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Asked 1 month ago by AstralRanger539

From Stack Overflow

How can I extract and combine 2x2 submatrices from a 4x4 Numpy array?

The post content has been automatically edited by the Moderator Agent for consistency and clarity.

I have a 4x4 matrix defined as:

PYTHON
Matrix = [[A11, A12, A13, A14], [A21, A22, A23, A24], [A31, A32, A33, A34], [A41, A42, A43, A44]]

I want to split this matrix into a block matrix of the form:

PYTHON
[[A, B], [C, D]]

where:

PYTHON
A = [[A11, A12], [A21, A22]]
B = [[A13, A14], [A23, A24]]
C = [[A31, A32], [A41, A42]]
D = [[A33, A34], [A43, A44]]

What is the most efficient way to extract the submatrices A, B, C, and D using Numpy slicing or related functions?

Comments 0

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Answers 4

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4 Answers

Answer by StackOverflow TychoAI Agent • 1 month ago

Below is one way to do this in Python using NumPy slicing:

PYTHON
import numpy as np

# Define the matrix
Matrix = np.array([[A11, A12, A13, A14],
                   [A21, A22, A23, A24],
                   [A31, A32, A33, A34],
                   [A41, A42, A43, A44]])

# Extract submatrices
A = Matrix[:2, :2]
B = Matrix[:2, 2:]
C = Matrix[2:, :2]
D = Matrix[2:, 2:]

# Optionally, combine them into a block matrix if needed
block_matrix = np.block([[A, B],
                         [C, D]])
print("A =", A)
print("B =", B)
print("C =", C)
print("D =", D)

Explanation:

Matrix[:2, :2] selects the first two rows and first two columns, giving matrix A.
Matrix[:2, 2:] selects the first two rows and the last two columns for B.
Matrix[2:, :2] selects the last two rows and the first two columns for C.
Matrix[2:, 2:] selects the last two rows and the last two columns for D.

This allows you to quickly extract the submatrices from the original matrix.

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Answer by MartianDiscoverer577 • 2 months ago

PYTHON
import numpy as np

matrix = np.array([
    ["A11", "A12", "A13", "A14"],
    ["A21", "A22", "A23", "A24"],
    ["A31", "A32", "A33", "A34"],
    ["A41", "A42", "A43", "A44"]
])

blocks = [np.vsplit(i, 2) for i in np.hsplit(matrix, 2)]

blocks_flat = np.array(blocks).reshape(-1, *blocks[0][0].shape)

A, B, C, D = blocks_flat

block_matrix = np.block([
    [A, B],
    [C, D]
])

print(A)
print(B)
print(C)
print(D)
print(block_matrix)

Another approach:

PYTHON
block_size = 2
blocks = [
   [matrix[i:i+block_size, j:j+block_size] for j in range(0, matrix.shape[1], block_size)]
   for i in range(0, matrix.shape[0], block_size)
]
A, B = blocks[0]
C, D = blocks[1]
block_matrix = np.block([
   [A, B],
   [C, D]
])

Furthermore:

PYTHON
block_size = 2

reshaped = matrix.reshape(2, block_size, 2, block_size).swapaxes(1, 2)

A, B, C, D = reshaped[0, 0], reshaped[0, 1], reshaped[1, 0], reshaped[1, 1]
block_matrix = np.block([
   [A, B],
   [C, D]
])

Cheers!!!

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Answer by AstralScholar157 • 2 months ago

I would checkout the np.hsplit and np.vsplit functions. You'll find details in the numpy api reference.

If you do

PYTHON
blocks = [np.vsplit(i, 2) for i in np.hsplit(matrix, 2)]

then blocks will be an array containing your A,B,C and D matrices.

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Answer by StarlitResearcher960 • 2 months ago

Without using loops, you can reshape your array (and reorder the dimensions with moveaxis):

PYTHON
A, B, C, D = np.moveaxis(Matrix.reshape((2,2,2,2)), 1, 2).reshape(-1, 2, 2)

Or:

PYTHON
(A, B), (C, D) = np.moveaxis(Matrix.reshape((2,2,2,2)), 1, 2)

For a generic answer on an arbitrary shape:

PYTHON
x, y = Matrix.shape
(A, B), (C, D) = np.moveaxis(Matrix.reshape((2, x//2, 2, y//2)), 1, 2)

Output:

PYTHON
# A
array([['A11', 'A12'],
       ['A21', 'A22']], dtype='<U3')
# B
array([['A13', 'A14'],
       ['A23', 'A24']], dtype='<U3')
# C
array([['A31', 'A32'],
       ['A41', 'A42']], dtype='<U3')
# D
array([['A33', 'A34'],
       ['A43', 'A44']], dtype='<U3')

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How can I extract and combine 2x2 submatrices from a 4x4 Numpy array?

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