Index a 2D Numpy array with 2 lists of indices

Question

I've got a strange situation.

I have a 2D Numpy array, x:

x = np.random.random_integers(0,5,(20,8))

And I have 2 indexers--one with indices for the rows, and one with indices for the column. In order to index X, I am having to do the following:

row_indices = [4,2,18,16,7,19,4]
col_indices = [1,2]
x_rows = x[row_indices,:]
x_indexed = x_rows[:,column_indices]

Instead of just:

x_new = x[row_indices,column_indices]

(which fails with: error, cannot broadcast (20,) with (2,))

---

I'd like to be able to do the indexing in one line using the broadcasting, since that would keep the code clean and readable...also, I don't know all that much about python under the hood, but as I understand it, it should be faster to do it in one line (and I'll be working with pretty big arrays).

---

Test Case:

x = np.random.random_integers(0,5,(20,8))

row_indices = [4,2,18,16,7,19,4]
col_indices = [1,2]
x_rows = x[row_indices,:]
x_indexed = x_rows[:,col_indices]

x_doesnt_work = x[row_indices,col_indices]

Solution 1

Your first try would work if you write it with np.newaxis

x_new = x[row_indices[:, np.newaxis],column_indices]

Solution 2

Selections or assignments with np.ix_ using indexing or boolean arrays/masks

1. With indexing-arrays

A. Selection

We can use np.ix_ to get a tuple of indexing arrays that are broadcastable against each other to result in a higher-dimensional combinations of indices. So, when that tuple is used for indexing into the input array, would give us the same higher-dimensional array. Hence, to make a selection based on two 1D indexing arrays, it would be -

x_indexed = x[np.ix_(row_indices,col_indices)]

B. Assignment

We can use the same notation for assigning scalar or a broadcastable array into those indexed positions. Hence, the following works for assignments -

x[np.ix_(row_indices,col_indices)] = # scalar or broadcastable array

2. With masks

We can also use boolean arrays/masks with np.ix_, similar to how indexing arrays are used. This can be used again to select a block off the input array and also for assignments into it.

A. Selection

Thus, with row_mask and col_mask boolean arrays as the masks for row and column selections respectively, we can use the following for selections -

x[np.ix_(row_mask,col_mask)]

B. Assignment

And the following works for assignments -

x[np.ix_(row_mask,col_mask)] = # scalar or broadcastable array

---

Sample Runs

1. Using np.ix_ with indexing-arrays

Input array and indexing arrays -

In [221]: x
Out[221]: 
array([[17, 39, 88, 14, 73, 58, 17, 78],
       [88, 92, 46, 67, 44, 81, 17, 67],
       [31, 70, 47, 90, 52, 15, 24, 22],
       [19, 59, 98, 19, 52, 95, 88, 65],
       [85, 76, 56, 72, 43, 79, 53, 37],
       [74, 46, 95, 27, 81, 97, 93, 69],
       [49, 46, 12, 83, 15, 63, 20, 79]])

In [222]: row_indices
Out[222]: [4, 2, 5, 4, 1]

In [223]: col_indices
Out[223]: [1, 2]

Tuple of indexing arrays with np.ix_ -

In [224]: np.ix_(row_indices,col_indices) # Broadcasting of indices
Out[224]: 
(array([[4],
        [2],
        [5],
        [4],
        [1]]), array([[1, 2]]))

Make selections -

In [225]: x[np.ix_(row_indices,col_indices)]
Out[225]: 
array([[76, 56],
       [70, 47],
       [46, 95],
       [76, 56],
       [92, 46]])

As suggested by OP, this is in effect same as performing old-school broadcasting with a 2D array version of row_indices that has its elements/indices sent to axis=0 and thus creating a singleton dimension at axis=1 and thus allowing broadcasting with col_indices. Thus, we would have an alternative solution like so -

In [227]: x[np.asarray(row_indices)[:,None],col_indices]
Out[227]: 
array([[76, 56],
       [70, 47],
       [46, 95],
       [76, 56],
       [92, 46]])

As discussed earlier, for the assignments, we simply do so.

Row, col indexing arrays -

In [36]: row_indices = [1, 4]

In [37]: col_indices = [1, 3]

Make assignments with scalar -

In [38]: x[np.ix_(row_indices,col_indices)] = -1

In [39]: x
Out[39]: 
array([[17, 39, 88, 14, 73, 58, 17, 78],
       [88, -1, 46, -1, 44, 81, 17, 67],
       [31, 70, 47, 90, 52, 15, 24, 22],
       [19, 59, 98, 19, 52, 95, 88, 65],
       [85, -1, 56, -1, 43, 79, 53, 37],
       [74, 46, 95, 27, 81, 97, 93, 69],
       [49, 46, 12, 83, 15, 63, 20, 79]])

Make assignments with 2D block(broadcastable array) -

In [40]: rand_arr = -np.arange(4).reshape(2,2)

In [41]: x[np.ix_(row_indices,col_indices)] = rand_arr

In [42]: x
Out[42]: 
array([[17, 39, 88, 14, 73, 58, 17, 78],
       [88,  0, 46, -1, 44, 81, 17, 67],
       [31, 70, 47, 90, 52, 15, 24, 22],
       [19, 59, 98, 19, 52, 95, 88, 65],
       [85, -2, 56, -3, 43, 79, 53, 37],
       [74, 46, 95, 27, 81, 97, 93, 69],
       [49, 46, 12, 83, 15, 63, 20, 79]])

2. Using np.ix_ with masks

Input array -

In [19]: x
Out[19]: 
array([[17, 39, 88, 14, 73, 58, 17, 78],
       [88, 92, 46, 67, 44, 81, 17, 67],
       [31, 70, 47, 90, 52, 15, 24, 22],
       [19, 59, 98, 19, 52, 95, 88, 65],
       [85, 76, 56, 72, 43, 79, 53, 37],
       [74, 46, 95, 27, 81, 97, 93, 69],
       [49, 46, 12, 83, 15, 63, 20, 79]])

Input row, col masks -

In [20]: row_mask = np.array([0,1,1,0,0,1,0],dtype=bool)

In [21]: col_mask = np.array([1,0,1,0,1,1,0,0],dtype=bool)

Make selections -

In [22]: x[np.ix_(row_mask,col_mask)]
Out[22]: 
array([[88, 46, 44, 81],
       [31, 47, 52, 15],
       [74, 95, 81, 97]])

Make assignments with scalar -

In [23]: x[np.ix_(row_mask,col_mask)] = -1

In [24]: x
Out[24]: 
array([[17, 39, 88, 14, 73, 58, 17, 78],
       [-1, 92, -1, 67, -1, -1, 17, 67],
       [-1, 70, -1, 90, -1, -1, 24, 22],
       [19, 59, 98, 19, 52, 95, 88, 65],
       [85, 76, 56, 72, 43, 79, 53, 37],
       [-1, 46, -1, 27, -1, -1, 93, 69],
       [49, 46, 12, 83, 15, 63, 20, 79]])

Make assignments with 2D block(broadcastable array) -

In [25]: rand_arr = -np.arange(12).reshape(3,4)

In [26]: x[np.ix_(row_mask,col_mask)] = rand_arr

In [27]: x
Out[27]: 
array([[ 17,  39,  88,  14,  73,  58,  17,  78],
       [  0,  92,  -1,  67,  -2,  -3,  17,  67],
       [ -4,  70,  -5,  90,  -6,  -7,  24,  22],
       [ 19,  59,  98,  19,  52,  95,  88,  65],
       [ 85,  76,  56,  72,  43,  79,  53,  37],
       [ -8,  46,  -9,  27, -10, -11,  93,  69],
       [ 49,  46,  12,  83,  15,  63,  20,  79]])

Solution 3

What about:

x[row_indices][:,col_indices]

For example,

x = np.random.random_integers(0,5,(5,5))
## array([[4, 3, 2, 5, 0],
##        [0, 3, 1, 4, 2],
##        [4, 2, 0, 0, 3],
##        [4, 5, 5, 5, 0],
##        [1, 1, 5, 0, 2]])

row_indices = [4,2]
col_indices = [1,2]
x[row_indices][:,col_indices]
## array([[1, 5],
##        [2, 0]])

Solution 4

import numpy as np
x = np.random.random_integers(0,5,(4,4))
x
array([[5, 3, 3, 2],
       [4, 3, 0, 0],
       [1, 4, 5, 3],
       [0, 4, 3, 4]])

# This indexes the elements 1,1 and 2,2 and 3,3
indexes = (np.array([1,2,3]),np.array([1,2,3]))
x[indexes]
# returns array([3, 5, 4])

Notice that numpy has very different rules depending on what kind of indexes you use. So indexing several elements should be by a tuple of np.ndarray (see indexing manual).

So you need only to convert your list to np.ndarray and it should work as expected.

Solution 5

I think you are trying to do one of the following (equlvalent) operations:

x_does_work = x[row_indices,:][:,col_indices]
x_does_work = x[:,col_indices][row_indices,:]

This will actually create a subset of x with only the selected rows, then select the columns from that, or vice versa in the second case. The first case can be thought of as

x_does_work = (x[row_indices,:])[:,col_indices]

View more solutions

Comments

[Chris]

Ah, so if I take the transpose of row_indices, should be the same?

[Shihab Shahriar Khan]

when elements of "indexes" tuple are of different size, it doesn't seem to work

[MSeifert]

@ShihabShahriar What would different sizes indicate? That you have partial indices? It seems like you have a different question, if that's the case please ask a new question.

[hpaulj]

This is fine for fetch, but fails for assignment. The row index makes a copy.

[monolith]

@hpaulj both make a copy because of advanced indexing, right?

[hpaulj]

@wedran, with one layer of indexing, x[[1,2,3]] = 2, the distinction between view and copy doesn't matter (x.__setitem__(..., 2). It's when you use sequential indexing that you have to pay attention to that issue. Then the __setitem__ modifies the first __getitem__.

[Joonho Park]

I think, you might need to change row[column]_indices into np.array.

[eric]

I like how explicit this is.