For what it’s worth, here’s how you’d do it using “fancy” striding tricks. I was going to post this yesterday, but got distracted by actual work! 🙂
@Paul & @eat both have nice implementations using various other ways of doing this. Just to continue things from the earlier question, I figured I’d post the N-dimensional equivalent.
You’re not going to be able to significantly beat scipy.ndimage functions for >1D arrays, however. (scipy.ndimage.uniform_filter should beat scipy.ndimage.convolve, though)
Moreover, if you’re trying to get a multidimensional moving window, you risk having memory usage blow up whenever you inadvertently make a copy of your array. While the initial “rolling” array is just a view into the memory of your original array, any intermediate steps that copy the array will make a copy that is orders of magnitude larger than your original array (i.e. Let’s say that you’re working with a 100×100 original array… The view into it (for a filter size of (3,3)) will be 98x98x3x3 but use the same memory as the original. However, any copies will use the amount of memory that a full 98x98x3x3 array would!!)
Basically, using crazy striding tricks is great for when you want to vectorize moving window operations on a single axis of an ndarray. It makes it really easy to calculate things like a moving standard deviation, etc with very little overhead. When you want to start doing this along multiple axes, it’s possible, but you’re usually better off with more specialized functions. (Such as scipy.ndimage, etc)
At any rate, here’s how you do it:
import numpy as np
def rolling_window_lastaxis(a, window):
"""Directly taken from Erik Rigtorp's post to numpy-discussion.
<http://www.mail-archive.com/[email protected]/msg29450.html>"""
if window < 1:
raise ValueError, "`window` must be at least 1."
if window > a.shape[-1]:
raise ValueError, "`window` is too long."
shape = a.shape[:-1] + (a.shape[-1] - window + 1, window)
strides = a.strides + (a.strides[-1],)
return np.lib.stride_tricks.as_strided(a, shape=shape, strides=strides)
def rolling_window(a, window):
if not hasattr(window, '__iter__'):
return rolling_window_lastaxis(a, window)
for i, win in enumerate(window):
if win > 1:
a = a.swapaxes(i, -1)
a = rolling_window_lastaxis(a, win)
a = a.swapaxes(-2, i)
return a
filtsize = (3, 3)
a = np.zeros((10,10), dtype=np.float)
a[5:7,5] = 1
b = rolling_window(a, filtsize)
blurred = b.mean(axis=-1).mean(axis=-1)
So what we get when we do b = rolling_window(a, filtsize) is an 8x8x3x3 array, that’s actually a view into the same memory as the original 10×10 array. We could have just as easily used different filter size along different axes or operated only along selected axes of an N-dimensional array (i.e. filtsize = (0,3,0,3) on a 4-dimensional array would give us a 6 dimensional view).
We can then apply an arbitrary function to the last axis repeatedly to effectively calculate things in a moving window.
However, because we’re storing temporary arrays that are much bigger than our original array on each step of mean (or std or whatever), this is not at all memory efficient! It’s also not going to be terribly fast, either.
The equivalent for ndimage is just:
blurred = scipy.ndimage.uniform_filter(a, filtsize, output=a)
This will handle a variety of boundary conditions, do the “blurring” in-place without requiring a temporary copy of the array, and be very fast. Striding tricks are a good way to apply a function to a moving window along one axis, but they’re not a good way to do it along multiple axes, usually….
Just my $0.02, at any rate…