random.pseudoinverse {ndl}

Calculate an approximation of the pseudoinverse of a matrix.

Description

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.

Usage

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

Value

The approximate pseudoinverse of the input matrix

Acknowledgements

Thanks to Gunnar for his help with this!

Note

No temporary files are used.

Author(s)

Cyrus Shaoul

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

See Also

estimateWeights, estimateWeightsCompact,

Examples

#None (internal function)