numpy 2d array anti diagonal averaging

The following piece of code averages the ante-diagonal elements of a 2d array x of size (m,n) with, for my purpose, m > n.

import numpy as np

"""Average antidiagonal elements of a 2d array
Parameters:
-----------
x : np.array
2d numpy array of size

Return:
-------
x1d : np.array
1d numpy array representing averaged antediangonal elements of x

"""
x1d = [np.mean(x[::-1, :].diagonal(i)) for i in
range(-x.shape + 1, x.shape)]
return np.array(x1d)

Example

x = np.arange(12).reshape(4,3)

yields

[  0.   2.   4.   7.   9.  11.]

I make an intensive use of this function in my code and it has been profiled as a performance bottleneck. The code was inspired from this answer. I haven't found any better way on my own. Any performance improvement would be appreciated.

General context

This code is associated with the Singular Spectrum Analysis algorithm for time series decomposition. Basically, I use time series of length 20k that are turned into a trajectory matrix of shape (10k,10k). The latter is decomposed using singular value decomposition in to 10k components. For a given number n of first singular components (usually 50), I reconstruct n 2d array and average their anti-diagonals elements to have back n time series. These are appreciated with a graphical plot of a correlation matrix.

I will not speed up the SVD algorithm, but SVD results are saved. The anti-diagonal averaging is used for exploration of the results but it is slow. Usually, the function average_diag runs n (50 by default) times on matrix of size (10k, 10k). It takes a bit more than 1 minutes on my PC. It seems slow to me, especially for generating a plot, and this is why I want to improve it if possible.

• Could you provide a bit more context about how the function is being used? In particular, what are typical sizes, what is typical data, and are there any patterns between the data provided to different calls to this function? That would help work out how performance could be improved. – Josiah Jun 1 '18 at 21:46
• @Josiah I have just edited my question to provide the context. Thank you – Delforge Jun 4 '18 at 10:21
• I'm afraid that I'm also unable to find further optimisations with those parameters. – Josiah Jun 4 '18 at 22:50