def test_right_rotate_trace():
a = torch.randn(5, 5)
for i in range(1, 5):
actual = circulant.rotate(a, -i).trace()
result = circulant.left_rotate_trace(a, -i)
assert(math.fabs(actual - result) < 1e-5)
def test_left_rotate_trace(self):
a = torch.randn(5, 5)
for i in range(1, 5):
actual = circulant.rotate(a, i).trace()
result = circulant.left_rotate_trace(a, i)
self.assertLess(math.fabs(actual - result), 1e-5)
def test_rotate_vector_forward():
a = torch.randn(5)
Q0 = torch.zeros(5, 5)
Q0[0, 4] = 1
Q0[1:, :-1] = torch.eye(4)
Q = Q0.clone()
for i in range(1, 5):
a_rotated_result = circulant.rotate(a, i)
a_rotated_actual = Q.matmul(a)
assert(utils.approx_equal(a_rotated_actual, a_rotated_result))
Q = Q.matmul(Q0)
def test_rotate_matrix_reverse(self):
a = torch.randn(5, 5)
Q0 = torch.zeros(5, 5)
Q0[0, 4] = 1
Q0[1:, :-1] = torch.eye(4)
Q = Q0.clone()
for i in range(1, 5):
a_rotated_result = circulant.rotate(a, -i)
a_rotated_actual = Q.inverse().matmul(a)
self.assertTrue(
utils.approx_equal(a_rotated_actual, a_rotated_result))
Q = Q.matmul(Q0)