Thomas Thomas - 2 months ago 5
Python Question

Delete repeated columns of array keeping the order

Is there a relatively simple way of removing columns of an (numpy) array and keeping the order of the columns?

As an example, consider this array:

a = np.array([[2, 1, 1, 3],
[2, 1, 1, 3]])


where I would like column three to be removed such that:

a = np.array([[2, 1, 3],
[2, 1, 3]])

Answer

Approach #1 Here's an approach using broadcasting -

a[:,~np.triu((a[:,None,:] == a[...,None]).all(0),1).any(0)]

Sample run -

In [115]: a
Out[115]: 
array([[2, 1, 3, 5, 1, 3, 7],
       [6, 5, 4, 6, 5, 4, 8]])

In [116]: a[:,~np.triu((a[:,None,:] == a[...,None]).all(0),1).any(0)]
Out[116]: 
array([[2, 1, 3, 5, 7],
       [6, 5, 4, 6, 8]])

Explanation

1) Input array -

In [156]: a
Out[156]: 
array([[2, 1, 3, 5, 1, 3, 7],
       [6, 5, 4, 6, 5, 4, 8]])

2) Use broadcasting to perform elementwise equality comparison keeping the first axis aligned, which would correspond to the column axis from original 2D array -

In [157]: a[:,None,:] == a[...,None]
Out[157]: 
array([[[ True, False, False, False, False, False, False],
        [False,  True, False, False,  True, False, False],
        [False, False,  True, False, False,  True, False],
        [False, False, False,  True, False, False, False],
        [False,  True, False, False,  True, False, False],
        [False, False,  True, False, False,  True, False],
        [False, False, False, False, False, False,  True]],

       [[ True, False, False,  True, False, False, False],
        [False,  True, False, False,  True, False, False],
        [False, False,  True, False, False,  True, False],
        [ True, False, False,  True, False, False, False],
        [False,  True, False, False,  True, False, False],
        [False, False,  True, False, False,  True, False],
        [False, False, False, False, False, False,  True]]], dtype=bool)

3) Since we are looking for duplicate cols, let's look for ALL matches along the first axis -

In [158]: (a[:,None,:] == a[...,None]).all(0)
Out[158]: 
array([[ True, False, False, False, False, False, False],
       [False,  True, False, False,  True, False, False],
       [False, False,  True, False, False,  True, False],
       [False, False, False,  True, False, False, False],
       [False,  True, False, False,  True, False, False],
       [False, False,  True, False, False,  True, False],
       [False, False, False, False, False, False,  True]], dtype=bool)

4) We are looking to keep the first occurrence only, so we can use a upper triangular matrix to set all diagonal and lower triangular elems as False -

In [163]: np.triu((a[:,None,:] == a[...,None]).all(0),1)
Out[163]: 
array([[False, False, False, False, False, False, False],
       [False, False, False, False,  True, False, False],
       [False, False, False, False, False,  True, False],
       [False, False, False, False, False, False, False],
       [False, False, False, False, False, False, False],
       [False, False, False, False, False, False, False],
       [False, False, False, False, False, False, False]], dtype=bool)

5) Next up, we look for ANY matches along the first axis indicating the duplicates -

In [164]: (np.triu((a[:,None,:] == a[...,None]).all(0),1)).any(0)
Out[164]: array([False, False, False, False,  True,  True, False], dtype=bool)

6) We are looking to remove those duplicates, so invert the mask -

In [165]: ~(np.triu((a[:,None,:] == a[...,None]).all(0),1)).any(0)
Out[165]: array([ True,  True,  True,  True, False, False,  True], dtype=bool)

7) Finally, we index into the columns of input array with the mask for final output -

In [166]: a[:,~(np.triu((a[:,None,:] == a[...,None]).all(0),1)).any(0)]
Out[166]: 
array([[2, 1, 3, 5, 7],
       [6, 5, 4, 6, 8]])

Approach #2 With focus on memory efficiency and might even be faster, here's an approach considering each column as an indexing tuple -

lidx = np.ravel_multi_index(a,a.max(1)+1)
out = a[:,np.sort(np.unique(lidx,return_index=1)[1])]

Explanation

1) Input array -

In [203]: a
Out[203]: 
array([[2, 1, 3, 5, 1, 3, 7],
       [6, 5, 4, 6, 5, 4, 8]])

2) Calculate linear index equivalents for each column -

In [207]: lidx = np.ravel_multi_index(a,a.max(1)+1)

In [208]: lidx
Out[208]: array([24, 14, 31, 51, 14, 31, 71])

3) Get the first occurence of each unique linear index

In [209]: np.unique(lidx,return_index=1)[1]
Out[209]: array([1, 0, 2, 3, 6])

4) Sort those and index into cols of input array for final o/p -

In [210]: np.sort(np.unique(lidx,return_index=1)[1])
Out[210]: array([0, 1, 2, 3, 6])

In [211]: a[:,np.sort(np.unique(lidx,return_index=1)[1])]
Out[211]: 
array([[2, 1, 3, 5, 7],
       [6, 5, 4, 6, 8]])

For a detailed info on the considerations related to converting to indexing tuples, please refer to this post.

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