCT==NULL ) {
printf ( "unable to allocate memory for descriptor for Z\n" );
return -1;
}
// strip of T (k,stripcols) is distributed across ICTXT2D starting in process (0,0) in blocks of size (blocksize,blocksize)
// the local leading dimension in this process is lld_T
descinit_ ( DESCT, &k, &stripcols, &blocksize, &blocksize, &i_zero, &i_zero, &ICTXT2D, &lld_T, &info );
if ( info!=0 ) {
printf ( "Descriptor of matrix Z returns info: %d\n",info );
return info;
}
// Allocation of memory for the strip of T' in all processes
Tblock= ( double* ) calloc ( pTblocks*blocksize*blocksize, sizeof ( double ) );
if ( Tblock==NULL ) {
printf ( "Error in allocating memory for a strip of Z in processor (%d,%d)",*position,* ( position+1 ) );
return -1;
}
// Initialisation of matrix D (all diagonal elements of D equal to lambda)
temp=Dmat;
for ( i=0,rowcur=0,colcur=0; i<Dblocks; ++i, ++colcur, ++rowcur ) {
if ( rowcur==*dims ) {
rowcur=0;
temp += blocksize;
}
if ( colcur==* ( dims+1 ) ) {
colcur=0;
temp += blocksize*lld_D;
}
if ( *position==rowcur && * ( position+1 ) == colcur ) {
for ( j=0; j<blocksize; ++j ) {
* ( temp + j * lld_D +j ) =lambda;
}
if ( i==Dblocks-1 && Ddim % blocksize != 0 ) {
for ( j=blocksize-1; j>= Ddim % blocksize; --j ) {
* ( temp + j * lld_D + j ) =0.0;
}
}
}
}
fT=fopen ( filenameT,"rb" );
if ( fT==NULL ) {
printf ( "Error opening file\n" );
return -1;
}
// Set up of matrix D and B per strip of T'
for ( ni=0; ni<nstrips; ++ni ) {
if ( ni==nstrips-1 ) {
if(Tblock != NULL)
free ( Tblock );
Tblock=NULL;
Tblock= ( double* ) calloc ( pTblocks*blocksize*blocksize, sizeof ( double ) );
if ( Tblock==NULL ) {
printf ( "Error in allocating memory for a strip of Z in processor (%d,%d)\n",*position,* ( position+1 ) );
return -1;
}
}
//Each process only reads in a part of the strip of T'
//When k is not a multiple of blocksize, read-in of the last elements of the rows of T is tricky
if ( ( nTblocks-1 ) % *dims == *position && k%blocksize !=0 ) {
if ( ni==0 ) {
info=fseek ( fT, ( long ) ( pcol * blocksize * ( k ) * sizeof ( double ) ),SEEK_SET );
if ( info!=0 ) {
printf ( "Error in setting correct begin position for reading Z file\nprocessor (%d,%d), error: %d \n", *position,pcol,info );
return -1;
}
} else {
info=fseek ( fT, ( long ) ( blocksize * ( * ( dims+1 )-1 ) * ( k ) * sizeof ( double ) ),SEEK_CUR );
if ( info!=0 ) {
printf ( "Error in setting correct begin position for reading Z file\nprocessor (%d,%d), error: %d \n", *position,pcol,info );
return -1;
}
}
for ( i=0; i<blocksize; ++i ) {
info=fseek ( fT, ( long ) ( blocksize * *position * sizeof ( double ) ),SEEK_CUR );
if ( info!=0 ) {
printf ( "Error in setting correct begin position for reading Z file\nprocessor (%d,%d), error: %d \n", *position,pcol,info );
return -1;
}
for ( j=0; j < pTblocks-1; ++j ) {
fread ( Tblock + i*pTblocks*blocksize + j*blocksize,sizeof ( double ),blocksize,fT );
info=fseek ( fT, ( long ) ( ( ( *dims ) -1 ) * blocksize * sizeof ( double ) ),SEEK_CUR );
if ( info!=0 ) {
printf ( "Error in setting correct begin position for reading Z file\nprocessor (%d,%d), error: %d \n", *position,pcol,info );
return -1;
}
}
fread ( Tblock + i*pTblocks*blocksize + j*blocksize,sizeof ( double ),k%blocksize,fT );
}
//Normal read-in of the strips of T from a binary file (each time blocksize elements are read in)
} else {
if ( ni==0 ) {
info=fseek ( fT, ( long ) ( pcol * blocksize * ( k ) * sizeof ( double ) ),SEEK_SET );
if ( info!=0 ) {
printf ( "Error in setting correct begin position for reading Z file\nprocessor (%d,%d), error: %d \n", *position,pcol,info );
return -1;
}
} else {
info=fseek ( fT, ( long ) ( blocksize * ( * ( dims+1 )-1 ) * ( k ) * sizeof ( double ) ),SEEK_CUR );
if ( info!=0 ) {
printf ( "Error in setting correct begin position for reading Z file\nprocessor (%d,%d), error: %d \n", *position,pcol,info );
return -1;
}
}
for ( i=0; i<blocksize; ++i ) {
info=fseek ( fT, ( long ) ( blocksize * *position * sizeof ( double ) ),SEEK_CUR );
if ( info!=0 ) {
printf ( "Error in setting correct begin position for reading Z file\nprocessor (%d,%d), error: %d \n", *position,pcol,info );
return -1;
}
for ( j=0; j < pTblocks-1; ++j ) {
fread ( Tblock + i*pTblocks*blocksize + j*blocksize,sizeof ( double ),blocksize,fT );
info=fseek ( fT, ( long ) ( ( * ( dims )-1 ) * blocksize * sizeof ( double ) ),SEEK_CUR );
if ( info!=0 ) {
printf ( "Error in setting correct begin position for reading Z file\nprocessor (%d,%d), error: %d \n", *position,pcol,info );
return -1;
}
}
fread ( Tblock + i*pTblocks*blocksize + j*blocksize,sizeof ( double ),blocksize,fT );
info=fseek ( fT, ( long ) ( ( k - blocksize * ( ( pTblocks-1 ) * *dims + *position +1 ) ) * sizeof ( double ) ),SEEK_CUR );
if ( info!=0 ) {
printf ( "Error in setting correct begin position for reading Z file\nprocessor (%d,%d), error: %d \n", *position,pcol,info );
return -1;
}
}
}
blacs_barrier_ ( &ICTXT2D,"A" );
// End of read-in
// Matrix D is the sum of the multiplications of all strips of T' by their transpose
// Up unitl now, the entire matrix is stored, not only upper/lower triangular, which is possible since D is symmetric
// Be aware, that you akways have to allocate memory for the enitre matrix, even when only dealing with the upper/lower triangular part
pdgemm_ ( "N","T",&k,&k,&stripcols,&d_one, Tblock,&i_one, &i_one,DESCT, Tblock,&i_one, &i_one,DESCT, &d_one, Dmat, &i_one, &i_one, DESCD ); //Z'Z
//pdsyrk_ ( "U","N",&k,&stripcols,&d_one, Tblock,&i_one, &i_one,DESCT, &d_one, Dmat, &t_plus, &t_plus, DESCD );
// Matrix B consists of X'T and Z'T, since each process only has some parts of T at its disposal,
// we need to make sure that the correct columns of Z and X are multiplied with the correct columns of T.
for ( i=0; i<pTblocks; ++i ) {
XtT_temp.ncols=k;
//This function multiplies the correct columns of X' with the blocks of T at the disposal of the process
// The result is also stored immediately at the correct positions of X'T. (see src/tools.cpp)
XtT_temp.clear();
mult_colsA_colsC ( Xtsparse, Tblock+i*blocksize, lld_T, ( * ( dims+1 ) * ni + pcol ) *blocksize, blocksize,
( *dims * i + *position ) *blocksize, blocksize, XtT_temp, 0 );
if ( XtT_temp.nonzeros>0 ) {
if ( XtT_sparse.nonzeros==0 ){
XtT_sparse.clear();
XtT_sparse.make2 ( XtT_temp.nrows,XtT_temp.ncols,XtT_temp.nonzeros,XtT_temp.pRows,XtT_temp.pCols,XtT_temp.pData );
}
else {
XtT_sparse.addBCSR ( XtT_temp );
}
}
}
//Same as above for calculating Z'T
for ( i=0; i<pTblocks; ++i ) {
ZtT_temp.ncols=k;
ZtT_temp.clear();
mult_colsA_colsC ( Ztsparse, Tblock+i*blocksize, lld_T, ( * ( dims+1 ) * ni + pcol ) *blocksize, blocksize,
blocksize * ( *dims * i + *position ), blocksize, ZtT_temp, 0 );
if ( ZtT_temp.nonzeros>0 ) {
if ( ZtT_sparse.nonzeros==0 ){
ZtT_sparse.clear();
ZtT_sparse.make2 ( ZtT_temp.nrows,ZtT_temp.ncols,ZtT_temp.nonzeros,ZtT_temp.pRows,ZtT_temp.pCols,ZtT_temp.pData );
}
else
ZtT_sparse.addBCSR ( ZtT_temp );
}
}
blacs_barrier_ ( &ICTXT2D,"A" );
}
XtT_temp.clear();
ZtT_temp.clear();
Xtsparse.clear();
Ztsparse.clear();
if(DESCT != NULL)
free ( DESCT );
DESCT=NULL;
if(Tblock != NULL)
free ( Tblock );
Tblock=NULL;
//printf("T read in\n");
info=fclose ( fT );
if ( info!=0 ) {
printf ( "Error in closing open streams" );
return -1;
}
if(filenameT != NULL)
free(filenameT);
filenameT=NULL;
//Each process only has calculated some parts of B
//All parts are collected by the root process (iam==0), which assembles B
//Each process then receives BT_i and B_j corresponding to the D_ij available to the process
if ( iam!=0 ) {
//Each process other than root sends its X' * T and Z' * T to the root process.
MPI_Send ( & ( XtT_sparse.nonzeros ),1, MPI_INT,0,iam,MPI_COMM_WORLD );
MPI_Send ( & ( XtT_sparse.pRows[0] ),XtT_sparse.nrows + 1, MPI_INT,0,iam+size,MPI_COMM_WORLD );
MPI_Send ( & ( XtT_sparse.pCols[0] ),XtT_sparse.nonzeros, MPI_INT,0,iam+2*size,MPI_COMM_WORLD );
MPI_Send ( & ( XtT_sparse.pData[0] ),XtT_sparse.nonzeros, MPI_DOUBLE,0,iam+3*size,MPI_COMM_WORLD );
XtT_sparse.clear();
MPI_Send ( & ( ZtT_sparse.nonzeros ),1, MPI_INT,0,iam,MPI_COMM_WORLD );
MPI_Send ( & ( ZtT_sparse.pRows[0] ),ZtT_sparse.nrows + 1, MPI_INT,0,4*size + iam,MPI_COMM_WORLD );
MPI_Send ( & ( ZtT_sparse.pCols[0] ),ZtT_sparse.nonzeros, MPI_INT,0,iam+ 5*size,MPI_COMM_WORLD );
MPI_Send ( & ( ZtT_sparse.pData[0] ),ZtT_sparse.nonzeros, MPI_DOUBLE,0,iam+6*size,MPI_COMM_WORLD );
ZtT_sparse.clear();
//printf("Process %d sent ZtT and XtT\n",iam);
// And eventually receives the necessary BT_i and B_j
// Blocking sends are used, which is why the order of the receives is critical depending on the coordinates of the process
int nonzeroes;
if (*position >= pcol) {
MPI_Recv ( &nonzeroes,1,MPI_INT,0,iam,MPI_COMM_WORLD,&status );
BT_i.allocate ( blocksize*Drows,m+l,nonzeroes );
MPI_Recv ( & ( BT_i.pRows[0] ),blocksize*Drows + 1, MPI_INT,0,iam + size,MPI_COMM_WORLD,&status );
int count;
MPI_Get_count(&status,MPI_INT,&count);
BT_i.nrows=count-1;
MPI_Recv ( & ( BT_i.pCols[0] ),nonzeroes, MPI_INT,0,iam+2*size,MPI_COMM_WORLD,&status );
MPI_Recv ( & ( BT_i.pData[0] ),nonzeroes, MPI_DOUBLE,0,iam+3*size,MPI_COMM_WORLD,&status );
MPI_Recv ( &nonzeroes,1, MPI_INT,0,iam+4*size,MPI_COMM_WORLD,&status );
B_j.allocate ( blocksize*Dcols,m+l,nonzeroes );
MPI_Recv ( & ( B_j.pRows[0] ),blocksize*Dcols + 1, MPI_INT,0,iam + 5*size,MPI_COMM_WORLD,&status );
MPI_Get_count(&status,MPI_INT,&count);
B_j.nrows=count-1;
MPI_Recv ( & ( B_j.pCols[0] ),nonzeroes, MPI_INT,0,iam+6*size,MPI_COMM_WORLD,&status );
MPI_Recv ( & ( B_j.pData[0] ),nonzeroes, MPI_DOUBLE,0,iam+7*size,MPI_COMM_WORLD,&status );
//Actually BT_j is sent, so it still needs to be transposed
B_j.transposeIt ( 1 );
}
else {
MPI_Recv ( &nonzeroes,1, MPI_INT,0,iam+4*size,MPI_COMM_WORLD,&status );
B_j.allocate ( blocksize*Dcols,m+l,nonzeroes );
MPI_Recv ( & ( B_j.pRows[0] ),blocksize*Dcols + 1, MPI_INT,0,iam + 5*size,MPI_COMM_WORLD,&status );
int count;
MPI_Get_count(&status,MPI_INT,&count);
B_j.nrows=count-1;
MPI_Recv ( & ( B_j.pCols[0] ),nonzeroes, MPI_INT,0,iam+6*size,MPI_COMM_WORLD,&status );
MPI_Recv ( & ( B_j.pData[0] ),nonzeroes, MPI_DOUBLE,0,iam+7*size,MPI_COMM_WORLD,&status );
B_j.transposeIt ( 1 );
MPI_Recv ( &nonzeroes,1,MPI_INT,0,iam,MPI_COMM_WORLD,&status );
BT_i.allocate ( blocksize*Drows,m+l,nonzeroes );
MPI_Recv ( & ( BT_i.pRows[0] ),blocksize*Drows + 1, MPI_INT,0,iam + size,MPI_COMM_WORLD,&status );
MPI_Get_count(&status,MPI_INT,&count);
BT_i.nrows=count-1;
MPI_Recv ( & ( BT_i.pCols[0] ),nonzeroes, MPI_INT,0,iam+2*size,MPI_COMM_WORLD,&status );
MPI_Recv ( & ( BT_i.pData[0] ),nonzeroes, MPI_DOUBLE,0,iam+3*size,MPI_COMM_WORLD,&status );
}
}
else {
for ( i=1; i<size; ++i ) {
// The root process receives parts of X' * T and Z' * T sequentially from all processes and directly adds them together.
int nonzeroes;
MPI_Recv ( &nonzeroes,1,MPI_INT,i,i,MPI_COMM_WORLD,&status );
if(nonzeroes>0) {
XtT_temp.allocate ( m,k,nonzeroes );
MPI_Recv ( & ( XtT_temp.pRows[0] ),m + 1, MPI_INT,i,i+size,MPI_COMM_WORLD,&status );
MPI_Recv ( & ( XtT_temp.pCols[0] ),nonzeroes, MPI_INT,i,i+2*size,MPI_COMM_WORLD,&status );
MPI_Recv ( & ( XtT_temp.pData[0] ),nonzeroes, MPI_DOUBLE,i,i+3*size,MPI_COMM_WORLD,&status );
XtT_sparse.addBCSR ( XtT_temp );
XtT_temp.clear();
}
MPI_Recv ( &nonzeroes,1, MPI_INT,i,i,MPI_COMM_WORLD,&status );
if(nonzeroes>0) {
ZtT_temp.allocate ( l,k,nonzeroes );
MPI_Recv ( & ( ZtT_temp.pRows[0] ),l + 1, MPI_INT,i,4*size + i,MPI_COMM_WORLD,&status );
MPI_Recv ( & ( ZtT_temp.pCols[0] ),nonzeroes, MPI_INT,i,i+ 5*size,MPI_COMM_WORLD,&status );
MPI_Recv ( & ( ZtT_temp.pData[0] ),nonzeroes, MPI_DOUBLE,i,i+6*size,MPI_COMM_WORLD,&status );
ZtT_sparse.addBCSR ( ZtT_temp );
ZtT_temp.clear();
}
}
XtT_sparse.transposeIt ( 1 );
ZtT_sparse.transposeIt ( 1 );
// B' is created by concatening blocks X'T and Z'T
create1x2BlockMatrix ( XtT_sparse, ZtT_sparse,Btsparse );
XtT_sparse.clear();
ZtT_sparse.clear();
/*Btsparse.transposeIt(1);
Btsparse.writeToFile("B_sparse.csr");
Btsparse.transposeIt(1);*/
// For each process row i BT_i is created which is also sent to processes in column i to become B_j.
for ( int rowproc= *dims - 1; rowproc>= 0; --rowproc ) {
BT_i.ncols=Btsparse.ncols;
BT_i.nrows=0;
BT_i.nonzeros=0;
int Drows_rowproc;
if (rowproc!=0) {
Drows_rowproc= ( Dblocks - rowproc ) % *dims == 0 ? ( Dblocks- rowproc ) / *dims : ( Dblocks- rowproc ) / *dims +1;
Drows_rowproc= Drows_rowproc<1? 1 : Drows_rowproc;
}
else
Drows_rowproc=Drows;
for ( i=0; i<Drows_rowproc; ++i ) {
//Each process in row i can hold several blocks of contiguous rows of D for which we need the corresponding rows of B_T
// Therefore we use the function extendrows to create BT_i (see src/tools.cpp)
BT_i.extendrows ( Btsparse, ( i * *dims + rowproc ) * blocksize,blocksize );
}
for ( int colproc= ( rowproc==0 ? 1 : 0 ); colproc < * ( dims+1 ); ++colproc ) {
int rankproc;
rankproc= blacs_pnum_ (&ICTXT2D, &rowproc,&colproc);
MPI_Send ( & ( BT_i.nonzeros ),1, MPI_INT,rankproc,rankproc,MPI_COMM_WORLD );
MPI_Send ( & ( BT_i.pRows[0] ),BT_i.nrows + 1, MPI_INT,rankproc,rankproc+size,MPI_COMM_WORLD );
MPI_Send ( & ( BT_i.pCols[0] ),BT_i.nonzeros, MPI_INT,rankproc,rankproc+2*size,MPI_COMM_WORLD );
MPI_Send ( & ( BT_i.pData[0] ),BT_i.nonzeros, MPI_DOUBLE,rankproc,rankproc+3*size,MPI_COMM_WORLD );
//printf("BT_i's sent to processor %d\n",rankproc);
rankproc= blacs_pnum_ (&ICTXT2D, &colproc,&rowproc);
MPI_Send ( & ( BT_i.nonzeros ),1, MPI_INT,rankproc,rankproc+4*size,MPI_COMM_WORLD );
MPI_Send ( & ( BT_i.pRows[0] ),BT_i.nrows + 1, MPI_INT,rankproc,rankproc+5*size,MPI_COMM_WORLD );
MPI_Send ( & ( BT_i.pCols[0] ),BT_i.nonzeros, MPI_INT,rankproc,rankproc+6*size,MPI_COMM_WORLD );
MPI_Send ( & ( BT_i.pData[0] ),BT_i.nonzeros, MPI_DOUBLE,rankproc,rankproc+7*size,MPI_COMM_WORLD );
//printf("B_j's sent to processor %d\n",rankproc);
}
}
B_j.make2 ( BT_i.nrows,BT_i.ncols,BT_i.nonzeros,BT_i.pRows,BT_i.pCols,BT_i.pData );
B_j.transposeIt ( 1 );
}
return 0;
}
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;
}
