Efficiently slice windows from a 1D numpy array, around indices given by second 2D array

Question

I want to extract multiple slices from the same 1D numpy array, where the slice indices are drawn from a random distribution. Basically, I want to achieve the following:

import numpy as np
import numpy.random

# generate some 1D data
data = np.random.randn(500)

# window size (slices are 2*winsize long)
winsize = 60

# number of slices to take from the data
inds_size = (100, 200)

# get random integers that function as indices into the data
inds = np.random.randint(low=winsize, high=len(data)-winsize, size=inds_size)

# now I want to extract slices of data, running from inds[0,0]-60 to inds[0,0]+60
sliced_data = np.zeros( (winsize*2,) + inds_size )
for k in range(inds_size[0]):
    for l in range(inds_size[1]):
        sliced_data[:,k,l] = data[inds[k,l]-winsize:inds[k,l]+winsize]

# sliced_data.shape is now (120, 100, 200)

The above nested loop works fine, but is very slow. In my real code, I will need to do this thousands of times, for data arrays a lot bigger than these. Is there any way to do this more efficiently?

Note that inds will always be 2D in my case, but after getting the slices I will always be summing over one of these two dimensions, so an approach that only accumulates the sum across the one dimension would be fine.

I found this question and this answer which seem almost the same. However, the question is only about a 1D indexing vector (as opposed to my 2D). Also, the answer lacks a bit of context, as I don't really understand how the suggested as_strided works. Since my problem does not seem uncommon, I thought I'd ask again in the hope of a more explanatory answer rather than just code.

Answer 1

Using as_strided in this way appears to be somewhat faster than Divakar's approach (20 ms vs 35 ms here), although memory usage might be an issue.

data_wins = as_strided(data, shape=(data.size - 2*winsize + 1, 2*winsize), strides=(8, 8))
inds = np.random.randint(low=0, high=data.size - 2*winsize, size=inds_size)
sliced = data_wins[inds]
sliced = sliced.transpose((2, 0, 1))    # to use the same index order as before

Strides are the steps in bytes for the index in each dimension. For example, with an array of shape (x, y, z) and a data type of size d (8 for float64), the strides will ordinarily be (y*z*d, z*d, d) , so that the second index steps over whole rows of z items. Setting both values to 8, data_wins[i, j] and data_wins[j, i] will refer to the same memory location.

>>> import numpy as np
>>> from numpy.lib.stride_tricks import as_strided
>>> a = np.arange(10, dtype=np.int8)
>>> as_strided(a, shape=(3, 10 - 2), strides=(1, 1))
array([[0, 1, 2, 3, 4, 5, 6, 7],
       [1, 2, 3, 4, 5, 6, 7, 8],
       [2, 3, 4, 5, 6, 7, 8, 9]], dtype=int8)

Answer 2

Here's a vectorized approach using broadcasting -

# Get 3D offsetting array and add to inds for all indices
allinds = inds + np.arange(-60,60)[:,None,None]

# Index into data with all indices for desired output
sliced_dataout = data[allinds]

Runtime test -

In [20]: # generate some 1D data
    ...: data = np.random.randn(500)
    ...: 
    ...: # window size (slices are 2*winsize long)
    ...: winsize = 60
    ...: 
    ...: # number of slices to take from the data
    ...: inds_size = (100, 200)
    ...: 
    ...: # get random integers that function as indices into the data
    ...: inds=np.random.randint(low=winsize,high=len(data)-winsize, size=inds_size)
    ...: 

In [21]: %%timeit 
    ...: sliced_data = np.zeros( (winsize*2,) + inds_size )
    ...: for k in range(inds_size[0]):
    ...:     for l in range(inds_size[1]):
    ...:         sliced_data[:,k,l] = data[inds[k,l]-winsize:inds[k,l]+winsize]
    ...: 
10 loops, best of 3: 66.9 ms per loop

In [22]: %%timeit 
    ...: allinds = inds + np.arange(-60,60)[:,None,None]
    ...: sliced_dataout = data[allinds]
    ...: 
10 loops, best of 3: 24.1 ms per loop

---

Memory consumption : Compromise solution

If memory consumption is an issue, here's a compromise solution with one loop -

sliced_dataout = np.zeros( (winsize*2,) + inds_size )
for k in range(sliced_data.shape[0]):
    sliced_dataout[k] = data[inds-winsize+k]