# Selecting specific rows and columns from NumPy array

PythonArraysNumpyMultidimensional ArrayNumpy Slicing## Python Problem Overview

I've been going crazy trying to figure out what stupid thing I'm doing wrong here.

I'm using NumPy, and I have specific row indices and specific column indices that I want to select from. Here's the gist of my problem:

```
import numpy as np
a = np.arange(20).reshape((5,4))
# array([[ 0, 1, 2, 3],
# [ 4, 5, 6, 7],
# [ 8, 9, 10, 11],
# [12, 13, 14, 15],
# [16, 17, 18, 19]])
# If I select certain rows, it works
print a[[0, 1, 3], :]
# array([[ 0, 1, 2, 3],
# [ 4, 5, 6, 7],
# [12, 13, 14, 15]])
# If I select certain rows and a single column, it works
print a[[0, 1, 3], 2]
# array([ 2, 6, 14])
# But if I select certain rows AND certain columns, it fails
print a[[0,1,3], [0,2]]
# Traceback (most recent call last):
# File "<stdin>", line 1, in <module>
# ValueError: shape mismatch: objects cannot be broadcast to a single shape
```

Why is this happening? Surely I should be able to select the 1st, 2nd, and 4th rows, and 1st and 3rd columns? The result I'm expecting is:

```
a[[0,1,3], [0,2]] => [[0, 2],
[4, 6],
[12, 14]]
```

## Python Solutions

## Solution 1 - Python

As Toan suggests, a simple hack would be to just select the rows first, and then select the columns over *that*.

```
>>> a[[0,1,3], :] # Returns the rows you want
array([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[12, 13, 14, 15]])
>>> a[[0,1,3], :][:, [0,2]] # Selects the columns you want as well
array([[ 0, 2],
[ 4, 6],
[12, 14]])
```

`np.ix_`

[Edit] The built-in method: I recently discovered that numpy gives you an in-built one-liner to doing *exactly* what @Jaime suggested, but without having to use broadcasting syntax (which suffers from lack of readability). From the docs:

> Using ix_ one can quickly construct index arrays that will index the
> cross product. `a[np.ix_([1,3],[2,5])]`

returns the array `[[a[1,2] a[1,5]], [a[3,2] a[3,5]]]`

.

So you use it like this:

```
>>> a = np.arange(20).reshape((5,4))
>>> a[np.ix_([0,1,3], [0,2])]
array([[ 0, 2],
[ 4, 6],
[12, 14]])
```

And the way it works is that it takes care of aligning arrays the way Jaime suggested, so that broadcasting happens properly:

```
>>> np.ix_([0,1,3], [0,2])
(array([[0],
[1],
[3]]), array([[0, 2]]))
```

Also, as MikeC says in a comment, `np.ix_`

has the advantage of returning a view, which my first (pre-edit) answer did not. This means you can now *assign* to the indexed array:

```
>>> a[np.ix_([0,1,3], [0,2])] = -1
>>> a
array([[-1, 1, -1, 3],
[-1, 5, -1, 7],
[ 8, 9, 10, 11],
[-1, 13, -1, 15],
[16, 17, 18, 19]])
```

## Solution 2 - Python

Fancy indexing requires you to provide all indices for each dimension. You are providing 3 indices for the first one, and only 2 for the second one, hence the error. You want to do something like this:

```
>>> a[[[0, 0], [1, 1], [3, 3]], [[0,2], [0,2], [0, 2]]]
array([[ 0, 2],
[ 4, 6],
[12, 14]])
```

That is of course a pain to write, so you can let broadcasting help you:

```
>>> a[[[0], [1], [3]], [0, 2]]
array([[ 0, 2],
[ 4, 6],
[12, 14]])
```

This is much simpler to do if you index with arrays, not lists:

```
>>> row_idx = np.array([0, 1, 3])
>>> col_idx = np.array([0, 2])
>>> a[row_idx[:, None], col_idx]
array([[ 0, 2],
[ 4, 6],
[12, 14]])
```

## Solution 3 - Python

USE:

```
>>> a[[0,1,3]][:,[0,2]]
array([[ 0, 2],
[ 4, 6],
[12, 14]])
```

OR:

```
>>> a[[0,1,3],::2]
array([[ 0, 2],
[ 4, 6],
[12, 14]])
```

## Solution 4 - Python

Using `np.ix_`

is the most convenient way to do it (as answered by others), but it also can be done as follows:

```
>>> rows = [0, 1, 3]
>>> cols = [0, 2]
>>> (a[rows].T)[cols].T
array([[ 0, 2],
[ 4, 6],
[12, 14]])
```