def test_BlockMatrix_2x2_inverse_numeric():
"""Test 2x2 block matrix inversion numerically for all 4 formulas"""
M = Matrix([[1, 2], [3, 4]])
# rank deficient matrices that have full rank when two of them combined
D1 = Matrix([[1, 2], [2, 4]])
D2 = Matrix([[1, 3], [3, 9]])
D3 = Matrix([[1, 4], [4, 16]])
assert D1.rank() == D2.rank() == D3.rank() == 1
assert (D1 + D2).rank() == (D2 + D3).rank() == (D3 + D1).rank() == 2
# Only A is invertible
K = BlockMatrix([[M, D1], [D2, D3]])
assert block_collapse(K.inv()).as_explicit() == K.as_explicit().inv()
# Only B is invertible
K = BlockMatrix([[D1, M], [D2, D3]])
assert block_collapse(K.inv()).as_explicit() == K.as_explicit().inv()
# Only C is invertible
K = BlockMatrix([[D1, D2], [M, D3]])
assert block_collapse(K.inv()).as_explicit() == K.as_explicit().inv()
# Only D is invertible
K = BlockMatrix([[D1, D2], [D3, M]])
assert block_collapse(K.inv()).as_explicit() == K.as_explicit().inv()
def test_issue_21866():
n = 10
I = Identity(n)
O = ZeroMatrix(n, n)
A = BlockMatrix([[ I, O, O, O ],
[ O, I, O, O ],
[ O, O, I, O ],
[ I, O, O, I ]])
Ainv = block_collapse(A.inv())
AinvT = BlockMatrix([[ I, O, O, O ],
[ O, I, O, O ],
[ O, O, I, O ],
[ -I, O, O, I ]])
assert Ainv == AinvT