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Creating Matrix(array) where each element itself is a matrix

I have four mxn matrices. From those matrices I want to create a mxn matrix of matrices such that each element of new matrix would be a 2x2 matrix taking respective elements from each matrix. So far I can think of stacking all four matrices and then reshape each element along z axis and replace it. I believe there is more elegant solution to this.
Sample input:

$$
beginbmatrix
A_11 & A_12\
A_21 & A_22
endbmatrix
,

beginbmatrix
B_11 & B_12\
B_21 & B_22
endbmatrix
,

beginbmatrix
C_11 & C_12\
C_21 & C_22
endbmatrix
,

beginbmatrix
D_11 & D_12\
D_21 & D_22
endbmatrix
$$


Expected output:

$$
beginbmatrix
beginbmatrix
A_11 & B_11\
C_11 & D_11
endbmatrix & beginbmatrix
A_12 & B_12\
C_12 & D_12
endbmatrix\
beginbmatrix
A_21 & B_21\
C_21 & D_21
endbmatrix & beginbmatrix
A_22 & B_12\
C_22 & D_22
endbmatrix
end{bmatrix
$$


2 Answers
2

A sample creating function:

In [510]: def foo(astr,m,n):
...: alist = [astr+'%d%d'%(i,j) for i in range(m) for j in range(n)]
...: return np.array(alist).reshape(m,n)
In [511]: foo('A',2,2)
Out[511]:
array([['A00', 'A01'],
['A10', 'A11']], dtype='<U3')


A list of 4 such arrays:

In [512]: alist = [foo('A',2,2),foo('B',2,2),foo('C',2,2),foo('D',2,2)]


Various ways of stacking:

In [513]: np.stack(alist)
Out[513]:
array([[['A00', 'A01'],
['A10', 'A11']],

[['B00', 'B01'],
['B10', 'B11']],

[['C00', 'C01'],
['C10', 'C11']],

[['D00', 'D01'],
['D10', 'D11']]], dtype='<U3')

In [514]: np.stack(alist,2)
Out[514]:
array([[['A00', 'B00', 'C00', 'D00'],
['A01', 'B01', 'C01', 'D01']],

[['A10', 'B10', 'C10', 'D10'],
['A11', 'B11', 'C11', 'D11']]], dtype='<U3')
In [515]: _.shape
Out[515]: (2, 2, 4)


This can be reshaped in various ways:

In [516]: __.reshape(2,2,2,2)
Out[516]:
array([[[['A00', 'B00'],
['C00', 'D00']],

[['A01', 'B01'],
['C01', 'D01']]],


[[['A10', 'B10'],
['C10', 'D10']],

[['A11', 'B11'],
['C11', 'D11']]]], dtype='<U3')
In [517]: _.reshape(4,2,2)
Out[517]:
array([[['A00', 'B00'],
['C00', 'D00']],

[['A01', 'B01'],
['C01', 'D01']],

[['A10', 'B10'],
['C10', 'D10']],

[['A11', 'B11'],
['C11', 'D11']]], dtype='<U3')


Instead different axis, you can create one and transpose the axes to your heart's content.

Since all have mxn elements, make mxn iterations and at each iteration, build a 2x2 matrix from each element of the 4 matrices and then add the list to your final mxn matrix.

matrix1 = [[1, 1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1]]
matrix2 = [[2, 2, 2, 2], [2, 2, 2, 2], [2, 2, 2, 2]]
matrix3 = [[3, 3, 3, 3], [3, 3, 3, 3], [3, 3, 3, 3]]
matrix4 = [[4, 4, 4, 4], [4, 4, 4, 4], [4, 4, 4, 4]]

matrixFinal =

for i in range(len(matrix1)):
matrixFinal.append()
for j in range(len(matrix1[i])):
matrixFinal[i].append ([[matrix1[i][j], matrix2[i][j]], [matrix3[i][j], matrix4[i][j]]])

print(matrixFinal)


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