# What is the best way to perform an anti-transpose in python?

## Question:

Lets say I have an array

```
a = np.arange(16).reshape((4,4))
0 1 2 3
4 5 6 7
8 9 10 11
12 13 14 15
```

But I want

```
15 11 7 3
14 10 6 2
13 9 5 1
12 8 4 0
```

which is a flip across the secondary diagonal, or a kind of anti-transpose.

How can I do this in numpy?

## Answers:

One could do one of the following:

`rot90(a,2).T`

`rot90(flipud(a),1)`

`rot90(fliplr(a), -1)`

or as hpaulj suggested in the comments (thanks hpaulj)

`a[::-1,::-1].T`

Here are the speed rankings as ratios of the slowest method after anti-transposing 1000 random 10000×10000 arrays.

- 63.5% –
`a[::-1,::-1].T`

- 85.6% –
`rot90(a,2).T`

- 97.8% –
`rot90(flipud(a),1)`

- 100% –
`rot90(fliplr(a),-1)`

Here’s another to throw into the mix.

```
a.ravel('F')[::-1].reshape(a.shape)
```

Try it in this manner,

```
np=np[::-1] #reverse the array
a = np.arange(16).reshape((4,4))
```

`np.flip(a).T`

From the `np.flip`

documentation & @hpaulj ‘s comment:

`flip(m) corresponds to m[::-1,::-1,...,::-1] with ::-1 at all positions.`