generalized mean

[nschloe]

np.mean computes the arithmetic mean, but there are many other interesting means, e.g, the root mean square, harmonic mean, or the geometric mean. They can all be parametrized with

$$M_p(x) = \left(\frac{1}{n} \sum_{i=1}^n x_i^p\right)^{1/p}$$

See Wikipedia on generalized means.

[bashtage]

Already available in np.linalg.norm.

[nschloe]

Yeah, except for the 1/n term and the fact that the absolute value is taken of all x. np.linalg.norm also doesn't work correctly for p=0 and +-np.inf. It also has problems for for p which are large in magnitude (due to overflow), but that possibly warrants a separate bug report.

Edit: cleaned up formatting (mattip)

[nschloe]

For future reference, I added a mean implementation to npx which correctly handles all the cases mentioned above.

[qbarthelemy]

This mean is available in the latest Scipy:
http://scipy.github.io/devdocs/reference/generated/scipy.stats.pmean.html
added by scipy/scipy#15729
@nschloe

[mattip]

I will close this as there are alternatives available. @nschloe if you feel np.linalg.norm could be improved please open a separate issue.