Numpy array and Matlab Matrix are mismatching [3D]

Question

The following octave code shows a sample 3D matrix using Octave/Matlab

octave:1> A=zeros(3,3,3);
octave:2> 
octave:2> A(:,:,1)= [[1 2 3];[4 5 6];[7         


        

Answer 1

MATLAB and Python index differently. To investigate this, lets create a linear array of number 1 to 8 and then reshape the result to be a 2-by-2-by-2 matrix in each language:

MATLAB:

M_flat = 1:8
M = reshape(M_flat, [2,2,2])

which returns

M =

ans(:,:,1) =

   1   3
   2   4

ans(:,:,2) =

   5   7
   6   8

Python:

import numpy as np
P_flat = np.array(range(1,9))
P = np.reshape(P, [2,2,2])

which returns

array([[[1, 2],
        [3, 4]],

       [[5, 6],
        [7, 8]]])

The first thing you should notice is that the first two dimensions have switched. This is because MATLAB uses column-major indexing which means we count down the columns first whereas Python use row-major indexing and hence it counts across the rows first.

Now let's try indexing them. So let's try slicing along the different dimensions. In MATLAB, I know to get a slice out of the third dimension I can do

M(:,:,1)

ans =

   1   3
   2   4

Now let's try the same in Python

P[:,:,0]

array([[1, 3],
       [5, 7]])

So that's completely different. To get the MATLAB 'equivalent' we need to go

P[0,:,:]

array([[1, 2],
       [3, 4]])

Now this returns the transpose of the MATLAB version which is to be expected due the the row-major vs column-major difference.

So what does this mean for indexing? It looks like Python puts the major index at the end which is the reverse of MALTAB.

Let's say I index as follows in MATLAB

M(1,2,2)

ans = 

    7

now to get the 7 from Python we should go

P(1,1,0)

which is the MATLAB syntax reversed. Note that is is reversed because we created the Python matrix with a row-major ordering in mind. If you create it as you did in your code you would have to swap the last 2 indices so rather create the matrix correctly in the first place as Ander has suggested in the comments.