def test_lll():
rng = ensure_rng(1)
for i in range(50):
x = rng.randint(4) + 1
mat = rng.randn(x, x + rng.randint(2))
c = 1.34 + .5 * rng.random_sample()
reduced_mat, coefs = lll.lll(mat)
assert lll.is_c_reduced(reduced_mat, c)
assert np.allclose(np.dot(mat.T, coefs), reduced_mat.T)
def test_lll():
np.random.seed(1)
for i in range(50):
x = np.random.randint(4) + 1
mat = np.random.randn(x, x + np.random.randint(2))
c = 1.34 + .5 * np.random.rand()
reduced_mat, coefs = lll.lll(mat)
assert lll.is_c_reduced(reduced_mat, c)
assert np.allclose(np.dot(mat.T, coefs), reduced_mat.T)
def test_cvp():
np.random.seed(0)
for i in range(10):
mat = np.random.randn(4, 4)
mat = lll.lll(mat)[0]
for j in range(4):
point = 50 * np.random.randn(4)
assert np.array_equal(lll.cvp(point, mat, 10)[:3],
lll.cvp(point, mat, 3))
def test_cvp():
rng = ensure_rng(0)
for i in range(1, 5):
for j in range(i, 5):
mat = rng.randn(i, j)
mat = lll.lll(mat)[0]
for k in range(4):
point = 50 * rng.randn(j)
assert np.array_equal(
lll.cvp(point, mat, 10)[:3], lll.cvp(point, mat, 3))
def test_cvp():
rng = ensure_rng(0)
for i in range(1, 5):
for j in range(i, 5):
mat = rng.randn(i, j)
mat = lll.lll(mat)[0]
for k in range(4):
point = 50 * rng.randn(j)
assert np.array_equal(
lll.cvp(point, mat, 10)[:3], lll.cvp(point, mat, 3))
# Test equidistant vectors
# Cubic lattice
basis = np.eye(3)
vec = np.zeros((3))
assert len(lll.cvp(vec, basis, n=2, group_by_length=True)) == 7
assert len(lll.cvp(vec, basis, n=3, group_by_length=True)) == 19
vec = 0.5 * np.array([1, 1, 1])
assert len(lll.cvp(vec, basis, group_by_length=True)) == 8
vec = 0.5 * np.array([1, 1, 0])
assert len(lll.cvp(vec, basis, group_by_length=True)) == 4
vec = 0.5 * np.array([1, 0, 0])
assert len(lll.cvp(vec, basis, group_by_length=True)) == 2
# Square lattice with offset
offset = np.array([0, 0, 1])
basis = np.eye(3)[:2]
vec = np.zeros((3)) + rng.rand() * offset
assert len(lll.cvp(vec, basis, n=2, group_by_length=True)) == 5
assert len(lll.cvp(vec, basis, n=3, group_by_length=True)) == 9
vec = 0.5 * np.array([1, 1, 0]) + rng.rand() * offset
assert len(lll.cvp(vec, basis, group_by_length=True)) == 4
vec = 0.5 * np.array([1, 0, 0]) + rng.rand() * offset
assert len(lll.cvp(vec, basis, group_by_length=True)) == 2
# Hexagonal lattice
basis = np.array([[1, 0], [-0.5, 0.5 * np.sqrt(3)]])
vec = np.zeros((2))
assert len(lll.cvp(vec, basis, n=2, group_by_length=True)) == 7
assert len(lll.cvp(vec, basis, n=3, group_by_length=True)) == 13
vec = np.array([0.5, 0.5 / np.sqrt(3)])
assert len(lll.cvp(vec, basis, group_by_length=True)) == 3
assert len(lll.cvp(vec, basis, n=2, group_by_length=True)) == 6
assert len(lll.cvp(vec, basis, n=3, group_by_length=True)) == 12
