By Tobias Wittwer

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CONJUGATE GRADIENT METHOD 45 using a second thread actually delivers a performance gain. When using the Goto BLAS, you may need to set the environment variable GOTO_NUM_THREADS to 1. 0d0, N2(1,threadnum),nmax+1) ... Note that a_block has the dimensions u × blocksize, and not blocksize × u. This is due to Fortran’s column-major array storage (arrays are stored column by column, not line by line as in C). build_a_line needs only one row of A at a time, which is achieved by making the rows the columns.

For very small problems and slow interconnects, computation times may even increase. The matrix multiplication N = AT A is sped up significantly, and may benefit even more for larger problem sizes. 4 GHz, per node) with Infiniband interconnect. 7 were used as software packages. 7 shows the resulting runtimes for the multiplication N = AT A (PDSYRK), the solving of Nx = b (PDPOSV), and the total program runtime. 2. DIRECT METHOD 39 the resulting performance and efficiency of the PDSYRK routine. For 4 and 8 nodes, efficiency is around 60%.

The number and ordering of the unknown parameters, and thus the actual computation of one line of A, remains unchanged. We keep the OpenMP parallelisation for multithreaded program runs on SMP nodes, which means that idx also has to be private. $OMP END DO Matrix multiplication and linear equation solving is done by replacing the DSYRK, DGEMV, and DPOSV routines with ScaLAPACK’s PDSYRK, PDGEMV, PDPOSV, and the appropriate parameters. 2. 5: Matrix distribution over processes call PDPOSV(’L’,u,1,N,1,1,descn,b,1,1,descb,info) After solving, the estimated parameters are contained in the distributed vector b.