Implementation of geometric mean of matrices

[tky823]

Summary

The geometric mean of matrices can be written in several forms. Which is faster?

A#B
= A^{1/2}(A^{-1/2}BA^{-1/2})^{1/2}A^{1/2} ... (i)
= A(A^{-1}B)^{1/2} = B(B^{-1}A)^{1/2} ... (ii)
= (AB^{-1})^{1/2}B = (BA^{-1})^{1/2}A

[tky823]

This is related to IPSDTA and MNMF.

ref #33, #34

[tky823]

In my experiments, (ii) is faster than (i).
https://colab.research.google.com/github/tky823/ssspy/blob/13e443f164f16b1ece2cfeab1af05241514743ed/notebooks/ISSUE/issue210.ipynb