Accessing columns of matlab matrix and its realization in numpy-CodePudding

I am trying to find a realization of accessing elements of numpy arrays corresponding to a feature of Matlab.

Suppose given a (2,2,2) Matlab matrix m in the form

m(:,:,1) = [1,2;3,4]
m(:,:,2) = [5,6;7,8]

Even though this is a 3-d array, Matlab allows accessing its column in the fashion like

m(:,1) = [1;3]
m(:,2) = [2;4]
m(:,3) = [5;7]
m(:,4) = [6;8]

I am curious to know that if numpy supports such indexing so that given the following array

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

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

One can also access columns in the fashion as Matlab listed above.

CodePudding user response：

My answer to this question is as following, suppose given the array listed as in the question

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

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

One can create a list, I call it m_list in the form such that

m_list = [m[i][:,j] for i in range(m.shape[0]) for j in range(m.shape[-1])]

This will output m_list in the form such that

m_list = [array([1, 3]), array([2, 4]), array([7, 9]), array([ 8, 10])]

Now we can access elements of m_list exactly as the fashion as Matlab as listed in the question.

CodePudding user response：

In [41]: m = np.arange(1,9).reshape(2,2,2)
In [42]: m
Out[42]: 
array([[[1, 2],
        [3, 4]],

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

Indexing the equivalent blocks:

In [47]: m[0,:,0]
Out[47]: array([1, 3])
In [48]: m[0,:,1]
Out[48]: array([2, 4])
In [49]: m[1,:,0]
Out[49]: array([5, 7])
In [50]: m[1,:,1]
Out[50]: array([6, 8])

We can reshape, to "flatten" one pair of dimensions:

In [84]: m = np.arange(1,9).reshape(2,2,2)
In [85]: m.reshape(2,4)
Out[85]: 
array([[1, 2, 3, 4],
       [5, 6, 7, 8]])
In [87]: m.reshape(2,4)[:,2]
Out[87]: array([3, 7])

and throw in a transpose:

In [90]: m.transpose(1,0,2).reshape(2,4)
Out[90]: 
array([[1, 2, 5, 6],
       [3, 4, 7, 8]])

MATLAB originally was strictly 2d. Then sometime around v3.9 (2000) they allowed for more, but in a kludgy way. They added a way to index the trailing dimension as though it was multidimensional. In another recent SO I noticed that when reshaping to (2,2,1,1) the result remained (2,2). Trailing size 1 dimensions are squeeze out.

I suspect the m(:,3) is a consequence of that as well.

Testing a 4d MATLAB

>> m=reshape(1:36,2,3,3,2);
>> m(:,:,1)
ans =

   1   3   5
   2   4   6

>> reshape(m,2,3,6)(:,:,1)
ans =

   1   3   5
   2   4   6

>> m(:,17)
ans =

   33
   34

>> reshape(m,2,18)(:,17)
ans =

   33
   34