def __init__(self, formula, filter_ir_out=None, filter_ir_mid=None, eps=1e-9, **irreps):
super().__init__(self, fx.Graph())
if filter_ir_out is not None:
filter_ir_out = [o3.Irrep(ir) for ir in filter_ir_out]
f0, formulas = germinate_formulas(formula)
irreps = {i: o3.Irreps(irs) for i, irs in irreps.items()}
for i in irreps:
if len(i) != 1:
raise TypeError(f"got an unexpected keyword argument '{i}'")
for _sign, p in formulas:
f = "".join(f0[i] for i in p)
for i, j in zip(f0, f):
if i in irreps and j in irreps and irreps[i] != irreps[j]:
raise RuntimeError(f'irreps of {i} and {j} should be the same')
if i in irreps:
irreps[j] = irreps[i]
if j in irreps:
irreps[i] = irreps[j]
for i in f0:
if i not in irreps:
raise RuntimeError(f'index {i} has no irreps associated to it')
for i in irreps:
if i not in f0:
raise RuntimeError(f'index {i} has an irreps but does not appear in the fomula')
base_perm, _ = reduce_permutation(
f0,
formulas,
dtype=torch.float64,
**{i: irs.dim for i, irs in irreps.items()}
)
Ps = collections.defaultdict(list)
for ir, path, base_o3 in _wigner_nj(*[irreps[i] for i in f0], filter_ir_mid=filter_ir_mid, dtype=torch.float64):
if filter_ir_out is None or ir in filter_ir_out:
P = base_o3.flatten(1) @ base_perm.flatten(1).T
if P.norm() > eps: # if this Irrep is present in the premutation basis we keep it
Ps[ir].append((path, base_o3))
outputs = []
change_of_basis = []
irreps_out = []
for ir in Ps:
mul = len(Ps[ir])
paths = [path for path, _ in Ps[ir]]
base_o3 = torch.stack([R for _, R in Ps[ir]])
R = base_o3.flatten(2) # [multiplicity, ir, input basis] (u,j,omega)
P = base_perm.flatten(1) # [permutation basis, input basis] (a,omega)
Xs = []
for j in range(ir.dim):
RR = R[:, j] @ R[:, j].T # (u,u)
PP = P @ P.T # (a,a)
RP = R[:, j] @ P.T # (u,a)
prob = torch.cat([
torch.cat([RR, -RP], dim=1),
torch.cat([-RP.T, PP], dim=1)
], dim=0)
eigenvalues, eigenvectors = torch.linalg.eigh(prob)
X = eigenvectors[:, eigenvalues < eps][:mul].T # [solutions, multiplicity]
X = torch.linalg.qr(X, mode='r').R
for i, x in enumerate(X):
for j in range(i, mul):
if x[j] < eps:
x.neg_()
if x[j] > eps:
break
X[X.abs() < eps] = 0
X = sorted([[x.item() for x in line] for line in X])
X = torch.tensor(X, dtype=torch.float64)
Xs.append(X)
for X in Xs:
assert (X - Xs[0]).abs().max() < eps
X = Xs[0]
for x in X:
C = torch.einsum("u,ui...->i...", x, base_o3)
correction = (ir.dim / C.pow(2).sum())**0.5
C = correction * C
outputs.append([((correction * v).item(), p) for v, p in zip(x, paths) if v.abs() > eps])
change_of_basis.append(C)
irreps_out.append((1, ir))
dtype, _ = explicit_default_types(None, None)
self.register_buffer('change_of_basis', torch.cat(change_of_basis).to(dtype=dtype))
tps = set()
for vp_list in outputs:
for v, p in vp_list:
for op in _get_ops(p):
tps.add(op)
tps = list(tps)
for i, op in enumerate(tps):
tp = o3.TensorProduct(op[0], op[1], op[2], [(0, 0, 0, 'uuu', False)])
setattr(self, f'tp{i}', tp)
graph = fx.Graph()
inputs = [
fx.Proxy(graph.placeholder(f"x{i}", torch.Tensor))
for i in f0
]
self.irreps_in = [irreps[i] for i in f0]
self.irreps_out = o3.Irreps(irreps_out).simplify()
values = dict()
def evaluate(path):
if path in values:
return values[path]
if isinstance(path, _INPUT):
out = inputs[path.tensor]
if (path.start, path.stop) != (0, self.irreps_in[path.tensor].dim):
out = out.narrow(-1, path.start, path.stop - path.start)
if isinstance(path, _TP):
x1 = evaluate(path.args[0]).node
x2 = evaluate(path.args[1]).node
out = fx.Proxy(graph.call_module(f'tp{tps.index(path.op)}', (x1, x2)))
values[path] = out
return out
outs = []
for vp_list in outputs:
v, p = vp_list[0]
out = evaluate(p)
if abs(v - 1.0) > eps:
out = v * out
for v, p in vp_list[1:]:
t = evaluate(p)
if abs(v - 1.0) > eps:
t = v * t
out = out + t
outs.append(out)
out = torch.cat(outs, dim=-1)
graph.output(out.node)
self.graph = graph
self.recompile()
def codegen_tensor_product(
irreps_in1: o3.Irreps,
in1_var: List[float],
irreps_in2: o3.Irreps,
in2_var: List[float],
irreps_out: o3.Irreps,
out_var: List[float],
instructions: List[Instruction],
normalization: str = 'component',
shared_weights: bool = False,
specialized_code: bool = True,
optimize_einsums: bool = True,
) -> Tuple[fx.GraphModule, fx.GraphModule]:
graph_out = fx.Graph()
graph_right = fx.Graph()
# = Function definitions =
x1s_out = fx.Proxy(graph_out.placeholder('x1', torch.Tensor))
x2s_out = fx.Proxy(graph_out.placeholder('x2', torch.Tensor))
ws_out = fx.Proxy(graph_out.placeholder('w', torch.Tensor))
x2s_right = fx.Proxy(graph_right.placeholder('x2', torch.Tensor))
ws_right = fx.Proxy(graph_right.placeholder('w', torch.Tensor))
empty_out = fx.Proxy(
graph_out.call_function(torch.empty, ((), ), dict(device='cpu')))
empty_right = fx.Proxy(
graph_right.call_function(torch.empty, ((), ), dict(device='cpu')))
if shared_weights:
size_out = torch.broadcast_tensors(
empty_out.expand(x1s_out.shape[:-1]),
empty_out.expand(x2s_out.shape[:-1]))[0].shape
size_right = x2s_right.shape[:-1]
else:
size_out = torch.broadcast_tensors(
empty_out.expand(x1s_out.shape[:-1]),
empty_out.expand(x2s_out.shape[:-1]),
empty_out.expand(ws_out.shape[:-1]))[0].shape
size_right = torch.broadcast_tensors(
empty_right.expand(x2s_right.shape[:-1]),
empty_right.expand(ws_right.shape[:-1]))[0].shape
# = Short-circut for zero dimensional =
# We produce no code for empty instructions
instructions = [ins for ins in instructions if 0 not in ins.path_shape]
if len(instructions) == 0:
out_out = x1s_out.new_zeros(size_out + (irreps_out.dim, ))
out_right = x2s_right.new_zeros(size_right + (
irreps_in1.dim,
irreps_out.dim,
))
graph_out.output(out_out.node, torch.Tensor)
graph_right.output(out_right.node, torch.Tensor)
# Short circut
return (fx.GraphModule({}, graph_out, "tp_forward"),
fx.GraphModule({}, graph_right, "tp_right"))
# = Broadcast inputs =
if shared_weights:
x1s_out, x2s_out = x1s_out.broadcast_to(
size_out + (-1, )), x2s_out.broadcast_to(size_out + (-1, ))
else:
x1s_out, x2s_out, ws_out = x1s_out.broadcast_to(
size_out + (-1, )), x2s_out.broadcast_to(
size_out + (-1, )), ws_out.broadcast_to(size_out + (-1, ))
x2s_right, ws_right = x2s_right.broadcast_to(
size_right + (-1, )), ws_right.broadcast_to(size_right + (-1, ))
outsize_out = size_out + (irreps_out.dim, )
outsize_right = size_right + (
irreps_in1.dim,
irreps_out.dim,
)
x1s_out = x1s_out.reshape(-1, irreps_in1.dim)
x2s_out = x2s_out.reshape(-1, irreps_in2.dim)
x2s_right = x2s_right.reshape(-1, irreps_in2.dim)
batch_out = x1s_out.shape[0]
batch_right = x2s_right.shape[0]
# = Determine number of weights and reshape weights ==
weight_numel = sum(
prod(ins.path_shape) for ins in instructions if ins.has_weight)
if weight_numel > 0:
ws_out = ws_out.reshape(-1, weight_numel)
ws_right = ws_right.reshape(-1, weight_numel)
del weight_numel
# = book-keeping for wigners =
w3j = []
w3j_dict_out = dict()
w3j_dict_right = dict()
# = extract individual input irreps =
# If only one input irrep, can avoid creating a view
if len(irreps_in1) == 1:
x1_list_out = [
x1s_out.reshape(batch_out, irreps_in1[0].mul, irreps_in1[0].ir.dim)
]
else:
x1_list_out = [
x1s_out[:, i].reshape(batch_out, mul_ir.mul, mul_ir.ir.dim)
for i, mul_ir in zip(irreps_in1.slices(), irreps_in1)
]
x2_list_out = []
x2_list_right = []
# If only one input irrep, can avoid creating a view
if len(irreps_in2) == 1:
x2_list_out.append(
x2s_out.reshape(batch_out, irreps_in2[0].mul,
irreps_in2[0].ir.dim))
x2_list_right.append(
x2s_right.reshape(batch_right, irreps_in2[0].mul,
irreps_in2[0].ir.dim))
else:
for i, mul_ir in zip(irreps_in2.slices(), irreps_in2):
x2_list_out.append(x2s_out[:, i].reshape(batch_out, mul_ir.mul,
mul_ir.ir.dim))
x2_list_right.append(x2s_right[:,
i].reshape(batch_right, mul_ir.mul,
mul_ir.ir.dim))
# The einsum string index to prepend to the weights if the weights are not shared and have a batch dimension
z = '' if shared_weights else 'z'
# Cache of input irrep pairs whose outer products (xx) have already been computed
xx_dict = dict()
# Current index in the flat weight tensor
flat_weight_index = 0
out_list_out = []
out_list_right = []
for ins in instructions:
mul_ir_in1 = irreps_in1[ins.i_in1]
mul_ir_in2 = irreps_in2[ins.i_in2]
mul_ir_out = irreps_out[ins.i_out]
assert mul_ir_in1.ir.p * mul_ir_in2.ir.p == mul_ir_out.ir.p
assert abs(mul_ir_in1.ir.l - mul_ir_in2.ir.l
) <= mul_ir_out.ir.l <= mul_ir_in1.ir.l + mul_ir_in2.ir.l
if mul_ir_in1.dim == 0 or mul_ir_in2.dim == 0 or mul_ir_out.dim == 0:
continue
alpha = ins.path_weight * out_var[ins.i_out] / sum(
in1_var[i.i_in1] * in2_var[i.i_in2]
for i in instructions if i.i_out == ins.i_out)
# Open the profiler block
name = f"{mul_ir_in1} x {mul_ir_in2} = {mul_ir_out} {ins.connection_mode} {ins.has_weight}"
handle_out = graph_out.call_function(
torch.ops.profiler._record_function_enter, (name, ))
handle_right = graph_right.call_function(
torch.ops.profiler._record_function_enter, (name, ))
x1_out = x1_list_out[ins.i_in1]
x2_out = x2_list_out[ins.i_in2]
x2_right = x2_list_right[ins.i_in2]
e1_right = fx.Proxy(
graph_right.call_function(
torch.eye, (mul_ir_in1.mul, ),
dict(dtype=x2s_right.dtype.node,
device=x2s_right.device.node)))
e2_right = fx.Proxy(
graph_right.call_function(
torch.eye, (mul_ir_in2.mul, ),
dict(dtype=x2s_right.dtype.node,
device=x2s_right.device.node)))
i1_right = fx.Proxy(
graph_right.call_function(
torch.eye, (mul_ir_in1.ir.dim, ),
dict(dtype=x2s_right.dtype.node,
device=x2s_right.device.node)))
assert ins.connection_mode in [
'uvw', 'uvu', 'uvv', 'uuw', 'uuu', 'uvuv'
]
alpha = sqrt(
alpha / {
'uvw': (mul_ir_in1.mul * mul_ir_in2.mul),
'uvu': mul_ir_in2.mul,
'uvv': mul_ir_in1.mul,
'uuw': mul_ir_in1.mul,
'uuu': 1,
'uvuv': 1,
}[ins.connection_mode])
if ins.has_weight:
# Extract the weight from the flattened weight tensor
w_out = ws_out[:, flat_weight_index:flat_weight_index +
prod(ins.path_shape)].reshape((
() if shared_weights else (-1, )) +
tuple(ins.path_shape))
w_right = ws_right[:, flat_weight_index:flat_weight_index +
prod(ins.path_shape)].reshape(
(() if shared_weights else (-1, )) +
tuple(ins.path_shape))
flat_weight_index += prod(ins.path_shape)
# Construct the general xx in case this instruction isn't specialized
# If this isn't used, the dead code will get removed
key = (ins.i_in1, ins.i_in2, ins.connection_mode[:2])
if key not in xx_dict:
if ins.connection_mode[:2] == 'uv':
xx_dict[key] = torch.einsum('zui,zvj->zuvij', x1_out, x2_out)
if ins.connection_mode[:2] == 'uu':
xx_dict[key] = torch.einsum('zui,zuj->zuij', x1_out, x2_out)
xx = xx_dict[key]
# Create a proxy & request for the relevant wigner w3j
# If not used (because of specialized code), will get removed later.
key = (mul_ir_in1.ir.l, mul_ir_in2.ir.l, mul_ir_out.ir.l)
if key not in w3j:
w3j_dict_out[key] = fx.Proxy(
graph_out.get_attr(f"_w3j_{key[0]}_{key[1]}_{key[2]}"))
w3j_dict_right[key] = fx.Proxy(
graph_right.get_attr(f"_w3j_{key[0]}_{key[1]}_{key[2]}"))
w3j.append(key)
w3j_out = w3j_dict_out[key]
w3j_right = w3j_dict_right[key]
exp = {'component': 1, 'norm': -1}[normalization]
if ins.connection_mode == 'uvw':
assert ins.has_weight
if specialized_code and key == (0, 0, 0):
ein_out = torch.einsum(
f"{z}uvw,zu,zv->zw", w_out,
x1_out.reshape(batch_out, mul_ir_in1.dim),
x2_out.reshape(batch_out, mul_ir_in2.dim))
ein_right = torch.einsum(
f"{z}uvw,zv->zuw", w_right,
x2_right.reshape(batch_right, mul_ir_in2.dim))
elif specialized_code and mul_ir_in1.ir.l == 0:
ein_out = torch.einsum(
f"{z}uvw,zu,zvj->zwj", w_out,
x1_out.reshape(batch_out, mul_ir_in1.dim), x2_out)
ein_right = torch.einsum(f"{z}uvw,zvi->zuwi", w_right,
x2_right)
elif specialized_code and mul_ir_in2.ir.l == 0:
ein_out = torch.einsum(
f"{z}uvw,zui,zv->zwi", w_out, x1_out,
x2_out.reshape(batch_out, mul_ir_in2.dim))
ein_right = torch.einsum(
f"{z}uvw,ij,zv->zuiwj", w_right, i1_right,
x2_right.reshape(batch_right, mul_ir_in2.dim))
elif specialized_code and mul_ir_out.ir.l == 0:
ein_out = torch.einsum(f"{z}uvw,zui,zvi->zw", w_out, x1_out,
x2_out) / sqrt(mul_ir_in1.ir.dim)**exp
ein_right = torch.einsum(f"{z}uvw,zvi->zuiw", w_right,
x2_right) / sqrt(
mul_ir_in1.ir.dim)**exp
else:
ein_out = torch.einsum(f"{z}uvw,ijk,zuvij->zwk", w_out,
w3j_out, xx)
ein_right = torch.einsum(f"{z}uvw,ijk,zvj->zuiwk", w_right,
w3j_right, x2_right)
if ins.connection_mode == 'uvu':
assert mul_ir_in1.mul == mul_ir_out.mul
if ins.has_weight:
if specialized_code and key == (0, 0, 0):
ein_out = torch.einsum(
f"{z}uv,zu,zv->zu", w_out,
x1_out.reshape(batch_out, mul_ir_in1.dim),
x2_out.reshape(batch_out, mul_ir_in2.dim))
ein_right = torch.einsum(
f"{z}uv,uw,zv->zuw", w_right, e1_right,
x2_right.reshape(batch_right, mul_ir_in2.dim))
elif specialized_code and mul_ir_in1.ir.l == 0:
ein_out = torch.einsum(
f"{z}uv,zu,zvj->zuj", w_out,
x1_out.reshape(batch_out, mul_ir_in1.dim), x2_out)
ein_right = torch.einsum(f"{z}uv,uw,zvi->zuwi", w_right,
e1_right, x2_right)
elif specialized_code and mul_ir_in2.ir.l == 0:
ein_out = torch.einsum(
f"{z}uv,zui,zv->zui", w_out, x1_out,
x2_out.reshape(batch_out, mul_ir_in2.dim))
ein_right = torch.einsum(
f"{z}uv,ij,uw,zv->zuiwj", w_right, i1_right, e1_right,
x2_right.reshape(batch_right, mul_ir_in2.dim))
elif specialized_code and mul_ir_out.ir.l == 0:
ein_out = torch.einsum(f"{z}uv,zui,zvi->zu", w_out, x1_out,
x2_out) / sqrt(
mul_ir_in1.ir.dim)**exp
ein_right = torch.einsum(f"{z}uv,uw,zvi->zuiw", w_right,
e1_right, x2_right) / sqrt(
mul_ir_in1.ir.dim)**exp
else:
ein_out = torch.einsum(f"{z}uv,ijk,zuvij->zuk", w_out,
w3j_out, xx)
ein_right = torch.einsum(f"{z}uv,ijk,uw,zvj->zuiwk",
w_right, w3j_right, e1_right,
x2_right)
else:
# not so useful operation because v is summed
ein_out = torch.einsum("ijk,zuvij->zuk", w3j_out, xx)
ein_right = torch.einsum("ijk,uw,zvj->zuiwk", w3j_right,
e1_right, x2_right)
if ins.connection_mode == 'uvv':
assert mul_ir_in2.mul == mul_ir_out.mul
if ins.has_weight:
if specialized_code and key == (0, 0, 0):
ein_out = torch.einsum(
f"{z}uv,zu,zv->zv", w_out,
x1_out.reshape(batch_out, mul_ir_in1.dim),
x2_out.reshape(batch_out, mul_ir_in2.dim))
ein_right = torch.einsum(
f"{z}uv,vw,zv->zuw", w_right, e2_right,
x2_right.reshape(batch_right, mul_ir_in2.dim))
elif specialized_code and mul_ir_in1.ir.l == 0:
ein_out = torch.einsum(
f"{z}uv,zu,zvj->zvj", w_out,
x1_out.reshape(batch_out, mul_ir_in1.dim), x2_out)
ein_right = torch.einsum(f"{z}uv,vw,zvi->zuwi", w_right,
e2_right, x2_right)
elif specialized_code and mul_ir_in2.ir.l == 0:
ein_out = torch.einsum(
f"{z}uv,zui,zv->zvi", w_out, x1_out,
x2_out.reshape(batch_out, mul_ir_in2.dim))
ein_right = torch.einsum(
f"{z}uv,ij,vw,zv->zuiwj", w_right, i1_right, e2_right,
x2_right.reshape(batch_right, mul_ir_in2.dim))
elif specialized_code and mul_ir_out.ir.l == 0:
ein_out = torch.einsum(f"{z}uv,zui,zvi->zv", w_out, x1_out,
x2_out) / sqrt(
mul_ir_in1.ir.dim)**exp
ein_right = torch.einsum(f"{z}uv,vw,zvi->zuiw", w_right,
e2_right, x2_right) / sqrt(
mul_ir_in1.ir.dim)**exp
else:
ein_out = torch.einsum(f"{z}uv,ijk,zuvij->zvk", w_out,
w3j_out, xx)
ein_right = torch.einsum(f"{z}uv,ijk,zvj->zuivk", w_right,
w3j_right, x2_right)
else:
# not so useful operation because u is summed
# only specialize out for this path
if specialized_code and key == (0, 0, 0):
ein_out = torch.einsum(
"zu,zv->zv", x1_out.reshape(batch_out, mul_ir_in1.dim),
x2_out.reshape(batch_out, mul_ir_in2.dim))
elif specialized_code and mul_ir_in1.ir.l == 0:
ein_out = torch.einsum(
"zu,zvj->zvj", x1_out.reshape(batch_out,
mul_ir_in1.dim), x2_out)
elif specialized_code and mul_ir_in2.ir.l == 0:
ein_out = torch.einsum(
"zui,zv->zvi", x1_out,
x2_out.reshape(batch_out, mul_ir_in2.dim))
elif specialized_code and mul_ir_out.ir.l == 0:
ein_out = torch.einsum("zui,zvi->zv", x1_out,
x2_out) / sqrt(
mul_ir_in1.ir.dim)**exp
else:
ein_out = torch.einsum("ijk,zuvij->zvk", w3j_out, xx)
s2ones = fx.Proxy(
graph_right.call_function(
torch.ones, (mul_ir_in1.mul, ),
dict(device=x2_right.device.node,
dtype=x2_right.dtype.node)))
ein_right = torch.einsum("u,ijk,zvj->zuivk", s2ones, w3j_right,
x2_right)
if ins.connection_mode == 'uuw':
assert mul_ir_in1.mul == mul_ir_in2.mul
if ins.has_weight:
if specialized_code and key == (0, 0, 0):
ein_out = torch.einsum(
f"{z}uw,zu,zu->zw", w_out,
x1_out.reshape(batch_out, mul_ir_in1.dim),
x2_out.reshape(batch_out, mul_ir_in2.dim))
elif specialized_code and mul_ir_in1.ir.l == 0:
ein_out = torch.einsum(
f"{z}uw,zu,zuj->zwj", w_out,
x1_out.reshape(batch_out, mul_ir_in1.dim), x2_out)
elif specialized_code and mul_ir_in2.ir.l == 0:
ein_out = torch.einsum(
f"{z}uw,zui,zu->zwi", w_out, x1_out,
x2_out.reshape(batch_out, mul_ir_in2.dim))
elif specialized_code and mul_ir_out.ir.l == 0:
ein_out = torch.einsum(f"{z}uw,zui,zui->zw", w_out, x1_out,
x2_out) / sqrt(
mul_ir_in1.ir.dim)**exp
else:
ein_out = torch.einsum(f"{z}uw,ijk,zuij->zwk", w_out,
w3j_out, xx)
# TODO: specialize right()
ein_right = torch.einsum(f"{z}uw,ijk,zuj->zuiwk", w_right,
w3j_right, x2_right)
else:
# equivalent to tp(x, y, 'uuu').sum('u')
assert mul_ir_out.mul == 1
ein_out = torch.einsum("ijk,zuij->zk", w3j_out, xx)
ein_right = torch.einsum("ijk,zuj->zuik", w3j_right, x2_right)
if ins.connection_mode == 'uuu':
assert mul_ir_in1.mul == mul_ir_in2.mul == mul_ir_out.mul
if ins.has_weight:
if specialized_code and key == (0, 0, 0):
ein_out = torch.einsum(
f"{z}u,zu,zu->zu", w_out,
x1_out.reshape(batch_out, mul_ir_in1.dim),
x2_out.reshape(batch_out, mul_ir_in2.dim))
ein_right = torch.einsum(
f"{z}u,uw,zu->zuw", w_right, e2_right,
x2_right.reshape(batch_right, mul_ir_in2.dim))
elif specialized_code and key == (
1, 1, 1) and normalization == "component":
ein_out = torch.einsum(f"{z}u,zui->zui", w_out,
torch.cross(x1_out, x2_out,
dim=2)) / sqrt(2)
# For cross product, use the general case right()
ein_right = torch.einsum(f"{z}u,ijk,uw,zuj->zuiwk",
w_right, w3j_right, e1_right,
x2_right)
elif specialized_code and mul_ir_in1.ir.l == 0:
ein_out = torch.einsum(
f"{z}u,zu,zuj->zuj", w_out,
x1_out.reshape(batch_out, mul_ir_in1.dim), x2_out)
ein_right = torch.einsum(f"{z}u,uw,zui->zuwi", w_right,
e2_right, x2_right)
elif specialized_code and mul_ir_in2.ir.l == 0:
ein_out = torch.einsum(
f"{z}u,zui,zu->zui", w_out, x1_out,
x2_out.reshape(batch_out, mul_ir_in2.dim))
ein_right = torch.einsum(
f"{z}u,ij,uw,zu->zuiwj", w_right, i1_right, e2_right,
x2_right.reshape(batch_right, mul_ir_in2.dim))
elif specialized_code and mul_ir_out.ir.l == 0:
ein_out = torch.einsum(f"{z}u,zui,zui->zu", w_out, x1_out,
x2_out) / sqrt(
mul_ir_in1.ir.dim)**exp
ein_right = torch.einsum(f"{z}u,uw,zui->zuiw", w_right,
e2_right, x2_right) / sqrt(
mul_ir_in1.ir.dim)**exp
else:
ein_out = torch.einsum(f"{z}u,ijk,zuij->zuk", w_out,
w3j_out, xx)
ein_right = torch.einsum(f"{z}u,ijk,uw,zuj->zuiwk",
w_right, w3j_right, e1_right,
x2_right)
else:
if specialized_code and key == (0, 0, 0):
ein_out = torch.einsum(
"zu,zu->zu", x1_out.reshape(batch_out, mul_ir_in1.dim),
x2_out.reshape(batch_out, mul_ir_in2.dim))
ein_right = torch.einsum(
"uw,zu->zuw", e2_right,
x2_right.reshape(batch_right, mul_ir_in2.dim))
elif specialized_code and key == (
1, 1, 1) and normalization == "component":
ein_out = torch.cross(x1_out, x2_out,
dim=2) * (1.0 / sqrt(2))
# For cross product, use the general case right()
ein_right = torch.einsum("ijk,uw,zuj->zuiwk", w3j_right,
e1_right, x2_right)
elif specialized_code and mul_ir_in1.ir.l == 0:
ein_out = torch.einsum(
"zu,zuj->zuj", x1_out.reshape(batch_out,
mul_ir_in1.dim), x2_out)
ein_right = torch.einsum("uw,zui->zuwi", e2_right,
x2_right)
elif specialized_code and mul_ir_in2.ir.l == 0:
ein_out = torch.einsum(
"zui,zu->zui", x1_out,
x2_out.reshape(batch_out, mul_ir_in2.dim))
ein_right = torch.einsum(
"ij,uw,zu->zuiwj", i1_right, e2_right,
x2_right.reshape(batch_right, mul_ir_in2.dim))
elif specialized_code and mul_ir_out.ir.l == 0:
ein_out = torch.einsum("zui,zui->zu", x1_out,
x2_out) / sqrt(
mul_ir_in1.ir.dim)**exp
ein_right = torch.einsum("uw,zui->zuiw", e2_right,
x2_right) / sqrt(
mul_ir_in1.ir.dim)**exp
else:
ein_out = torch.einsum("ijk,zuij->zuk", w3j_out, xx)
ein_right = torch.einsum("ijk,uw,zuj->zuiwk", w3j_right,
e1_right, x2_right)
if ins.connection_mode == 'uvuv':
assert mul_ir_in1.mul * mul_ir_in2.mul == mul_ir_out.mul
if ins.has_weight:
# TODO implement specialized code
ein_out = torch.einsum(f"{z}uv,ijk,zuvij->zuvk", w_out,
w3j_out, xx)
ein_right = torch.einsum(f"{z}uv,ijk,uw,zvj->zuiwvk", w_right,
w3j_right, e1_right, x2_right)
else:
# TODO implement specialized code
ein_out = torch.einsum("ijk,zuvij->zuvk", w3j_out, xx)
ein_right = torch.einsum("ijk,uw,zvj->zuiwvk", w3j_right,
e1_right, x2_right)
ein_out = alpha * ein_out
ein_right = alpha * ein_right
out_list_out += [ein_out.reshape(batch_out, mul_ir_out.dim)]
out_list_right += [
ein_right.reshape(batch_right, mul_ir_in1.dim, mul_ir_out.dim)
]
# Close the profiler block
graph_out.call_function(torch.ops.profiler._record_function_exit,
(handle_out, ))
graph_right.call_function(torch.ops.profiler._record_function_exit,
(handle_right, ))
# Remove unused w3js:
if len(w3j_out.node.users) == 0 and len(w3j_right.node.users) == 0:
del w3j[-1]
# The w3j nodes are reshapes, so we have to remove them from the graph
# Although they are dead code, they try to reshape to dimensions that don't exist
# (since the corresponding w3js are not in w3j)
# so they screw up the shape propagation, even though they would be removed later as dead code by TorchScript.
graph_out.erase_node(w3j_dict_out.pop(key).node)
graph_right.erase_node(w3j_dict_right.pop(key).node)
# = Return the result =
out_out = [
_sum_tensors([
out for ins, out in zip(instructions, out_list_out)
if ins.i_out == i_out
],
shape=(batch_out, mul_ir_out.dim),
like=x1s_out)
for i_out, mul_ir_out in enumerate(irreps_out) if mul_ir_out.mul > 0
]
if len(out_out) > 1:
out_out = torch.cat(out_out, dim=1)
else:
# Avoid an unnecessary copy in a size one torch.cat
out_out = out_out[0]
out_right = [
torch.cat([
_sum_tensors([
out for ins, out in zip(instructions, out_list_right)
if (ins.i_in1, ins.i_out) == (i_in1, i_out)
],
shape=(batch_right, mul_ir_in1.dim, mul_ir_out.dim),
like=x2s_right)
for i_out, mul_ir_out in enumerate(irreps_out)
if mul_ir_out.mul > 0
],
dim=2) for i_in1, mul_ir_in1 in enumerate(irreps_in1)
if mul_ir_in1.mul > 0
]
if len(out_right) > 1:
out_right = torch.cat(out_right, dim=1)
else:
out_right = out_right[0]
out_out = out_out.reshape(outsize_out)
out_right = out_right.reshape(outsize_right)
graph_out.output(out_out.node, torch.Tensor)
graph_right.output(out_right.node, torch.Tensor)
# check graphs
graph_out.lint()
graph_right.lint()
# Make GraphModules
wigner_mats = {}
for l_1, l_2, l_out in w3j:
wig = o3.wigner_3j(l_1, l_2, l_out)
if normalization == 'component':
wig *= (2 * l_out + 1)**0.5
if normalization == 'norm':
wig *= (2 * l_1 + 1)**0.5 * (2 * l_2 + 1)**0.5
wigner_mats[f"_w3j_{l_1}_{l_2}_{l_out}"] = wig
# By putting the constants in a Module rather than a dict,
# we force FX to copy them as buffers instead of as attributes.
#
# FX seems to have resolved this issue for dicts in 1.9, but we support all the way back to 1.8.0.
constants_root = torch.nn.Module()
for wkey, wmat in wigner_mats.items():
constants_root.register_buffer(wkey, wmat)
graphmod_out = fx.GraphModule(constants_root,
graph_out,
class_name="tp_forward")
graphmod_right = fx.GraphModule(constants_root,
graph_right,
class_name="tp_right")
# == Optimize ==
# TODO: when eliminate_dead_code() is in PyTorch stable, use that
if optimize_einsums:
# Note that for our einsums, we can optimize _once_ for _any_ batch dimension
# and still get the right path for _all_ batch dimensions.
# This is because our einsums are essentially of the form:
# zuvw,ijk,zuvij->zwk OR uvw,ijk,zuvij->zwk
# In the first case, all but one operands have the batch dimension
# => The first contraction gains the batch dimension
# => All following contractions have batch dimension
# => All possible contraction paths have cost that scales linearly in batch size
# => The optimal path is the same for all batch sizes
# For the second case, this logic follows as long as the first contraction is not between the first two operands. Since those two operands do not share any indexes, contracting them first is a rare pathological case. See
# https://github.com/dgasmith/opt_einsum/issues/158
# for more details.
#
# TODO: consider the impact maximum intermediate result size on this logic
# \- this is the `memory_limit` option in opt_einsum
# TODO: allow user to choose opt_einsum parameters?
#
# We use float32 and zeros to save memory and time, since opt_einsum_fx looks only at traced shapes, not values or dtypes.
batchdim = 4
example_inputs = (
torch.zeros((batchdim, irreps_in1.dim)),
torch.zeros((batchdim, irreps_in2.dim)),
torch.zeros(
1 if shared_weights else batchdim,
flat_weight_index,
),
)
graphmod_out = jitable(
optimize_einsums_full(graphmod_out, example_inputs))
graphmod_right = jitable(
optimize_einsums_full(graphmod_right, example_inputs[1:]))
return graphmod_out, graphmod_right
