CODEWITHSUNDEEP
pythonpython-3.xnumpy
tachyon
tachyon

Reputation: 479

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:

$$
\begin{bmatrix}
A_{11} & A_{12}\\ 
A_{21} & A_{22}
\end{bmatrix}
,

\begin{bmatrix}
B_{11} & B_{12}\\ 
B_{21} & B_{22}
\end{bmatrix}
,

\begin{bmatrix}
C_{11} & C_{12}\\ 
C_{21} & C_{22}
\end{bmatrix}
,

\begin{bmatrix}
D_{11} & D_{12}\\ 
D_{21} & D_{22}
\end{bmatrix}
$$

Expected output:

$$
\begin{bmatrix}
\begin{bmatrix}
A_{11} & B_{11}\\ 
C_{11} & D_{11}
\end{bmatrix} & \begin{bmatrix}
A_{12} & B_{12}\\ 
C_{12} & D_{12}
\end{bmatrix}\\ 
\begin{bmatrix}
A_{21} & B_{21}\\ 
C_{21} & D_{21}
\end{bmatrix} & \begin{bmatrix}
A_{22} & B_{12}\\ 
C_{22} & D_{22}
\end{bmatrix}
\end{bmatrix
$$

Upvotes: 1

Views: 579

Answers (2)

hpaulj
hpaulj

Reputation: 231325

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.

Upvotes: 1

dgkr
dgkr

Reputation: 345

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)

Upvotes: 0

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