def test_hierarchical_matrix():
n = 30
X = np.linspace(0, 1, n)
Y = np.linspace(10, 11, n)
def f(i, j):
return 1 / abs(X[i] - Y[j])
S = np.array([[f(i, j) for j in range(n)] for i in range(n)])
HS = BlockMatrix([
[
S[:n // 2, :n // 2],
LowRankMatrix.from_full_matrix_with_ACA(S[n // 2:, :n // 2],
tol=1e-5)
],
[
LowRankMatrix.from_full_matrix_with_ACA(S[:n // 2, n // 2:],
tol=1e-5), S[n // 2:,
n // 2:]
],
])
assert np.allclose(HS.full_matrix(), S, rtol=2e-1)
doubled = HS + HS
assert np.allclose(2 * S, doubled.full_matrix(), rtol=2e-1)
def test_low_rank_blocks():
n = 10
# Test initialization
a, b = np.random.rand(n, 1), np.random.rand(1, n)
LR = LowRankMatrix(a, b)
assert LR.shape == LR.full_matrix().shape
assert matrix_rank(LR.full_matrix()) == LR.rank == 1
assert LR.density == 2 * n / n**2
a, b = np.random.rand(n, 2), np.random.rand(2, n)
LR = LowRankMatrix(a, b)
assert LR.shape == LR.full_matrix().shape
assert matrix_rank(LR.full_matrix()) == LR.rank == 2
# Test creation from SVD
A = np.arange(n**2).reshape((n, n)) + 1.0
dumb_low_rank = LowRankMatrix.from_full_matrix_with_SVD(A, n)
assert np.allclose(dumb_low_rank.full_matrix() - A, 0.0)
A_rank_1 = LowRankMatrix.from_full_matrix_with_SVD(A, 1)
assert matrix_rank(A_rank_1.full_matrix()) == A_rank_1.rank == 1
# Test recompression
recompressed = dumb_low_rank.recompress(new_rank=2)
assert recompressed.rank == matrix_rank(recompressed.full_matrix()) == 2
recompressed = dumb_low_rank.recompress(tol=1e-1)
assert recompressed.rank <= dumb_low_rank.rank
# Test multiplication with vector
b = np.random.rand(n)
assert np.allclose(A_rank_1 @ b, A_rank_1.full_matrix() @ b)
# Test creation with ACA
full_A_rank_1 = A_rank_1.full_matrix()
A_rank_1_again = LowRankMatrix.from_full_matrix_with_ACA(full_A_rank_1,
max_rank=5)
assert matrix_rank(A_rank_1_again.full_matrix()) == 1
assert np.allclose(A_rank_1_again.full_matrix(), full_A_rank_1)
# Test creation from function with ACA
X = np.linspace(0, 1, n)
Y = np.linspace(10, 11, n)
def f(i, j):
return 1 / abs(X[i] - Y[j])
S = np.array([[f(i, j) for j in range(n)] for i in range(n)])
SLR = LowRankMatrix.from_function_with_ACA(f, n, n, max_rank=2, tol=1e-2)
assert SLR.shape == (n, n)
assert np.allclose(SLR.full_matrix(), S, atol=1e-2)
with pytest.raises(NoConvergenceOfACA):
LowRankMatrix.from_function_with_ACA(f, n, n, max_rank=1, tol=1e-3)
summed = SLR + A_rank_1
assert summed.rank == 1
