python – Sorting arrays in NumPy by column

The Question :

368 people think this question is useful

How can I sort an array in NumPy by the nth column?

For example,

a = array([[9, 2, 3],
           [4, 5, 6],
           [7, 0, 5]])

I’d like to sort rows by the second column, such that I get back:

array([[7, 0, 5],
       [9, 2, 3],
       [4, 5, 6]])

The Question Comments :
  • This is a really bad example since np.sort(a, axis=0) would be a satisfactory solution for the given matrix. I suggested an edit with a better example but was rejected, although actually the question would be much more clear. The example should be something like a = numpy.array([[1, 2, 3], [6, 5, 2], [3, 1, 1]]) with desired output array([[3, 1, 1], [1, 2, 3], [6, 5, 2]])
  • David, you don’t get the point of the question. He wants to keep the order within each row the same.
  • @marcorossi I did get the point, but the example was very badly formulated because, as I said, there were multiple possible answers (which, however, wouldn’t have satisfied the OP’s request). A later edit based on my comment has indeed been approved (funny that mine got rejected, though). So now everything is fine.

The Answer 1

154 people think this answer is useful

@steve‘s answer is actually the most elegant way of doing it.

For the “correct” way see the order keyword argument of numpy.ndarray.sort

However, you’ll need to view your array as an array with fields (a structured array).

The “correct” way is quite ugly if you didn’t initially define your array with fields…

As a quick example, to sort it and return a copy:

In [1]: import numpy as np

In [2]: a = np.array([[1,2,3],[4,5,6],[0,0,1]])

In [3]: np.sort(a.view('i8,i8,i8'), order=['f1'], axis=0).view(np.int)
Out[3]: 
array([[0, 0, 1],
       [1, 2, 3],
       [4, 5, 6]])

To sort it in-place:

In [6]: a.view('i8,i8,i8').sort(order=['f1'], axis=0) #<-- returns None

In [7]: a
Out[7]: 
array([[0, 0, 1],
       [1, 2, 3],
       [4, 5, 6]])

@Steve’s really is the most elegant way to do it, as far as I know…

The only advantage to this method is that the “order” argument is a list of the fields to order the search by. For example, you can sort by the second column, then the third column, then the first column by supplying order=[‘f1′,’f2′,’f0’].

The Answer 2

812 people think this answer is useful

I suppose this works: a[a[:,1].argsort()]

This indicates the second column of a and sort it based on it accordingly.

The Answer 3

35 people think this answer is useful

You can sort on multiple columns as per Steve Tjoa’s method by using a stable sort like mergesort and sorting the indices from the least significant to the most significant columns:

a = a[a[:,2].argsort()] # First sort doesn't need to be stable.
a = a[a[:,1].argsort(kind='mergesort')]
a = a[a[:,0].argsort(kind='mergesort')]

This sorts by column 0, then 1, then 2.

The Answer 4

21 people think this answer is useful

From the Python documentation wiki, I think you can do:

a = ([[1, 2, 3], [4, 5, 6], [0, 0, 1]]); 
a = sorted(a, key=lambda a_entry: a_entry[1]) 
print a

The output is:

[[[0, 0, 1], [1, 2, 3], [4, 5, 6]]]

The Answer 5

20 people think this answer is useful

In case someone wants to make use of sorting at a critical part of their programs here’s a performance comparison for the different proposals:

import numpy as np
table = np.random.rand(5000, 10)

%timeit table.view('f8,f8,f8,f8,f8,f8,f8,f8,f8,f8').sort(order=['f9'], axis=0)
1000 loops, best of 3: 1.88 ms per loop

%timeit table[table[:,9].argsort()]
10000 loops, best of 3: 180 µs per loop

import pandas as pd
df = pd.DataFrame(table)
%timeit df.sort_values(9, ascending=True)
1000 loops, best of 3: 400 µs per loop

So, it looks like indexing with argsort is the quickest method so far…

The Answer 6

18 people think this answer is useful

From the NumPy mailing list, here’s another solution:

>>> a
array([[1, 2],
       [0, 0],
       [1, 0],
       [0, 2],
       [2, 1],
       [1, 0],
       [1, 0],
       [0, 0],
       [1, 0],
      [2, 2]])
>>> a[np.lexsort(np.fliplr(a).T)]
array([[0, 0],
       [0, 0],
       [0, 2],
       [1, 0],
       [1, 0],
       [1, 0],
       [1, 0],
       [1, 2],
       [2, 1],
       [2, 2]])

The Answer 7

5 people think this answer is useful

I had a similar problem.

My Problem:

I want to calculate an SVD and need to sort my eigenvalues in descending order. But I want to keep the mapping between eigenvalues and eigenvectors. My eigenvalues were in the first row and the corresponding eigenvector below it in the same column.

So I want to sort a two-dimensional array column-wise by the first row in descending order.

My Solution

a = a[::, a[0,].argsort()[::-1]]

So how does this work?

a[0,] is just the first row I want to sort by.

Now I use argsort to get the order of indices.

I use [::-1] because I need descending order.

Lastly I use a[::, ...] to get a view with the columns in the right order.

The Answer 8

3 people think this answer is useful
import numpy as np
a=np.array([[21,20,19,18,17],[16,15,14,13,12],[11,10,9,8,7],[6,5,4,3,2]])
y=np.argsort(a[:,2],kind='mergesort')# a[:,2]=[19,14,9,4]
a=a[y]
print(a)

Desired output is [[6,5,4,3,2],[11,10,9,8,7],[16,15,14,13,12],[21,20,19,18,17]]

note that argsort(numArray) returns the indices of an numArray as it was supposed to be arranged in a sorted manner.

example

x=np.array([8,1,5]) 
z=np.argsort(x) #[1,3,0] are the **indices of the predicted sorted array**
print(x[z]) #boolean indexing which sorts the array on basis of indices saved in z

answer would be [1,5,8]

The Answer 9

1 people think this answer is useful

A little more complicated lexsort example – descending on the 1st column, secondarily ascending on the 2nd. The tricks with lexsort are that it sorts on rows (hence the .T), and gives priority to the last.

In [120]: b=np.array([[1,2,1],[3,1,2],[1,1,3],[2,3,4],[3,2,5],[2,1,6]])
In [121]: b
Out[121]: 
array([[1, 2, 1],
       [3, 1, 2],
       [1, 1, 3],
       [2, 3, 4],
       [3, 2, 5],
       [2, 1, 6]])
In [122]: b[np.lexsort(([1,-1]*b[:,[1,0]]).T)]
Out[122]: 
array([[3, 1, 2],
       [3, 2, 5],
       [2, 1, 6],
       [2, 3, 4],
       [1, 1, 3],
       [1, 2, 1]])

The Answer 10

0 people think this answer is useful

Here is another solution considering all columns (more compact way of J.J‘s answer);

ar=np.array([[0, 0, 0, 1],
             [1, 0, 1, 0],
             [0, 1, 0, 0],
             [1, 0, 0, 1],
             [0, 0, 1, 0],
             [1, 1, 0, 0]])

Sort with lexsort,

ar[np.lexsort(([ar[:, i] for i in range(ar.shape[1]-1, -1, -1)]))]

Output:

array([[0, 0, 0, 1],
       [0, 0, 1, 0],
       [0, 1, 0, 0],
       [1, 0, 0, 1],
       [1, 0, 1, 0],
       [1, 1, 0, 0]])

The Answer 11

0 people think this answer is useful

Simply using sort, use coloumn number based on which you want to sort.

a = np.array([1,1], [1,-1], [-1,1], [-1,-1]])
print (a)
a=a.tolist() 
a = np.array(sorted(a, key=lambda a_entry: a_entry[0]))
print (a)

The Answer 12

0 people think this answer is useful

It is an old question but if you need to generalize this to a higher than 2 dimension arrays, here is the solution than can be easily generalized:

np.einsum('ij->ij', a[a[:,1].argsort(),:])

This is an overkill for two dimensions and a[a[:,1].argsort()] would be enough per @steve’s answer, however that answer cannot be generalized to higher dimensions. You can find an example of 3D array in this question.

Output:

[[7 0 5]
 [9 2 3]
 [4 5 6]]

The Answer 13

0 people think this answer is useful

#for sorting along column 1

indexofsort=np.argsort(dataset[:,0],axis=-1,kind='stable') 
dataset   = dataset[indexofsort,:]

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