Getting a grid of a matrix via logical indexing in Numpy

Question

I'm trying to rewrite a function using numpy which is originally in MATLAB. There's a logical indexing part which is as follows in MATLAB:

X = reshape(1:16, 4, 4).';
idx = [true, false, false, true];
X(idx, idx)

ans =

     1     4
    13    16

When I try to make it in numpy, I can't get the correct indexing:

X = np.arange(1, 17).reshape(4, 4)
idx = [True, False, False, True] 
X[idx, idx]
# Output: array([6, 1, 1, 6])

What's the proper way of getting a grid from the matrix via logical indexing?

Answer 1

You could also write:

>>> X[np.ix_(idx,idx)]
array([[ 1,  4],
       [13, 16]])

Answer 2

In [1]: X = np.arange(1, 17).reshape(4, 4)

In [2]: idx = np.array([True, False, False, True])  # note that here idx has to
                                                    # be an array (not a list)
                                                    # or boolean values will be 
                                                    # interpreted as integers

In [3]: X[idx][:,idx]
Out[3]: 
array([[ 1,  4],
       [13, 16]])

Answer 3

In numpy this is called fancy indexing. To get the items you want you should use a 2D array of indices.

You can use an outer to make from your 1D idx a proper 2D array of indices. The outers, when applied to two 1D sequences, compare each element of one sequence to each element of the other. Recalling that True*True=True and False*True=False, the np.multiply.outer(), which is the same as np.outer(), can give you the 2D indices:

idx_2D = np.outer(idx,idx)
#array([[ True, False, False,  True],
#       [False, False, False, False],
#       [False, False, False, False],
#       [ True, False, False,  True]], dtype=bool)

Which you can use:

x[ idx_2D ]
array([ 1,  4, 13, 16])

In your real code you can use x=[np.outer(idx,idx)] but it does not save memory, working the same as if you included a del idx_2D after doing the slice.