random.pseudoinverse function

Calculate an approximation of the pseudoinverse of a matrix.

An internal function that uses an approximation of the SVD using the first k singular values of A to calculate the pseudo-inverse. Only used when the cue-cue matrix contains more than 20,000 cues.

random.pseudoinverse(m, verbose=F, k = 0)

Arguments

• m: A matrix.
• k: If k = 0, the default, k will be set to the size of 3/4 of the singular values. If not, the k-rank approximation will be calculated.
• verbose: Display diagnostic messages or not.

Details

This idea was proposed by Gunnar Martinsson Associate Professor and Director of Graduate Studies Department of Applied Mathematics, University of Colorado at Boulder http://amath.colorado.edu/faculty/martinss/ And with ideas from: Yoel Shkolnisky and his Out-of-Core SVD code: https://sites.google.com/site/yoelshkolnisky/software

Returns

The approximate pseudoinverse of the input matrix

References

"Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions" Nathan Halko, Per-Gunnar Martinsson, Joel A. Tropp http://arxiv.org/abs/0909.4061

Author(s)

Cyrus Shaoul

Note

No temporary files are used.

Acknowledgements

Thanks to Gunnar for his help with this!

See Also

estimateWeights , estimateWeightsCompact ,

Examples

#None (internal function)