def check_network_equivariance(network, Rs_in, Rs_out, vector_output: bool = False, batch: int = 2,
n_atoms: int = 6) -> bool:
"""
from user func(input_data, alpha, beta, gamma, parity)
from user func(output_data, alpha, beta, gamma, parity)
Checks rotation equivariance for a function. Network output transforms with the wigner d matrices.
:param network: Often the forward pass of an object inheriting from torch.nn.Module
:param Rs_in: Rs for the input of the network.
:param Rs_out: Rs for the output of the network.
:param vector_output: When True, the network outputs vectors which have already been converted to xyz basis.
:param batch: Batch size of test case.
:param n_atoms: Number of atoms of test case.
:return: None
"""
def check_parity(Rs):
"""Does Rs require a test of parity equivariance."""
if any(p != 0 for _, _, p in normalizeRs(Rs)):
return True
else:
return False
# Make sure that all parameters are on the same device. Set that to calculation device.
devices = [i.device for i in network.parameters()]
device = devices[0]
assert all([device == i for i in devices])
Rs_in = normalizeRs(Rs_in)
Rs_out = normalizeRs(Rs_out)
parity = check_parity(Rs_in) or check_parity(Rs_out)
abc = torch.randn(3, device=device) # Rotation seed of euler angles.
D_in = rep(Rs_in, *abc)
geo_rotation_matrix = -rot(*abc) if parity else rot(*abc) # Geometry is odd parity.
D_out = rep(Rs_out, *abc)
c = sum([mul * (2 * l + 1) for mul, l, _ in Rs_in])
feat = torch.randn(batch, n_atoms, c, device=device) # Transforms with wigner D matrix
geo = torch.randn(batch, n_atoms, 3, device=device) # Transforms with rotation matrix.
F = network(feat, geo)
if vector_output:
RF = torch.einsum("ij,zkj->zki", geo_rotation_matrix, F)
else:
RF = torch.einsum("ij,zkj->zki", D_out, F)
FR = network(feat @ D_in.t(), geo @ geo_rotation_matrix.t()) # [batch, feat, N]
return (RF - FR).norm() < 10e-5 * RF.norm()
def rotate(x, alpha):
t = time_logging.start()
y = x.cpu().detach().numpy()
R = rot(alpha, 0, 0)
y = rotate_scalar(y, R)
x = x.new_tensor(y)
time_logging.end("rotate", t)
return x
def rotation_from_orientations(t1, f1, t2, f2):
from se3cnn.SO3 import x_to_alpha_beta, rot
zero = t1.new_tensor(0)
r_e_t1 = rot(*x_to_alpha_beta(t1), zero)
r_e_t2 = rot(*x_to_alpha_beta(t2), zero)
f1_e = r_e_t1.t() @ f1
f2_e = r_e_t2.t() @ f2
c = torch.atan2(f2_e[1], f2_e[0]) - torch.atan2(f1_e[1], f1_e[0])
r_f1_f2 = rot(zero, zero, c)
r = r_e_t2 @ r_f1_f2 @ r_e_t1.t()
# t2 = r @ t1
# f2 ~ r @ f1
return r
def rotate(x, alpha, beta, gamma):
t = time_logging.start()
y = x.cpu().detach().numpy()
R = rot(alpha, beta, gamma)
if x.ndimension() == 4:
for i in range(y.shape[0]):
y[i] = rotate_scalar(y[i], R)
else:
y = rotate_scalar(y, R)
x = x.new_tensor(y)
if x.ndimension() == 4 and x.size(0) == 3:
rep = irr_repr(1, alpha, beta, gamma, x.dtype).to(x.device)
x = torch.einsum("ij,jxyz->ixyz", (rep, x))
time_logging.end("rotate", t)
return x
def _get_random_affine_trafo(self):
if self.rotate:
alpha, beta, gamma = np.pi * np.array([2, 1, 2
]) * np.random.rand(3)
aff = rot(alpha, beta, gamma)
else:
aff = np.eye(3) # only non-homogeneous coord part
fl = (-1)**np.random.randint(low=0, high=2) if self.flip else 1
if self.scale is not None:
sx, sy, sz = np.random.uniform(low=self.scale[0],
high=self.scale[1],
size=3)
else:
sx, sy, sz = 1
aff[:, 0] *= sx * fl
aff[:, 1] *= sy
aff[:, 2] *= sz
center = self.vol_shape / 2
offset = center - center @ aff.T # correct offset to apply trafo around center
if self.translate:
offset += np.random.uniform(low=-.5, high=.5, size=3)
return partial(affine_transform, matrix=aff, offset=offset)
def get_volumes(size=20, pad=8, rotate=False, rotate90=False):
assert size >= 4
tetris_tensorfields = [
[(0, 0, 0), (0, 0, 1), (1, 0, 0), (1, 1, 0)], # chiral_shape_1
[(0, 1, 0), (0, 1, 1), (1, 1, 0), (1, 0, 0)], # chiral_shape_2
[(0, 0, 0), (1, 0, 0), (0, 1, 0), (1, 1, 0)], # square
[(0, 0, 0), (0, 0, 1), (0, 0, 2), (0, 0, 3)], # line
[(0, 0, 0), (0, 0, 1), (0, 1, 0), (1, 0, 0)], # corner
[(0, 0, 0), (0, 0, 1), (0, 0, 2), (0, 1, 0)], # L
[(0, 0, 0), (0, 0, 1), (0, 0, 2), (0, 1, 1)], # T
[(0, 0, 0), (1, 0, 0), (1, 1, 0), (2, 1, 0)], # zigzag
]
labels = np.arange(len(tetris_tensorfields))
tetris_vox = []
for shape in tetris_tensorfields:
volume = np.zeros((4, 4, 4))
for xi_coords in shape:
volume[xi_coords] = 1
volume = zoom(volume, size / 4, order=0)
volume = np.pad(volume, pad, 'constant')
if rotate:
a, c = np.random.rand(2) * 2 * np.pi
b = np.arccos(np.random.rand() * 2 - 1)
volume = rotate_scalar(volume, rot(a, b, c))
if rotate90:
volume = rot_volume_90(volume)
tetris_vox.append(volume[np.newaxis, ...])
tetris_vox = np.stack(tetris_vox).astype(np.float32)
return tetris_vox, labels
def train_step(item, top, front, model, optimizer):
from se3cnn.SO3 import rot
model.train()
abc = 15 * (torch.rand(3) * 2 - 1) / 180 * math.pi
r = rot(*abc).to(item.device)
tip = torch.cat(
[torch.einsum("ij,...j->...i", (r, x)) for x in [top, front]], dim=1)
tip = tip.view(tip.size(0), tip.size(1), 1, 1,
1).expand(tip.size(0), tip.size(1), item.size(2),
item.size(3), item.size(4))
input = torch.cat([item, tip], dim=1)
prediction = model(input)
pred_top, pred_front = prediction[:, :3], prediction[:, 3:]
overlap_top = overlap(pred_top, top)
overlap_front = overlap(pred_front, front)
overlap_orth = overlap(pred_top, pred_front)
optimizer.zero_grad()
(-overlap_top - overlap_front + overlap_orth.abs()).mean().backward()
optimizer.step()
a = torch.mean(
torch.tensor([
angle_from_rotation(
rotation_from_orientations(top[i], front[i], pred_top[i],
pred_front[i]))
for i in range(len(item))
]))
return overlap_top.mean().item(), overlap_front.mean().item(
), overlap_orth.abs().mean().item(), a.item()