### Question :

I’m pretty new in `numpy`

and I am having a hard time understanding how to extract from a `np.array`

a sub matrix with defined columns and rows:

```
Y = np.arange(16).reshape(4,4)
```

If I want to extract columns/rows 0 and 3, I should have:

```
[[0 3]
[12 15]]
```

I tried all the reshape functions…but cannot figure out how to do this. Any ideas?

##
Answer #1:

Give `np.ix_`

a try:

```
Y[np.ix_([0,3],[0,3])]
```

This returns your desired result:

```
In [25]: Y = np.arange(16).reshape(4,4)
In [26]: Y[np.ix_([0,3],[0,3])]
Out[26]:
array([[ 0, 3],
[12, 15]])
```

##
Answer #2:

One solution is to index the rows/columns by slicing/striding. Here’s an example where you are extracting every third column/row from the first to last columns (i.e. the first and fourth columns)

```
In [1]: import numpy as np
In [2]: Y = np.arange(16).reshape(4, 4)
In [3]: Y[0:4:3, 0:4:3]
Out[1]: array([[ 0, 3],
[12, 15]])
```

This gives you the output you were looking for.

For more info, check out this page on indexing in `NumPy`

.

##
Answer #3:

```
print y[0:4:3,0:4:3]
```

is the shortest and most appropriate fix .

##
Answer #4:

First of all, your `Y`

only has 4 col and rows, so there is no col4 or row4, at most col3 or row3.

To get 0, 3 cols: `Y[[0,3],:]`

To get 0, 3 rows: `Y[:,[0,3]]`

So to get the array you request: `Y[[0,3],:][:,[0,3]]`

Note that if you just `Y[[0,3],[0,3]]`

it is equivalent to `[Y[0,0], Y[3,3]]`

and the result will be of two elements: `array([ 0, 15])`

##
Answer #5:

You can also do this using:

```
Y[[[0],[3]],[0,3]]
```

which is equivalent to doing this using indexing arrays:

```
idx = np.array((0,3)).reshape(2,1)
Y[idx,idx.T]
```

To make the broadcasting work as desired, you need the non-singleton dimension of your indexing array to be aligned with the axis you’re indexing into, e.g. for an n x m 2D subarray:

```
Y[<n x 1 array>,<1 x m array>]
```

This doesn’t create an intermediate array, unlike CT Zhu’s answer, which creates the intermediate array `Y[(0,3),:]`

, then indexes into it.

##
Answer #6:

This can also be done by slicing: `Y[[0,3],:][:,[0,3]]`

. More elegantly, it is possible to slice arrays (or even reorder them) by given sets of indices for rows, columns, pages, etcetera:

```
r=np.array([0,3])
c=np.array([0,3])
print(Y[r,:][:,c]) #>>[[ 0 3][12 15]]
```

for reordering try this:

```
r=np.array([0,3])
c=np.array([3,0])
print(Y[r,:][:,c])#>>[[ 3 0][15 12]]
```