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
def full_like(A, value, dtype=np.float64):
"""A matrix of the same kind and shape as A but filled with a single value."""
if isinstance(A, BlockMatrix):
new_matrix = []
for i in range(A._stored_nb_blocks[0]):
line = []
for j in range(A._stored_nb_blocks[1]):
line.append(
full_like(A._stored_blocks[i, j], value, dtype=dtype))
new_matrix.append(line)
return A.__class__(new_matrix)
elif isinstance(A, LowRankMatrix):
return LowRankMatrix(np.ones((A.shape[0], 1)),
np.full((1, A.shape[1]), value))
elif isinstance(A, np.ndarray):
return np.full_like(A, value, dtype=dtype)