By Tobias Wittwer
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Additional info for An Introduction to Parallel Programming
1 shows the resulting matrix sizes for some typical maximum degrees nmax and 100,000 observations. 1: Number of unknowns and matrix sizes depending on nmax , for 100,000 observations The design matrix A does not have to be kept in memory. 11) j=1 but with the disadvantage that A has to be built several times if, for example, residuals are to be calculated: eˆ = y − Aˆx. 12) It is possible to compute A j for only one observation at a time. This should be avoided, though, as the matrix multiplication ATj A j for an A j of only one line is very inefficient.
6. 0d0 do i=1,rb idx=indxl2g(i, blocksize, myrow, 0, nprow) x(idx) = b(i) end do call dgsum2d(ictxt,’A’,’ ’,1,u,x,1,-1,-1) The final step is exiting the BLACS process grid. 5 is parallelised as described above. 604 38 CHAPTER 5. 266 The problem size in the example is too small for A setup or solving benefiting significantly from the second CPU. 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.
Call blacs_gridinfo(ictxt,nprow,npcol,myrow,mycol) call calc_sizes_descinit(blocksize,ictxt,myrow,mycol,nprow,npcol, nobs,u,desca,ra,ca) ... The distributed setup of A is pretty straightforward. 5. Since ScaLAPACK uses a block-cyclic distribution, it is not that (in the case of two processes) the first process is assigned the first half 36 CHAPTER 5. 4: Row-style process grid of the matrix, the second process the other half. Blocks are distributed in a round-robin fashion. For setting up A, we need to know to which global row index the local row index in the loop corresponds.