Sparse Matrices and Machine Precision

I have a large sparse matrix, K. My problem is that over time some values in K that where once non-zero will change to zero through some matrix calculations. However, due to floating point precision inaccuracies the values don't reach exactly zero. Thus Matlab allows these near zero values to be represented as non-zero values.

Currently my solution is

K(abs(K)<threshold) = 0;

where threshold is some small value. This does help, however this operation is slow and as K is changed by matrix operations often, it needs to be re-run often.

Is there a way to force sparse matrices to see values smaller than a certain threshold as zero? Or is there another solution?

Thanks

Answer 1

[John D'Errico]

There is no way to do so in the existing sparse form, and you would not want that behavior to exist in many linear algebra operations. As linear algebra goes, it is a rather nonlinear thing.

You can always just store the non-zero elements separately, implicitly building your own sparse form.

Answer 2

[James Tursa]

If you are really desperate for speed one could write a mex routine to do this operation in-place. My guess is it probably wouldn't take too much time ... but that is just a guess. You would have to manually call this function, however. As John noted, you cannot make MATLAB automatically do this for all of your linear algebra calculations.

[Superfish]

Do you mean write a C or fortran file to do the matrix adjusting calculations, and perform a zero threshold check when writing the value?

I think it would be slow as I doubt i'd be able to beat MATLABs optimizations on matrix multiplication.

[James Tursa]

No. I mean have MATLAB do the matrix multiplication, but after the fact have a mex routine clean it of small values in-place.