Jaroslav Hajek wrote: > hi all, > > I contributed a toy implementation of block sparse matrices to the > linear-algebra package (also attached). > This is probably not meant for serious business, as all the code is > m-files only, but is rather a demonstration of what can now be done in > Octave. > > Basic operations (+, -, *, ', .') are supported. No division, of course. > > Curiously enough, despite the m-file implementation, already for a > 1000x1000 matrix with 10x10 blocks and 4 blocks per row > (corresponds to a FE matrix of 1000-element conforming triangular grid > with 3-rd order discontinuous polynomial elements), > this toy implementation can outperform the built-in sparse matrices: > > nb = 10; n = 1000; nrhs = 1; > [i, j] = find (sprand (n, n, 3/n) + speye (n)); > a = rand (nb, nb, length (i)); > s = blksparse (i, j, a, n, n); > > v = rand (nb*n, nrhs); > > tic; > for it = 1:100/nrhs > s * v; > endfor > toc > > s = sparse (s); > tic; > for it = 1:100/nrhs > s * v; > endfor > toc > > On my computer (Core 2 Duo, g++ -O3 -march=native), I get: > > octave:1> ttbs > Elapsed time is 0.180152 seconds. > Elapsed time is 0.344266 seconds. > > with nrhs=10 (thus reducing interpreter overhead and improving cache > locality for blksparse), it gets even better: > > octave:3> ttbs > Elapsed time is 0.0802341 seconds. > Elapsed time is 0.34509 seconds. > > Of course, as division is unsupported, the usefulness of this > implementation is quite limited, but still it can be used e.g. for > iterative solvers. > > Comments? Suggestions? > Note that this code requires Octave tip as it relies on certain recent > additions (blkmm, accumdim). > > Well, I'd wondered about revisiting the * sparse operator in Octave to see if the CXSPARSE code that matlab now uses is faster. We already have a dependency on CXSPARSE and so doing this might be a benefit without the cost of a new dependency.
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