def __init__(self, Rs, acts):
'''
Can be used only with scalar fields
:param acts: list of tuple (multiplicity, activation)
'''
super().__init__()
Rs = o3.simplify(Rs)
n1 = sum(mul for mul, _, _ in Rs)
n2 = sum(mul for mul, _ in acts if mul > 0)
# normalize the second moment
acts = [(mul, normalize2mom(act)) for mul, act in acts]
for i, (mul, act) in enumerate(acts):
if mul == -1:
acts[i] = (n1 - n2, act)
assert n1 - n2 >= 0
assert n1 == sum(mul for mul, _ in acts)
i = 0
while i < len(Rs):
mul_r, l, p_r = Rs[i]
mul_a, act = acts[i]
if mul_r < mul_a:
acts[i] = (mul_r, act)
acts.insert(i + 1, (mul_a - mul_r, act))
if mul_a < mul_r:
Rs[i] = (mul_a, l, p_r)
Rs.insert(i + 1, (mul_r - mul_a, l, p_r))
i += 1
x = torch.linspace(0, 10, 256)
Rs_out = []
for (mul, l, p_in), (mul_a, act) in zip(Rs, acts):
assert mul == mul_a
a1, a2 = act(x), act(-x)
if (a1 - a2).abs().max() < a1.abs().max() * 1e-10:
p_act = 1
elif (a1 + a2).abs().max() < a1.abs().max() * 1e-10:
p_act = -1
else:
p_act = 0
p = p_act if p_in == -1 else p_in
Rs_out.append((mul, 0, p))
if p_in != 0 and p == 0:
raise ValueError("warning! the parity is violated")
self.Rs_out = o3.simplify(Rs_out)
self.acts = acts
def __repr__(self):
return "{name}({Rs_in1} x {Rs_in2} -> {Rs_out} {nw} weights)".format(
name=self.__class__.__name__,
Rs_in1=o3.format_Rs(o3.simplify(self.Rs_in1)),
Rs_in2=o3.format_Rs(o3.simplify(self.Rs_in2)),
Rs_out=o3.format_Rs(o3.simplify(self.Rs_out)),
nw=self.nweight,
)
def __init__(self, *Rs_outs):
super().__init__()
self.Rs_outs = tuple(o3.simplify(Rs) for Rs in Rs_outs)
def key(rs):
_mul, l, p = rs
return (l, p)
self.Rs_in = o3.simplify(
sorted((x for Rs in self.Rs_outs for x in Rs), key=key))
def __init__(self, Rs_in, Rs_out):
super().__init__()
self.Rs_in = o3.simplify(Rs_in)
self.Rs_out = o3.simplify(Rs_out)
assert self.Rs_in == self.Rs_out
output_mask = torch.cat(
[torch.ones(mul * (2 * l + 1)) for mul, l, p in self.Rs_out])
self.register_buffer('output_mask', output_mask)
def WeightedTensorProduct(Rs_in1,
Rs_in2,
Rs_out,
normalization='component',
own_weight=True,
weight_batch=False):
Rs_in1 = o3.simplify(Rs_in1)
Rs_in2 = o3.simplify(Rs_in2)
Rs_out = o3.simplify(Rs_out)
instr = [(i_1, i_2, i_out, 'uvw', True)
for i_1, (_, l_1, p_1) in enumerate(Rs_in1)
for i_2, (_, l_2, p_2) in enumerate(Rs_in2)
for i_out, (_, l_out, p_out) in enumerate(Rs_out)
if abs(l_1 - l_2) <= l_out <= l_1 + l_2 and p_1 * p_2 == p_out]
return CustomWeightedTensorProduct(Rs_in1, Rs_in2, Rs_out, instr,
normalization, own_weight, weight_batch)
def spherical_harmonics_alpha_z_y(Rs, alpha, z, y):
"""
spherical harmonics
"""
Rs = o3.simplify(Rs)
sha = spherical_harmonics_alpha(o3.lmax(Rs), alpha.flatten()) # [z, m]
shz = spherical_harmonics_z(Rs, z.flatten(), y.flatten()) # [z, l * m]
out = mul_m_lm(Rs, sha, shz)
return out.reshape(alpha.shape + (shz.shape[1], ))
def spherical_harmonics_z(Rs, z, y=None):
"""
the z component of the spherical harmonics
(useful to perform fourier transform)
:param z: tensor of shape [...]
:return: tensor of shape [..., l * m]
"""
Rs = o3.simplify(Rs)
for _, l, p in Rs:
assert p in [0, (-1)**l]
ls = [l for mul, l, _ in Rs]
return legendre(ls, z, y) # [..., l * m]
def __init__(self,
Rs_in,
Rs_out,
Rs_sh,
rad_hs,
normalization='component'):
super().__init__(aggr='add')
self.Rs_in = o3.simplify(Rs_in)
self.Rs_out = o3.simplify(Rs_out)
self.Rs_sh = o3.simplify(Rs_sh)
self.si = Linear(self.Rs_in, self.Rs_out)
self.lin1 = Linear(self.Rs_in, self.Rs_in)
instr = []
Rs = []
for i_1, (mul_1, l_1, p_1) in enumerate(self.Rs_in):
for i_2, (_, l_2, p_2) in enumerate(self.Rs_sh):
for l_out in range(abs(l_1 - l_2), l_1 + l_2 + 1):
p_out = p_1 * p_2
if (l_out, p_out) in [(l, p) for _, l, p in self.Rs_out]:
r = (mul_1, l_out, p_out)
if r in Rs:
i_out = Rs.index(r)
else:
i_out = len(Rs)
Rs.append(r)
instr += [(i_1, i_2, i_out, 'uvu', True)]
self.tp = CustomWeightedTensorProduct(self.Rs_in,
self.Rs_sh,
Rs,
instr,
own_weight=False,
weight_batch=True)
self.nn = FC(rad_hs + (self.tp.nweight, ), swish)
self.lin2 = Linear(Rs, self.Rs_out)
self.normalization = normalization
def rep(Rs, alpha, beta, gamma, parity=None):
"""
Representation of O(3). Parity applied (-1)**parity times.
"""
Rs = o3.simplify(Rs)
if parity is None:
return direct_sum(*[
irrep(l, alpha, beta, gamma) for mul, l, _ in Rs
for _ in range(mul)
])
else:
assert all(parity != 0 for _, _, parity in Rs)
return direct_sum(*[(p**parity) * irrep(l, alpha, beta, gamma)
for mul, l, p in Rs for _ in range(mul)])
def ElementwiseTensorProduct(Rs_in1, Rs_in2, normalization='component'):
Rs_in1 = o3.simplify(Rs_in1)
Rs_in2 = o3.simplify(Rs_in2)
assert sum(mul for mul, _, _ in Rs_in1) == sum(mul for mul, _, _ in Rs_in2)
i = 0
while i < len(Rs_in1):
mul_1, l_1, p_1 = Rs_in1[i]
mul_2, l_2, p_2 = Rs_in2[i]
if mul_1 < mul_2:
Rs_in2[i] = (mul_1, l_2, p_2)
Rs_in2.insert(i + 1, (mul_2 - mul_1, l_2, p_2))
if mul_2 < mul_1:
Rs_in1[i] = (mul_2, l_1, p_1)
Rs_in1.insert(i + 1, (mul_1 - mul_2, l_1, p_1))
i += 1
Rs_out = []
instr = []
for i, ((mul, l_1, p_1), (mul_2, l_2,
p_2)) in enumerate(zip(Rs_in1, Rs_in2)):
assert mul == mul_2
for l in list(range(abs(l_1 - l_2), l_1 + l_2 + 1)):
i_out = len(Rs_out)
Rs_out.append((mul, l, p_1 * p_2))
instr += [(i, i, i_out, 'uuu', False)]
return CustomWeightedTensorProduct(Rs_in1,
Rs_in2,
Rs_out,
instr,
normalization,
own_weight=False)
def __init__(self, Rs_in, Rs_out, normalization: str = 'component'):
super().__init__()
self.Rs_in = o3.simplify(Rs_in)
self.Rs_out = o3.simplify(Rs_out)
instr = [(i_in, 0, i_out, 'uvw', True)
for i_in, (_, l_in, p_in) in enumerate(self.Rs_in)
for i_out, (_, l_out, p_out) in enumerate(self.Rs_out)
if l_in == l_out and p_in == p_out]
self.tp = CustomWeightedTensorProduct(self.Rs_in, [(1, 0, 1)],
self.Rs_out,
instr,
normalization,
own_weight=True)
output_mask = torch.cat([
torch.ones(mul * (2 * l + 1)) if any(
l_in == l and p_in == p
for _, l_in, p_in in self.Rs_in) else torch.zeros(mul *
(2 * l + 1))
for mul, l, p in self.Rs_out
])
self.register_buffer('output_mask', output_mask)
def __init__(self, Rs_scalars, act_scalars, Rs_gates, act_gates,
Rs_nonscalars):
super().__init__()
self.sc = Sortcut(Rs_scalars, Rs_gates)
self.Rs_scalars, self.Rs_gates = self.sc.Rs_outs
self.Rs_nonscalars = o3.simplify(Rs_nonscalars)
self.Rs_in = self.sc.Rs_in + self.Rs_nonscalars
self.act_scalars = Activation(Rs_scalars, act_scalars)
Rs_scalars = self.act_scalars.Rs_out
self.act_gates = Activation(Rs_gates, act_gates)
Rs_gates = self.act_gates.Rs_out
self.mul = nn.ElementwiseTensorProduct(Rs_nonscalars, Rs_gates)
Rs_nonscalars = self.mul.Rs_out
self.Rs_out = Rs_scalars + Rs_nonscalars
def make_gated_block(Rs_in, muls, ps, Rs_sh):
"""
Make a `GatedBlockParity` assuming many things
"""
Rs_available = [(l, p_in * p_sh) for _, l_in, p_in in o3.simplify(Rs_in)
for _, l_sh, p_sh in Rs_sh
for l in range(abs(l_in - l_sh), l_in + l_sh + 1)]
scalars = [(muls[0], 0, p) for p in ps if (0, p) in Rs_available]
act_scalars = [(mul, swish if p == 1 else torch.tanh)
for mul, l, p in scalars]
nonscalars = [(muls[l], l, p * (-1)**l) for l in range(1, len(muls))
for p in ps if (l, p * (-1)**l) in Rs_available]
if (0, +1) in Rs_available:
gates = [(o3.mul_dim(nonscalars), 0, +1)]
act_gates = [(-1, torch.sigmoid)]
else:
gates = [(o3.mul_dim(nonscalars), 0, -1)]
act_gates = [(-1, torch.tanh)]
return GatedBlockParity(scalars, act_scalars, gates, act_gates, nonscalars)
def __init__(self,
muls=(128, 8, 0),
ps=(1, -1),
lmax=1,
num_layers=6,
cutoff=10.0,
rad_gaussians=50,
rad_hs=(128, ),
num_neighbors=20,
readout='add',
dipole=False,
mean=None,
std=None,
scale=None,
atomref=None,
options="res"):
super().__init__()
assert readout in ['add', 'sum', 'mean']
self.readout = readout
self.cutoff = cutoff
self.dipole = dipole
self.mean = mean
self.std = std
self.scale = scale
self.num_neighbors = num_neighbors
self.options = options
self.embedding = Embedding(100, muls[0])
self.Rs_in = [(muls[0], 0, 1)]
self.radial = GaussianRadialModel(rad_gaussians, cutoff)
self.Rs_sh = [(1, l, (-1)**l) for l in range(lmax + 1)
] # spherical harmonics representation
Rs = self.Rs_in
modules = []
for _ in range(num_layers):
act = make_gated_block(Rs, muls, ps, self.Rs_sh)
conv = Conv(Rs, act.Rs_in, self.Rs_sh, (rad_gaussians, ) + rad_hs)
if 'res' in self.options:
if Rs == act.Rs_out:
shortcut = Identity(Rs, act.Rs_out)
else:
shortcut = Linear(Rs, act.Rs_out)
else:
shortcut = None
Rs = o3.simplify(act.Rs_out)
modules += [torch.nn.ModuleList([conv, act, shortcut])]
self.layers = torch.nn.ModuleList(modules)
self.Rs_out = [(1, 0, p) for p in ps]
self.layers.append(
Conv(Rs, self.Rs_out, self.Rs_sh, (rad_gaussians, ) + rad_hs))
self.register_buffer('initial_atomref', atomref)
self.atomref = None
if atomref is not None:
self.atomref = Embedding(100, 1)
self.atomref.weight.data.copy_(atomref)
def reduce_tensor(formula, eps=1e-9, has_parity=None, **kw_Rs):
"""
Usage
Rs, Q = rs.reduce_tensor('ijkl=jikl=ikjl=ijlk', i=[(1, 1)])
Rs = 0,2,4
Q = tensor of shape [15, 81]
"""
dtype = torch.get_default_dtype()
with torch_default_dtype(torch.float64):
# reformat `formulas` and make checks
formulas = [
(-1 if f.startswith('-') else 1, f.replace('-', ''))
for f in formula.split('=')
]
s0, f0 = formulas[0]
assert s0 == 1
for _s, f in formulas:
if len(set(f)) != len(f) or set(f) != set(f0):
raise RuntimeError(f'{f} is not a permutation of {f0}')
if len(f0) != len(f):
raise RuntimeError(f'{f0} and {f} don\'t have the same number of indices')
# `formulas` is a list of (sign, permutation of indices)
# each formula can be viewed as a permutation of the original formula
formulas = {(s, tuple(f.index(i) for i in f0)) for s, f in formulas} # set of generators (permutations)
# they can be composed, for instance if you have ijk=jik=ikj
# you also have ijk=jki
# applying all possible compositions creates an entire group
while True:
n = len(formulas)
formulas = formulas.union([(s, perm.inverse(p)) for s, p in formulas])
formulas = formulas.union([
(s1 * s2, perm.compose(p1, p2))
for s1, p1 in formulas
for s2, p2 in formulas
])
if len(formulas) == n:
break # we break when the set is stable => it is now a group \o/
# lets clean the `kw_Rs` before checking that they are compatible with the formulas
for i in kw_Rs:
if not callable(kw_Rs[i]):
Rs = o3.convention(kw_Rs[i])
if has_parity is None:
has_parity = any(p != 0 for _, _, p in Rs)
if not has_parity and not all(p == 0 for _, _, p in Rs):
raise RuntimeError(f'{o3.format_Rs(Rs)} parity has to be specified everywhere or nowhere')
if has_parity and any(p == 0 for _, _, p in Rs):
raise RuntimeError(f'{o3.format_Rs(Rs)} parity has to be specified everywhere or nowhere')
kw_Rs[i] = Rs
if has_parity is None:
raise RuntimeError(f'please specify the argument `has_parity`')
group = O3() if has_parity else SO3()
# here we check that each index has one and only one representation
for _s, p in formulas:
f = "".join(f0[i] for i in p)
for i, j in zip(f0, f):
if i in kw_Rs and j in kw_Rs and kw_Rs[i] != kw_Rs[j]:
raise RuntimeError(f'Rs of {i} (Rs={o3.format_Rs(kw_Rs[i])}) and {j} (Rs={o3.format_Rs(kw_Rs[j])}) should be the same')
if i in kw_Rs:
kw_Rs[j] = kw_Rs[i]
if j in kw_Rs:
kw_Rs[i] = kw_Rs[j]
for i in f0:
if i not in kw_Rs:
raise RuntimeError(f'index {i} has not Rs associated to it')
ide = group.identity()
dims = {i: len(kw_Rs[i](*ide)) if callable(kw_Rs[i]) else o3.dim(kw_Rs[i]) for i in f0} # dimension of each index
full_base = list(itertools.product(*(range(dims[i]) for i in f0))) # (0, 0, 0), (0, 0, 1), (0, 0, 2), ... (3, 3, 3)
# len(full_base) degrees of freedom in an unconstrained tensor
# but there is constraints given by the group `formulas`
# For instance if `ij=-ji`, then 00=-00, 01=-01 and so on
base = set()
for x in full_base:
# T[x] is a coefficient of the tensor T and is related to other coefficient T[y]
# if x and y are related by a formula
xs = {(s, tuple(x[i] for i in p)) for s, p in formulas}
# s * T[x] are all equal for all (s, x) in xs
# if T[x] = -T[x] it is then equal to 0 and we lose this degree of freedom
if not (-1, x) in xs:
# the sign is arbitrary, put both possibilities
base.add(frozenset({
frozenset(xs),
frozenset({(-s, x) for s, x in xs})
}))
# len(base) is the number of degrees of freedom in the tensor.
# Now we want to decompose these degrees of freedom into irreps
base = sorted([sorted([sorted(xs) for xs in x]) for x in base]) # requested for python 3.7 but not for 3.8 (probably a bug in 3.7)
# First we compute the change of basis (projection) between full_base and base
d_sym = len(base)
d = len(full_base)
Q = torch.zeros(d_sym, d)
for i, x in enumerate(base):
x = max(x, key=lambda xs: sum(s for s, x in xs))
for s, e in x:
j = full_base.index(e)
Q[i, j] = s / len(x)**0.5
assert torch.allclose(Q @ Q.T, torch.eye(d_sym))
if d_sym == 0:
return [], torch.zeros(d_sym, d).to(dtype=dtype)
# We project the representation on the basis `base`
def representation(g):
def re(r):
if callable(r):
return r(*g)
return o3.rep(r, *g)
m = kron(*(re(kw_Rs[i]) for i in f0))
return Q @ m @ Q.T
# And check that after this projection it is still a representation
assert is_representation(group, representation, eps)
# The rest of the code simply extract the irreps present in this representation
Rs_out = []
A = Q.clone()
for r in group.irrep_indices():
if group.irrep(r)(ide).shape[0] > d_sym - o3.dim(Rs_out):
break
mul, B, representation = reduce(group, representation, group.irrep(r), eps)
A = direct_sum(torch.eye(d_sym - B.shape[0]), B) @ A
A = _round_sqrt(A, eps)
if has_parity:
Rs_out += [(mul,) + r]
else:
Rs_out += [(mul, r)]
if o3.dim(Rs_out) == d_sym:
break
if o3.dim(Rs_out) != d_sym:
raise RuntimeError(f'unable to decompose into irreducible representations')
return o3.simplify(Rs_out), A.to(dtype=dtype)
