Slicing of a NumPy 2d array, or how do I extract an mxm submatrix from an nxn array (n>m)?

Asked 2010-11-23T15:05:08.323

199

I want to slice a NumPy nxn array. I want to extract an arbitrary selection of m rows and columns of that array (i.e. without any pattern in the numbers of rows/columns), making it a new, mxm array. For this example let us say the array is 4x4 and I want to extract a 2x2 array from it.

Here is our array:

from numpy import *
x = range(16)
x = reshape(x,(4,4))

print x
[[ 0  1  2  3]
 [ 4  5  6  7]
 [ 8  9 10 11]
 [12 13 14 15]]

The line and columns to remove are the same. The easiest case is when I want to extract a 2x2 submatrix that is at the beginning or at the end, i.e. :

In [33]: x[0:2,0:2]
Out[33]: 
array([[0, 1],
       [4, 5]])

In [34]: x[2:,2:]
Out[34]: 
array([[10, 11],
       [14, 15]])

But what if I need to remove another mixture of rows/columns? What if I need to remove the first and third lines/rows, thus extracting the submatrix [[5,7],[13,15]]? There can be any composition of rows/lines. I read somewhere that I just need to index my array using arrays/lists of indices for both rows and columns, but that doesn't seem to work:

In [35]: x[[1,3],[1,3]]
Out[35]: array([ 5, 15])

I found one way, which is:

    In [61]: x[[1,3]][:,[1,3]]
Out[61]: 
array([[ 5,  7],
       [13, 15]])

First issue with this is that it is hardly readable, although I can live with that. If someone has a better solution, I'd certainly like to hear it.

Other thing is I read on a forum that indexing arrays with arrays forces NumPy to make a copy of the desired array, thus when treating with large arrays this could become a problem. Why is that so / how does this mechanism work?

python numpy slice

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2 Answers

I don't think that x[[1,3]][:,[1,3]] is hardly readable. If you want to be more clear on your intent, you can do:

a[[1,3],:][:,[1,3]]

I am not an expert in slicing but typically, if you try to slice into an array and the values are continuous, you get back a view where the stride value is changed.

e.g. In your inputs 33 and 34, although you get a 2x2 array, the stride is 4. Thus, when you index the next row, the pointer moves to the correct position in memory.

Clearly, this mechanism doesn't carry well into the case of an array of indices. Hence, numpy will have to make the copy. After all, many other matrix math function relies on size, stride and continuous memory allocation.

answered 2010-11-23T15:19:01.177

With numpy, you can pass a slice for each component of the index - so, your x[0:2,0:2] example above works.

If you just want to evenly skip columns or rows, you can pass slices with three components (i.e. start, stop, step).

Again, for your example above:

>>> x[1:4:2, 1:4:2]
array([[ 5,  7],
       [13, 15]])

Which is basically: slice in the first dimension, with start at index 1, stop when index is equal or greater than 4, and add 2 to the index in each pass. The same for the second dimension. Again: this only works for constant steps.

The syntax you got to do something quite different internally - what x[[1,3]][:,[1,3]] actually does is create a new array including only rows 1 and 3 from the original array (done with the x[[1,3]] part), and then re-slice that - creating a third array - including only columns 1 and 3 of the previous array.

answered 2010-11-23T15:13:15.493

Slicing of a NumPy 2d array, or how do I extract an mxm submatrix from an nxn array (n>m)?

2 Answers

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