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up vote 4 down vote favorite

I have a very large sparse array, and the computation of individual matrix elements is fairly expensive. The Matrix is Hermitian and traceless, so I would like to construct only the sub-diagonal elements explicitly.

A sketch of my attempt:

M = SparseArray[{}, {imax, imax}];
SetSharedVariable[M];
ParallelDo[
  If[j < i, M[[i, j]] = f[i, j]],
  {i, 1, imax}, {j, 1, imax}];

My understanding is that setting M as a shared variable this way is very expensive. Is there a good way to parallelize this process?

Note: I have seen examples where people calculate dense matrices by constructing the submatrices on separate kernels, but for my matrix the computation time of a submatrix is difficult to estimate so trying to distribute the computation time manually is difficult.

share|improve this question
    
Try to use the common scheme: SparseArray[ids -> vals], where ids = {{i1,j1},{i2,j2},...} is a list of indexes and vals is a list of correcpoding values. You can calulate vals with ParallelTable. Moreover, adding elements to existing SparseArray takes sensible amount of time. –  ybeltukov yesterday

1 Answer 1

up vote 6 down vote accepted

You can use ParallelTable and generate the SparseArray form the table. 

f[i_, j_] := i + j;
imax = 50;

AbsoluteTiming[
M = SparseArray[{}, {imax, imax}];
SetSharedVariable[M];
ParallelDo[If[j < i, M[[i, j]] = f[i, j]], {i, 1, imax}, {j, 1, imax}]
]
(*{8.259472, Null}*)

AbsoluteTiming[
M2 = SparseArray[Flatten[ParallelTable[{{i, j} -> f[i, j]}, {i, 1, imax}, {j, 1, i - 1}]],{imax,imax}];
]
(*{0.038002,Null}*)
share|improve this answer
    
Why the j=2? It seems to work without that. –  Cory Schillaci yesterday
    
Ups, I forgot to remove this from the code. Corrected, Thanks. –  paw yesterday
    
Also the sparse array shape should be specified, otherwise it's not a square matrix. Thanks for you answer! –  Cory Schillaci yesterday
    
Good point, if your matrix has to be square you can specifiy the size as you did in your question. –  paw yesterday

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