ICC_rep_anova speedup suggestion

[kristoferm94]

Summary

ICC_rep_anova can be sped up by rearranging the matrix multiplication order and using the hermitian=True flag in pinv

Actual behavior

As implemented, pinv is called without the hermitian=True flag.
dot(X.T, X) will always be a hermitian matrix so speedup can be achieved by setting the hermitian flag in pinv to True.

The matrix multiplication in line 117 in icc.py is arranged in a way that fat matrices end up being multiplied together.
The matrix multiplication order can be rearranged in a way that we end up multiplying fat matrices with column vectors most of the time.

Script/Workflow details

Suggested modification in lines 117: https://github.com/kristoferm94/nipype/blob/linalg-speedup/nipype/algorithms/icc.py

I.e. replace:

predicted_Y = dot(dot(dot(X, pinv(dot(X.T, X))), X.T), Y.flatten("F"))

with

predicted_Y = X @ (pinv(X.T @ X, hermitian=True) @ (X.T @ Y.flatten("F")))

[effigies]

Seems like a good idea. Would you mind also changing dot(a, b) with a @ b in these expressions?

[kristoferm94]

Sure. I've updated the first comment.

[effigies]

Sorry, should have been clearer: Do you want to submit a quick PR?

[kristoferm94]

No problem.
Sure, I've submitted a pull request with the proposed change: #3453