I have an array like this:
A = array([1,2,3,4,5,6,7,8,9,10])
B = array([[1,2,3],
width = 3 # fixed arbitrary width
length = 10000 # length of A which I wish to use
B = A[0:length + 1]
for i in range (1, length):
B = np.vstack((B, A[i, i + width + 1]))
Actually, there's an even more efficient way to do this... The downside to using
vstack etc, is that you're making a copy of the array.
Incidentally, this is effectively identical to @Paul's answer, but I'm posting this just to explain things in a bit more detail...
There's a way to do this with just views so that no memory is duplicated.
The basic trick is to directly manipulate the strides of the array (For one-dimensional arrays):
import numpy as np def rolling(a, window): shape = (a.size - window + 1, window) strides = (a.itemsize, a.itemsize) return np.lib.stride_tricks.as_strided(a, shape=shape, strides=strides) a = np.arange(10) print rolling(a, 3)
a is your input array and
window is the length of the window that you want (3, in your case).
[[0 1 2] [1 2 3] [2 3 4] [3 4 5] [4 5 6] [5 6 7] [6 7 8] [7 8 9]]
However, there is absolutely no duplication of memory between the original
a and the returned array. This means that it's fast and scales much better than other options.
For example (using
a = np.arange(100000) and
%timeit np.vstack([a[i:i-window] for i in xrange(window)]).T 1000 loops, best of 3: 256 us per loop %timeit rolling(a, window) 100000 loops, best of 3: 12 us per loop
If we generalize this to a "rolling window" along the last axis for an N-dimensional array, we get Erik Rigtorp's "rolling window" function:
import numpy as np def rolling_window(a, window): """ Make an ndarray with a rolling window of the last dimension Parameters ---------- a : array_like Array to add rolling window to window : int Size of rolling window Returns ------- Array that is a view of the original array with a added dimension of size w. Examples -------- >>> x=np.arange(10).reshape((2,5)) >>> rolling_window(x, 3) array([[[0, 1, 2], [1, 2, 3], [2, 3, 4]], [[5, 6, 7], [6, 7, 8], [7, 8, 9]]]) Calculate rolling mean of last dimension: >>> np.mean(rolling_window(x, 3), -1) array([[ 1., 2., 3.], [ 6., 7., 8.]]) """ 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)
So, let's look into what's going on here... Manipulating an array's
strides may seem a bit magical, but once you understand what's going on, it's not at all. The strides of a numpy array describe the size in bytes of the steps that must be taken to increment one value along a given axis. So, in the case of a 1-dimensional array of 64-bit floats, the length of each item is 8 bytes, and
x = np.arange(9) print x.strides
Now, if we reshape this into a 2D, 3x3 array, the strides will be
(3 * 8, 8), as we would have to jump 24 bytes to increment one step along the first axis, and 8 bytes to increment one step along the second axis.
y = x.reshape(3,3) print y.strides
Similarly a transpose is the same as just reversing the strides of an array:
print y y.strides = y.strides[::-1] print y
Clearly, the strides of an array and the shape of an array are intimately linked. If we change one, we have to change the other accordingly, otherwise we won't have a valid description of the memory buffer that actually holds the values of the array.
Therefore, if you want to change both the shape and size of an array simultaneously, you can't do it just by setting
x.shape, even if the new strides and shape are compatible.
numpy.lib.as_strided comes in. It's actually a very simple function that just sets the strides and shape of an array simultaneously.
It checks that the two are compatible, but not that the old strides and new shape are compatible, as would happen if you set the two independently. (It actually does this through numpy's
__array_interface__, which allows arbitrary classes to describe a memory buffer as a numpy array.)
So, all we've done is made it so that steps one item forward (8 bytes in the case of a 64-bit array) along one axis, but also only steps 8 bytes forward along the other axis.
In other words, in case of a "window" size of 3, the array has a shape of
(whatever, 3), but instead of stepping a full
3 * x.itemsize for the second dimension, it only steps one item forward, effectively making the rows of new array a "moving window" view into the original array.
(This also means that
x.shape * x.shape will not be the same as
x.size for your new array.)
At any rate, hopefully that makes things slightly clearer..