Affine Matrix Decomposition

Problem

Split a 3x3 affine matrix into its translation and linear parts.

The last row must be [0, 0, 1] within 1e-9; otherwise return None. Return [t, L] where t is the translation [M[0][2], M[1][2]] and L is the leading 2x2 block.

Hint

The translation lives in the third column; the linear map lives in the top-left 2x2 block.

Test cases

case 1

in: [[[1,0,5],[0,1,-2],[0,0,1]]]

expected: [[5,-2],[[1,0],[0,1]]]

case 2

in: [[[2,0,0],[0,3,0],[0,0,1]]]

expected: [[0,0],[[2,0],[0,3]]]

case 3

in: [[[0,-1,4],[1,0,7],[0,0,1]]]

expected: [[4,7],[[0,-1],[1,0]]]

case 4

in: [[[1,0,0],[0,1,0],[0,0,1]]]

expected: [[0,0],[[1,0],[0,1]]]

case 5

in: [[[1,0,0],[0,1,0],[1,0,1]]]

expected: null

Starter codePython

def affine_matrix_decomposition(M):
    # Your code here
    pass

5 test cases · run your code against them in the editor