def __init__(self, n, lmax):
super().__init__()
self.n = n
self.lmax = lmax
R = o3.rot(math.pi / 2, math.pi / 2, math.pi / 2)
self.xyz1, self.proj1 = self.precompute(R)
R = o3.rot(0, 0, 0)
self.xyz2, self.proj2 = self.precompute(R)
def find_peaks(self, res=100):
x1, f1 = self.signal_on_grid(res)
abc = pi / 2, pi / 2, pi / 2
R = o3.rot(*abc)
D = rs.rep(self.Rs, *abc)
rtensor = SphericalTensor(D @ self.signal)
rx2, f2 = rtensor.signal_on_grid(res)
x2 = torch.einsum('ij,baj->bai', R.T, rx2)
ij = _find_peaks_2d(f1)
x1p = torch.stack([x1[i, j] for i, j in ij])
f1p = torch.stack([f1[i, j] for i, j in ij])
ij = _find_peaks_2d(f2)
x2p = torch.stack([x2[i, j] for i, j in ij])
f2p = torch.stack([f2[i, j] for i, j in ij])
# Union of the results
mask = torch.cdist(x1p, x2p) < 2 * pi / res
x = torch.cat([x1p[mask.sum(1) == 0], x2p])
f = torch.cat([f1p[mask.sum(1) == 0], f2p])
return x, f
def test1(self):
with torch_default_dtype(torch.float64):
Rs_in = [(3, 0), (3, 1), (2, 0), (1, 2)]
Rs_out = [(3, 0), (3, 1), (1, 2), (3, 0)]
f = GatedBlock(Rs_out, rescaled_act.Softplus(beta=5),
rescaled_act.sigmoid)
c = Convolution(Kernel(Rs_in, f.Rs_in, ConstantRadialModel))
abc = torch.randn(3)
D_in = o3.direct_sum(
*
[o3.irr_repr(l, *abc) for mul, l in Rs_in for _ in range(mul)])
D_out = o3.direct_sum(*[
o3.irr_repr(l, *abc) for mul, l in Rs_out for _ in range(mul)
])
x = torch.randn(1, 5, sum(mul * (2 * l + 1) for mul, l in Rs_in))
geo = torch.randn(1, 5, 3)
rx = torch.einsum("ij,zaj->zai", (D_in, x))
rgeo = geo @ o3.rot(*abc).t()
y = f(c(x, geo), dim=2)
ry = torch.einsum("ij,zaj->zai", (D_out, y))
self.assertLess((f(c(rx, rgeo)) - ry).norm(), 1e-10 * ry.norm())
def test_equivariance_wtp(Rs_in, Rs_out, n_source, n_target, n_edge):
torch.set_default_dtype(torch.float64)
mp = WTPConv(Rs_in, Rs_out, 3, ConstantRadialModel)
features = rs.randn(n_target, Rs_in)
edge_index = torch.stack([
torch.randint(n_source, size=(n_edge, )),
torch.randint(n_target, size=(n_edge, )),
])
size = (n_target, n_source)
edge_r = torch.randn(n_edge, 3)
if n_edge > 1:
edge_r[0] = 0
out1 = mp(features, edge_index, edge_r, size=size)
angles = o3.rand_angles()
D_in = rs.rep(Rs_in, *angles)
D_out = rs.rep(Rs_out, *angles)
R = o3.rot(*angles)
out2 = mp(features @ D_in.T, edge_index, edge_r @ R.T, size=size) @ D_out
assert (out1 - out2).abs().max() < 1e-10
def check_rotation(batch: int = 10, n_atoms: int = 25):
# Setup the network.
K = partial(Kernel, RadialModel=ConstantRadialModel)
Rs_in = [(1, 0), (1, 1)]
Rs_out = [(1, 0), (1, 1), (1, 2)]
act = GatedBlock(
Rs_out,
scalar_activation=sigmoid,
gate_activation=absolute,
)
conv = Convolution(K, Rs_in, act.Rs_in)
# Setup the data. The geometry, input features, and output features must all rotate.
abc = torch.randn(3) # Rotation seed of euler angles.
rot_geo = o3.rot(*abc)
D_in = rs.rep(Rs_in, *abc)
D_out = rs.rep(Rs_out, *abc)
feat = torch.randn(batch, n_atoms, rs.dim(Rs_in)) # Transforms with wigner D matrix
geo = torch.randn(batch, n_atoms, 3) # Transforms with rotation matrix.
# Test equivariance.
F = act(conv(feat, geo))
RF = torch.einsum("ij,zkj->zki", D_out, F)
FR = act(conv(feat @ D_in.t(), geo @ rot_geo.t()))
return (RF - FR).norm() < 10e-5 * RF.norm()
def check_rotation_parity(batch: int = 10, n_atoms: int = 25):
# Setup the network.
K = partial(Kernel, RadialModel=ConstantRadialModel)
Rs_in = [(1, 0, +1)]
act = GatedBlockParity(
Rs_scalars=[(4, 0, +1)],
act_scalars=[(-1, relu)],
Rs_gates=[(8, 0, +1)],
act_gates=[(-1, tanh)],
Rs_nonscalars=[(4, 1, -1), (4, 2, +1)]
)
conv = Convolution(K, Rs_in, act.Rs_in)
Rs_out = act.Rs_out
# Setup the data. The geometry, input features, and output features must all rotate and observe parity.
abc = torch.randn(3) # Rotation seed of euler angles.
rot_geo = -o3.rot(*abc) # Negative because geometry has odd parity. i.e. improper rotation.
D_in = rs.rep(Rs_in, *abc, parity=1)
D_out = rs.rep(Rs_out, *abc, parity=1)
feat = torch.randn(batch, n_atoms, rs.dim(Rs_in)) # Transforms with wigner D matrix and parity.
geo = torch.randn(batch, n_atoms, 3) # Transforms with rotation matrix and parity.
# Test equivariance.
F = act(conv(feat, geo))
RF = torch.einsum("ij,zkj->zki", D_out, F)
FR = act(conv(feat @ D_in.t(), geo @ rot_geo.t()))
return (RF - FR).norm() < 10e-5 * RF.norm()
def test3(self):
"""Test rotation equivariance on GatedBlock and dependencies."""
with torch_default_dtype(torch.float64):
Rs_in = [(2, 0), (0, 1), (2, 2)]
Rs_out = [(2, 0), (2, 1), (2, 2)]
K = partial(Kernel, RadialModel=ConstantRadialModel)
act = GatedBlock(Rs_out,
scalar_activation=sigmoid,
gate_activation=sigmoid)
conv = Convolution(K, Rs_in, act.Rs_in)
abc = torch.randn(3)
rot_geo = o3.rot(*abc)
D_in = o3.direct_sum(
*
[o3.irr_repr(l, *abc) for mul, l in Rs_in for _ in range(mul)])
D_out = o3.direct_sum(*[
o3.irr_repr(l, *abc) for mul, l in Rs_out for _ in range(mul)
])
fea = torch.randn(1, 4, sum(mul * (2 * l + 1) for mul, l in Rs_in))
geo = torch.randn(1, 4, 3)
x1 = torch.einsum("ij,zaj->zai", (D_out, act(conv(fea, geo))))
x2 = act(
conv(torch.einsum("ij,zaj->zai", (D_in, fea)),
torch.einsum("ij,zaj->zai", rot_geo, geo)))
self.assertLess((x1 - x2).norm(), 10e-5 * x1.norm())
def rotation_gated_block(self, K):
"""Test rotation equivariance on GatedBlock and dependencies."""
with torch_default_dtype(torch.float64):
Rs_in = [(2, 0), (0, 1), (2, 2)]
Rs_out = [(2, 0), (2, 1), (2, 2)]
K = partial(K, RadialModel=ConstantRadialModel)
act = GatedBlock(Rs_out,
scalar_activation=sigmoid,
gate_activation=sigmoid)
conv = Convolution(K(Rs_in, act.Rs_in))
abc = torch.randn(3)
rot_geo = o3.rot(*abc)
D_in = rs.rep(Rs_in, *abc)
D_out = rs.rep(Rs_out, *abc)
fea = torch.randn(1, 4, rs.dim(Rs_in))
geo = torch.randn(1, 4, 3)
x1 = torch.einsum("ij,zaj->zai", (D_out, act(conv(fea, geo))))
x2 = act(
conv(torch.einsum("ij,zaj->zai", (D_in, fea)),
torch.einsum("ij,zaj->zai", rot_geo, geo)))
self.assertLess((x1 - x2).norm(), 10e-5 * x1.norm())
def test_rot_to_abc(self):
with o3.torch_default_dtype(torch.float64):
R = o3.rand_rot()
abc = o3.rot_to_abc(R)
R2 = o3.rot(*abc)
d = (R - R2).norm() / R.norm()
self.assertTrue(d < 1e-10, d)
def parity_rotation_gated_block_parity(self, K):
"""Test parity and rotation equivariance on GatedBlockParity and dependencies."""
with torch_default_dtype(torch.float64):
mul = 2
Rs_in = [(mul, l, p) for l in range(3 + 1) for p in [-1, 1]]
K = partial(K, RadialModel=ConstantRadialModel)
scalars = [(mul, 0, +1), (mul, 0, -1)], [(mul, relu),
(mul, absolute)]
rs_nonscalars = [(mul, 1, +1), (mul, 1, -1), (mul, 2, +1),
(mul, 2, -1), (mul, 3, +1), (mul, 3, -1)]
n = 3 * mul
gates = [(n, 0, +1), (n, 0, -1)], [(n, sigmoid), (n, tanh)]
act = GatedBlockParity(*scalars, *gates, rs_nonscalars)
conv = Convolution(K(Rs_in, act.Rs_in))
abc = torch.randn(3)
rot_geo = -o3.rot(*abc)
D_in = rs.rep(Rs_in, *abc, 1)
D_out = rs.rep(act.Rs_out, *abc, 1)
fea = torch.randn(1, 4, rs.dim(Rs_in))
geo = torch.randn(1, 4, 3)
x1 = torch.einsum("ij,zaj->zai", (D_out, act(conv(fea, geo))))
x2 = act(
conv(torch.einsum("ij,zaj->zai", (D_in, fea)),
torch.einsum("ij,zaj->zai", rot_geo, geo)))
self.assertLess((x1 - x2).norm(), 10e-5 * x1.norm())
def random_rotate_translate(positions, rotation=True, translation=1):
while True:
trans = torch.rand(3) * 2 - 1
if trans.norm() <= 1:
break
rot = o3.rot(*torch.rand(3) * 6.2832).type(torch.float32)
return [rot @ pos + translation * trans for pos in positions]
def test_equivariance(Rs_in, Rs_out, n_source, n_target, n_edge):
torch.set_default_dtype(torch.float64)
mp = Convolution(Kernel(Rs_in, Rs_out, ConstantRadialModel))
groups = 4
mp_group = Convolution(
GroupKernel(Rs_in, Rs_out,
partial(Kernel, RadialModel=ConstantRadialModel), groups))
features = rs.randn(n_target, Rs_in)
features2 = rs.randn(n_target, Rs_in * groups)
r_source = torch.randn(n_source, 3)
r_target = torch.randn(n_target, 3)
edge_index = torch.stack([
torch.randint(n_source, size=(n_edge, )),
torch.randint(n_target, size=(n_edge, )),
])
size = (n_target, n_source)
if n_edge == 0:
edge_r = torch.zeros(0, 3)
else:
edge_r = torch.stack(
[r_target[j] - r_source[i] for i, j in edge_index.T])
print(features.shape, edge_index.shape, edge_r.shape, size)
out1 = mp(features, edge_index, edge_r, size=size)
out1_groups = mp(features2, edge_index, edge_r, size=size, groups=groups)
out1_kernel_groups = mp_group(features2,
edge_index,
edge_r,
size=size,
groups=groups)
angles = o3.rand_angles()
D_in = rs.rep(Rs_in, *angles)
D_out = rs.rep(Rs_out, *angles)
D_in_groups = rs.rep(Rs_in * groups, *angles)
D_out_groups = rs.rep(Rs_out * groups, *angles)
R = o3.rot(*angles)
out2 = mp(features @ D_in.T, edge_index, edge_r @ R.T, size=size) @ D_out
out2_groups = mp(features2 @ D_in_groups.T,
edge_index,
edge_r @ R.T,
size=size,
groups=groups) @ D_out_groups
out2_kernel_groups = mp_group(features2 @ D_in_groups.T,
edge_index,
edge_r @ R.T,
size=size,
groups=groups) @ D_out_groups
assert (out1 - out2).abs().max() < 1e-10
assert (out1_groups - out2_groups).abs().max() < 1e-10
assert (out1_kernel_groups - out2_kernel_groups).abs().max() < 1e-10
def test_xyz_vector_basis_to_spherical_basis(self, ):
with o3.torch_default_dtype(torch.float64):
A = o3.xyz_vector_basis_to_spherical_basis()
a, b, c = torch.rand(3)
r1 = A.t() @ o3.irr_repr(1, a, b, c) @ A
r2 = o3.rot(a, b, c)
self.assertLess((r1 - r2).abs().max(), 1e-10)
def test_xyz_to_irreducible_basis(self, ):
with o3.torch_default_dtype(torch.float64):
A = o3.xyz_to_irreducible_basis()
a, b, c = torch.rand(3)
r1 = A.t() @ o3.irr_repr(1, a, b, c) @ A
r2 = o3.rot(a, b, c)
assert torch.allclose(r1, r2)
def test_equivariance():
torch.set_default_dtype(torch.float64)
n_edge = 3
n_source = 4
n_target = 2
Rs_in = [(3, 0), (0, 1)]
Rs_mid1 = [(5, 0), (1, 1)]
Rs_mid2 = [(5, 0), (1, 1), (1, 2)]
Rs_out = [(5, 1), (3, 2)]
convolution = lambda Rs_in, Rs_out: Convolution(Kernel(Rs_in, Rs_out, ConstantRadialModel))
convolution_groups = lambda Rs_in, Rs_out: Convolution(
GroupKernel(Rs_in, Rs_out, partial(Kernel, RadialModel=ConstantRadialModel), groups))
groups = 4
mp = DepthwiseConvolution(Rs_in, Rs_out, Rs_mid1, Rs_mid2, groups, convolution)
mp_groups = DepthwiseConvolution(Rs_in, Rs_out, Rs_mid1, Rs_mid2, groups, convolution_groups)
features = rs.randn(n_target, Rs_in)
r_source = torch.randn(n_source, 3)
r_target = torch.randn(n_target, 3)
edge_index = torch.stack([
torch.randint(n_source, size=(n_edge,)),
torch.randint(n_target, size=(n_edge,)),
])
size = (n_target, n_source)
if n_edge == 0:
edge_r = torch.zeros(0, 3)
else:
edge_r = torch.stack([
r_target[j] - r_source[i]
for i, j in edge_index.T
])
print(features.shape, edge_index.shape, edge_r.shape, size)
out1 = mp(features, edge_index, edge_r, size=size)
out1_groups = mp_groups(features, edge_index, edge_r, size=size)
angles = o3.rand_angles()
D_in = rs.rep(Rs_in, *angles)
D_out = rs.rep(Rs_out, *angles)
R = o3.rot(*angles)
out2 = mp(features @ D_in.T, edge_index, edge_r @ R.T, size=size) @ D_out
out2_groups = mp_groups(features @ D_in.T, edge_index, edge_r @ R.T, size=size) @ D_out
assert (out1 - out2).abs().max() < 1e-10
assert (out1_groups - out2_groups).abs().max() < 1e-10
def rotation_kernel(self, K):
"""Test rotation equivariance on Kernel."""
with torch_default_dtype(torch.float64):
Rs_in = [(2, 0), (0, 1), (2, 2)]
Rs_out = [(2, 0), (2, 1), (2, 2)]
k = K(Rs_in, Rs_out, ConstantRadialModel)
r = torch.randn(3)
abc = torch.randn(3)
D_in = rs.rep(Rs_in, *abc)
D_out = rs.rep(Rs_out, *abc)
W1 = D_out @ k(r) # [i, j]
W2 = k(o3.rot(*abc) @ r) @ D_in # [i, j]
self.assertLess((W1 - W2).norm(), 10e-5 * W1.norm())
def test_s2conv_network():
torch.set_default_dtype(torch.float64)
lmax = 3
Rs = [(1, l, 1) for l in range(lmax + 1)]
model = S2ConvNetwork(Rs, 4, Rs, lmax)
features = rs.randn(1, 4, Rs)
geometry = torch.randn(1, 4, 3)
output = model(features, geometry)
angles = o3.rand_angles()
D = rs.rep(Rs, *angles, 1)
R = -o3.rot(*angles)
ein = torch.einsum
output2 = ein('ij,zaj->zai', D.T, model(ein('ij,zaj->zai', D, features), ein('ij,zaj->zai', R, geometry)))
assert (output - output2).abs().max() < 1e-10 * output.abs().max()
def test2(self):
"""Test rotation equivariance on Kernel."""
with torch_default_dtype(torch.float64):
Rs_in = [(2, 0), (0, 1), (2, 2)]
Rs_out = [(2, 0), (2, 1), (2, 2)]
k = Kernel(Rs_in, Rs_out, ConstantRadialModel)
r = torch.randn(3)
abc = torch.randn(3)
D_in = o3.direct_sum(
*
[o3.irr_repr(l, *abc) for mul, l in Rs_in for _ in range(mul)])
D_out = o3.direct_sum(*[
o3.irr_repr(l, *abc) for mul, l in Rs_out for _ in range(mul)
])
W1 = D_out @ k(r) # [i, j]
W2 = k(o3.rot(*abc) @ r) @ D_in # [i, j]
self.assertLess((W1 - W2).norm(), 10e-5 * W1.norm())
def test_equivariance_gatedconvnetwork(self):
with torch_default_dtype(torch.float64):
mul = 3
Rs_in = [(mul, l) for l in range(3 + 1)]
Rs_out = [(mul, l) for l in range(3 + 1)]
net = GatedConvNetwork(Rs_in, [(10, 0), (1, 1), (1, 2), (1, 3)],
Rs_out)
abc = torch.randn(3)
rot_geo = o3.rot(*abc)
D_in = rs.rep(Rs_in, *abc)
D_out = rs.rep(Rs_out, *abc)
fea = torch.randn(1, 10, rs.dim(Rs_in))
geo = torch.randn(1, 10, 3)
x1 = torch.einsum("ij,zaj->zai", D_out, net(fea, geo))
x2 = net(torch.einsum("ij,zaj->zai", D_in, fea),
torch.einsum("ij,zaj->zai", rot_geo, geo))
self.assertLess((x1 - x2).norm(), 10e-5 * x1.norm())
def test6(self):
"""Test parity and rotation equivariance on GatedBlockParity and dependencies."""
with torch_default_dtype(torch.float64):
mul = 2
Rs_in = [(mul, l, p) for l in range(6) for p in [-1, 1]]
K = partial(Kernel, RadialModel=ConstantRadialModel)
scalars = [(mul, 0, +1), (mul, 0, -1)], [(mul, relu),
(mul, absolute)]
rs_nonscalars = [(mul, 1, +1), (mul, 1, -1), (mul, 2, +1),
(mul, 2, -1), (mul, 3, +1), (mul, 3, -1)]
n = 3 * mul
gates = [(n, 0, +1), (n, 0, -1)], [(n, sigmoid), (n, tanh)]
act = GatedBlockParity(*scalars, *gates, rs_nonscalars)
conv = Convolution(K, Rs_in, act.Rs_in)
abc = torch.randn(3)
rot_geo = -o3.rot(*abc)
D_in = o3.direct_sum(*[
p * o3.irr_repr(l, *abc) for mul, l, p in Rs_in
for _ in range(mul)
])
D_out = o3.direct_sum(*[
p * o3.irr_repr(l, *abc) for mul, l, p in act.Rs_out
for _ in range(mul)
])
fea = torch.randn(1, 4,
sum(mul * (2 * l + 1) for mul, l, p in Rs_in))
geo = torch.randn(1, 4, 3)
x1 = torch.einsum("ij,zaj->zai", (D_out, act(conv(fea, geo))))
x2 = act(
conv(torch.einsum("ij,zaj->zai", (D_in, fea)),
torch.einsum("ij,zaj->zai", rot_geo, geo)))
self.assertLess((x1 - x2).norm(), 10e-5 * x1.norm())
def test_irr_repr_wigner_3j(self):
"""Test irr_repr and wigner_3j equivariance."""
with torch_default_dtype(torch.float64):
l_in = 3
l_out = 2
for l_f in range(abs(l_in - l_out), l_in + l_out + 1):
r = torch.randn(100, 3)
Q = o3.wigner_3j(l_out, l_in, l_f)
abc = torch.randn(3)
D_in = o3.irr_repr(l_in, *abc)
D_out = o3.irr_repr(l_out, *abc)
Y = rsh.spherical_harmonics_xyz([l_f], r @ o3.rot(*abc).t())
W = torch.einsum("ijk,zk->zij", (Q, Y))
W1 = torch.einsum("zij,jk->zik", (W, D_in))
Y = rsh.spherical_harmonics_xyz([l_f], r)
W = torch.einsum("ijk,zk->zij", (Q, Y))
W2 = torch.einsum("ij,zjk->zik", (D_out, W))
self.assertLess((W1 - W2).norm(), 1e-5 * W.norm(), l_f)
