def test_quaternion_0():
q = uniform_quaternion(random_state=2)
eq(np.sum(q**2), np.float64(1.0))
eq(q.shape, (4, ))
q2 = uniform_quaternion(size=2)
eq(np.sum(q2**2, axis=1), np.ones(2))
eq(q2.shape, (2, 4))
q2 = uniform_quaternion(size=(6, 6))
eq(np.sum(q2**2, axis=2), np.ones((6, 6)))
eq(q2.shape, (6, 6, 4))
def test_quaternion_0():
q = uniform_quaternion(random_state=2)
eq(np.sum(q**2), np.float64(1.0))
eq(q.shape, (4,))
q2 = uniform_quaternion(size=2)
eq(np.sum(q2**2, axis=1), np.ones(2))
eq(q2.shape, (2,4))
q2 = uniform_quaternion(size=(6,6))
eq(np.sum(q2**2, axis=2), np.ones((6,6)))
eq(q2.shape, (6,6,4))
def test_quaternion_1():
q = uniform_quaternion(random_state=2)
rot = rotation_matrix_from_quaternion(q)
eq(rot.shape, (3,3))
eq(np.linalg.det(rot), np.double(1.0))
eq(np.linalg.inv(rot), rot.T)
def test_lprmsd_3(get_fn):
# resolve rotation and permutation togetehr
t1 = md.load(get_fn('alanine-dipeptide-explicit.pdb'))[0]
t2 = md.load(get_fn('alanine-dipeptide-explicit.pdb'))[0]
h2o_o_indices = [a.index for a in t1.topology.atoms if a.residue.name == 'HOH' and a.element.symbol == 'O'][0:20]
h2o_h_indices = [a.index for a in t1.topology.atoms if a.residue.name == 'HOH' and a.element.symbol == 'H'][0:20]
backbone_indices = [a.index for a in t1.topology.atoms if a.element.symbol in ['C', 'N']][:5]
# scramble two groups of indices
t2.xyz[:, random.permutation(h2o_o_indices)] = t2.xyz[:, h2o_o_indices]
t2.xyz[:, random.permutation(h2o_h_indices)] = t2.xyz[:, h2o_h_indices]
# offset the backbone indices slightly
t2.xyz[:, backbone_indices] += 0.001 * random.randn(len(backbone_indices), 3)
# rotate everything
rot = rotation_matrix_from_quaternion(uniform_quaternion())
t2.xyz[0].dot(rot)
print('raw distinguishable indices', backbone_indices)
atom_indices = np.concatenate((h2o_o_indices, backbone_indices))
value = md.lprmsd(t2, t1, atom_indices=atom_indices, permute_groups=[h2o_o_indices])
t1.xyz[:, h2o_o_indices] += random.randn(len(h2o_o_indices), 3)
print('final value', value)
assert value[0] < 1e-2
def test_quaternion_1():
q = uniform_quaternion(random_state=2)
rot = rotation_matrix_from_quaternion(q)
eq(rot.shape, (3, 3))
eq(np.linalg.det(rot), np.double(1.0))
eq(np.linalg.inv(rot), rot.T)
def test_lprmsd_1():
# resolve a random rotation with no permutation
ref = random.randn(1, 50, 3).astype(np.float32)
mapping = np.arange(50)
rot = rotation_matrix_from_quaternion(uniform_quaternion())
new = ref[:, mapping].dot(rot)
value = lprmsd(Trajectory(xyz=new, topology=None), Trajectory(xyz=ref, topology=None), permute_groups=[[]])
assert value[0] < 1e-2
def test_lprmsd_2():
# resolve a random rotation with some permutation
ref = random.randn(1, 50, 3).astype(np.float32)
# first half of the atoms can permute, last 10 are fixed permutation
mapping = np.concatenate((random.permutation(10), 10 + np.arange(40)))
rot = rotation_matrix_from_quaternion(uniform_quaternion())
new = ref[:, mapping].dot(rot)
value = lprmsd(Trajectory(xyz=new, topology=None), Trajectory(xyz=ref, topology=None), permute_groups=[np.arange(10)])
assert value[0] < 1e-2
def test_quaternion_2():
q = uniform_quaternion(size=2)
rot = rotation_matrix_from_quaternion(q)
eq(rot.shape, (2, 3, 3))
# check 1st rotation matrix
eq(np.linalg.det(rot[0]), np.double(1.0))
eq(np.linalg.inv(rot[0]), rot[0].T)
# check 2nd rotation matrix
eq(np.linalg.det(rot[1]), np.double(1.0))
eq(np.linalg.inv(rot[1]), rot[1].T)
def test_quaternion_2():
q = uniform_quaternion(size=2)
rot = rotation_matrix_from_quaternion(q)
eq(rot.shape, (2, 3, 3))
# check 1st rotation matrix
eq(np.linalg.det(rot[0]), np.double(1.0))
eq(np.linalg.inv(rot[0]), rot[0].T)
# check 2nd rotation matrix
eq(np.linalg.det(rot[1]), np.double(1.0))
eq(np.linalg.inv(rot[1]), rot[1].T)