def batched_spmm(nzt, adj, x, m=None, n=None):
"""
Args:
nzt: Tensor [num_edges, heads] -- non-zero tensor
adj: Tensor or list(Tensor) -- adjacency matrix (COO)
x: Tensor [num_nodes, channels] -- feature matrix
m: int
n: int
"""
num_edges, heads = nzt.shape[-2:]
num_nodes, channels = x.shape[-2:]
# preparation of data
# x_ = torch.cat(heads * [x]) # duplicate x for heads times
# nzt_ = nzt.view(-1)
x_ = repeat(x, 't n c -> t (h n) c', h=heads)
nzt_ = rearrange(nzt, 't e h -> t (h e)')
if isinstance(adj, Tensor):
m = maybe_num_nodes(adj[0], m)
n = max(num_nodes, maybe_num_nodes(adj[1], n))
offset = torch.tensor([[m], [n]])
adj_ = torch.cat([adj + offset * i for i in range(heads)], dim=1)
else: # adj is list of adjacency matrices
assert heads == len(
adj), "the number of heads and the number of adjacency matrices are not matched"
m = max([maybe_num_nodes(adj_[0], m) for adj_ in adj])
n = max([maybe_num_nodes(adj_[1], n) for adj_ in adj])
offset = torch.tensor([[m], [n]])
adj_ = torch.cat([adj[i] + offset * i for i in range(heads)], dim=1)
if len(x.shape) == 2:
out = spmm(adj_, nzt_, heads * m, heads * n, x_)
return out.view(-1, m, channels) # [heads, m, channels]
else:
_size = x_.shape[0]
out = torch.stack([spmm(adj_, nzt_[i], heads * m, heads * n, x_[i]) for i in range(_size)])
return out # [batch, heads * num_nodes, channels]
def gcn_no_norm(edge_index,
edge_weight=None,
num_nodes=None,
improved=False,
add_self_loops=True,
dtype=None):
fill_value = 2. if improved else 1.
if isinstance(edge_index, SparseTensor):
adj_t = edge_index
if not adj_t.has_value():
adj_t = adj_t.fill_value(1., dtype=dtype)
if add_self_loops:
adj_t = fill_diag(adj_t, fill_value)
return adj_t
else:
num_nodes = maybe_num_nodes(edge_index, num_nodes)
if edge_weight is None:
edge_weight = torch.ones((edge_index.size(1), ),
dtype=dtype,
device=edge_index.device)
if add_self_loops:
edge_index, tmp_edge_weight = add_remaining_self_loops(
edge_index, edge_weight, fill_value, num_nodes)
assert tmp_edge_weight is not None
edge_weight = tmp_edge_weight
row, col = edge_index[0], edge_index[1]
return edge_index, edge_weight
def add_self_loops(edge_index, edge_weight: Optional[torch.Tensor] = None,
fill_value: float = 1., num_nodes: Optional[int] = None):
r"""Adds a self-loop :math:`(i,i) \in \mathcal{E}` to every node
:math:`i \in \mathcal{V}` in the graph given by :attr:`edge_index`.
In case the graph is weighted, self-loops will be added with edge weights
denoted by :obj:`fill_value`.
Args:
edge_index (LongTensor): The edge indices.
edge_weight (Tensor, optional): One-dimensional edge weights.
(default: :obj:`None`)
fill_value (float, optional): If :obj:`edge_weight` is not :obj:`None`,
will add self-loops with edge weights of :obj:`fill_value` to the
graph. (default: :obj:`1.`)
num_nodes (int, optional): The number of nodes, *i.e.*
:obj:`max_val + 1` of :attr:`edge_index`. (default: :obj:`None`)
:rtype: (:class:`LongTensor`, :class:`Tensor`)
"""
N = maybe_num_nodes(edge_index, num_nodes)
loop_index = torch.arange(0, N, dtype=torch.long, device=edge_index.device)
loop_index = loop_index.unsqueeze(0).repeat(2, 1)
new_edge_index = torch.cat([edge_index, loop_index], dim=1)
return new_edge_index, edge_weight
def __init__(self, edge_index: Union[Tensor, SparseTensor],
sizes: List[int], node_idx: Optional[Tensor] = None,
num_nodes: Optional[int] = None, return_e_id: bool = True,
**kwargs):
self.sizes = sizes
self.return_e_id = return_e_id
self.is_sparse_tensor = isinstance(edge_index, SparseTensor)
self.__val__ = None
# Obtain a *transposed* `SparseTensor` instance.
edge_index = edge_index.to('cpu')
if not self.is_sparse_tensor:
num_nodes = maybe_num_nodes(edge_index, num_nodes)
value = torch.arange(edge_index.size(1)) if return_e_id else None
self.adj_t = SparseTensor(row=edge_index[0], col=edge_index[1],
value=value,
sparse_sizes=(num_nodes, num_nodes)).t()
else:
adj_t = edge_index
if return_e_id:
self.__val__ = adj_t.storage.value()
value = torch.arange(adj_t.nnz())
adj_t = adj_t.set_value(value, layout='coo')
self.adj_t = adj_t
self.adj_t.storage.rowptr()
if node_idx is None:
node_idx = torch.arange(self.adj_t.sparse_size(0))
elif node_idx.dtype == torch.bool:
node_idx = node_idx.nonzero(as_tuple=False).view(-1)
super(NeighborSampler, self).__init__(
node_idx.view(-1).tolist(), collate_fn=self.sample, **kwargs)
def real_softmax(src, index, num_nodes=None):
r"""Computes a sparsely evaluated softmax.
Given a value tensor :attr:`src`, this function first groups the values
along the first dimension based on the indices specified in :attr:`index`,
and then proceeds to compute the softmax individually for each group.
Args:
src (Tensor): The source tensor.
index (LongTensor): The indices of elements for applying the softmax.
num_nodes (int, optional): The number of nodes, *i.e.*
:obj:`max_val + 1` of :attr:`index`. (default: :obj:`None`)
:rtype: :class:`Tensor`
"""
num_nodes = maybe_num_nodes(index, num_nodes)
src = src - scatter_max(src, index, dim=0, dim_size=num_nodes)[0][index]
out = src.exp()
assert not nan_or_inf(out)
oout = out / (scatter_add(out, index, dim=0, dim_size=num_nodes)[index] +
1e-16)
assert not nan_or_inf(oout)
return oout
def remove_isolated_nodes(edge_index, edge_attr=None, num_nodes=None):
num_nodes = maybe_num_nodes(edge_index, num_nodes)
out = segregate_self_loops(edge_index, edge_attr)
edge_index, edge_attr, loop_edge_index, loop_edge_attr = out
mask = torch.zeros(num_nodes, dtype=torch.bool, device=edge_index.device)
mask[edge_index.view(-1)] = 1
assoc = torch.full((num_nodes, ), -1, dtype=torch.long, device=mask.device)
assoc[mask] = torch.arange(mask.type(torch.long).sum(), device=assoc.device)
edge_index = assoc[edge_index]
loop_mask = torch.zeros_like(mask)
loop_mask[loop_edge_index[0]] = 1
loop_mask = loop_mask.type(torch.uint8) & mask.type(torch.uint8)
loop_assoc = torch.full_like(assoc, -1)
loop_assoc[loop_edge_index[0]] = torch.arange(loop_edge_index.size(1),
device=loop_assoc.device)
loop_idx = loop_assoc[loop_mask]
loop_edge_index = assoc[loop_edge_index[:, loop_idx]]
edge_index = torch.cat([edge_index, loop_edge_index], dim=1)
if edge_attr is not None:
loop_edge_attr = loop_edge_attr[loop_idx]
edge_attr = torch.cat([edge_attr, loop_edge_attr], dim=0)
return edge_index, edge_attr, mask
def entropy(src, edge_index, num_nodes=None):
EPS = 1e-32
index, _ = edge_index
num_nodes = maybe_num_nodes(index, num_nodes)
# out = src - scatter_max(src, index, dim=0, dim_size=num_nodes)[0][index]
out = -src * torch.log(src + EPS)
out = scatter_add(out, index, dim=0, dim_size=num_nodes)
return out
def batched_transpose(adj, value, m=None, n=None):
"""
Args:
adj: Tensor or list of Tensor
value: Tensor [num_edges, ]
m: int
n: int
"""
if isinstance(adj, Tensor):
m = maybe_num_nodes(adj[0], m)
n = maybe_num_nodes(adj[1], n)
return transpose(adj, value, m, n)
else: # adj is a list of Tensor
adj_ = [None] * value.shape[1]
vs = torch.zeros(value.shape)
m = max([maybe_num_nodes(a_[0], m) for a_ in adj])
n = max([maybe_num_nodes(a_[1], n) for a_ in adj])
for j in range(len(adj)):
adj_[j], vs[:, j] = transpose(adj[j], value[:, j], m, n)
return adj_, vs
def message(self, x_j, pos_j, pos_i, edge_index):
dist = (pos_j - pos_i).pow(2).sum(dim=1).pow(0.5)
dist = torch.max(dist, torch.Tensor([1e-10]).to(dist.device, dist.dtype))
weight = 1.0 / dist # (E,)
row, col = edge_index
index = col
num_nodes = maybe_num_nodes(index, None)
wsum = scatter_add(weight, col, dim=0, dim_size=num_nodes)[index] + 1e-16 # (E,)
weight /= wsum
return weight.view(-1, 1) * x_j
def softmax(src: Tensor, index: Optional[Tensor], ptr: Optional[Tensor] = None,
num_nodes: Optional[int] = None) -> Tensor:
out = src
if src.numel() > 0:
out = out - src.max()
out = out.exp()
if ptr is not None:
out_sum = gather_csr(segment_csr(out, ptr, reduce='sum'), ptr)
elif index is not None:
N = maybe_num_nodes(index, num_nodes)
out_sum = scatter(out, index, dim=0, dim_size=N, reduce='sum')[index]
else:
raise NotImplementedError
return out / (out_sum + 1e-16)
def gcn_norm(edge_index,
edge_weight=None,
num_nodes=None,
improved=False,
add_self_loops=True,
flow="source_to_target",
dtype=None):
fill_value = 2. if improved else 1.
if isinstance(edge_index, SparseTensor):
assert flow in ["source_to_target"]
adj_t = edge_index
if not adj_t.has_value():
adj_t = adj_t.fill_value(1., dtype=dtype)
if add_self_loops:
adj_t = fill_diag(adj_t, fill_value)
deg = sparsesum(adj_t, dim=1)
deg_inv_sqrt = deg.pow_(-0.5)
deg_inv_sqrt.masked_fill_(deg_inv_sqrt == float('inf'), 0.)
adj_t = mul(adj_t, deg_inv_sqrt.view(-1, 1))
adj_t = mul(adj_t, deg_inv_sqrt.view(1, -1))
return adj_t
else:
assert flow in ["source_to_target", "target_to_source"]
num_nodes = maybe_num_nodes(edge_index, num_nodes)
if edge_weight is None:
edge_weight = torch.ones((edge_index.size(1), ),
dtype=dtype,
device=edge_index.device)
if add_self_loops:
edge_index, tmp_edge_weight = add_remaining_self_loops(
edge_index, edge_weight, fill_value, num_nodes)
assert tmp_edge_weight is not None
edge_weight = tmp_edge_weight
row, col = edge_index[0], edge_index[1]
idx = col if flow == "source_to_target" else row
deg = scatter_add(edge_weight, idx, dim=0, dim_size=num_nodes)
deg_inv_sqrt = deg.pow_(-0.5)
deg_inv_sqrt.masked_fill_(deg_inv_sqrt == float('inf'), 0)
return edge_index, deg_inv_sqrt[row] * edge_weight * deg_inv_sqrt[col]
def add_self_loops_mul(edge_index,
edge_weight=None,
fill_value=1,
num_nodes=None):
num_nodes = maybe_num_nodes(edge_index, num_nodes)
loop_index = torch.arange(0,
num_nodes,
dtype=torch.long,
device=edge_index.device)
loop_index = loop_index.unsqueeze(0).repeat(2, 1)
if edge_weight is not None:
loop_weight = edge_weight.new_full((num_nodes, edge_weight.shape[1]),
fill_value)
edge_weight = torch.cat([edge_weight, loop_weight], dim=0)
edge_index = torch.cat([edge_index, loop_index], dim=1)
return edge_index, edge_weight
def forward(self, x, edge_index, M=None, batch=None, num_nodes=None):
""""""
if batch is None:
batch = edge_index.new_zeros(x.size(0))
# Path integral
num_nodes = maybe_num_nodes(edge_index, num_nodes)
edge_index, edge_weight = self.panentropy_sparse(edge_index, num_nodes)
# weighted degree
num_nodes = x.size(0)
degree = torch.zeros(num_nodes, device=edge_index.device)
degree = scatter_add(edge_weight, edge_index[0], out=degree)
# linear transform
xtransform = torch.matmul(x, self.transform)
# aggregate score
x_transform_norm = xtransform #/ xtransform.norm(p=2, dim=-1)
degree_norm = degree #/ degree.norm(p=2, dim=-1)
score = self.pan_pool_weight[
0] * x_transform_norm + self.pan_pool_weight[1] * degree_norm
if self.min_score is None:
score = self.nonlinearity(score)
else:
score = softmax(score, batch)
perm = self.topk(score, self.ratio, batch, self.min_score)
x = x[perm] * score[perm].view(-1, 1)
x = self.multiplier * x if self.multiplier != 1 else x
batch = batch[perm]
edge_index, edge_weight = self.filter_adj(edge_index,
edge_weight,
perm,
num_nodes=score.size(0))
return x, edge_index, edge_weight, batch, perm, score[perm]
def add_self_loops_no_zero(edge_index, num_nodes=None):
r"""Adds a self-loop :math:`(i,i) \in \mathcal{E}` to every node
:math:`i \in \mathcal{V}` in the graph given by :attr:`edge_index`, for
:math:`i \neq 0`. Modified from `torch_geometric.utils.loop.add_self_loops`.
Args:
edge_index (LongTensor): The edge indices.
num_nodes (int, optional): The number of nodes, *i.e.*
:obj:`max_val + 1` of :attr:`edge_index`. (default: :obj:`None`)
:rtype: (:class:`LongTensor`)
"""
num_nodes = maybe_num_nodes(edge_index, num_nodes)
loop_index = torch.arange(1,
num_nodes,
dtype=torch.long,
device=edge_index.device)
loop_index = loop_index.unsqueeze(0).repeat(2, 1)
edge_index = torch.cat([edge_index, loop_index], dim=1)
return edge_index
def gcn_norm(self,
edge_index,
num_nodes=None,
dtype=None,
add_self_loops=True):
num_nodes = maybe_num_nodes(edge_index, num_nodes)
if edge_weight is None:
edge_weight = torch.ones((edge_index.size(1), ),
dtype=dtype,
device=edge_index.device)
if add_self_loops:
edge_index, tmp_edge_weight = add_remaining_self_loops(
edge_index, edge_weight, fill_value=1, num_nodes=num_nodes)
assert tmp_edge_weight is not None
edge_weight = tmp_edge_weight
row, col = edge_index[0], edge_index[1]
deg = degree(col, x.size(0), dtype=x.dtype)
deg_inv_sqrt = deg.pow(-0.5)
deg_inv_sqrt[deg_inv_sqrt == float('inf')] = 0
return deg_inv_sqrt[row] * deg_inv_sqrt[col]
def softmax(src, index, num_nodes=None):
r"""Computes a sparsely evaluated softmax along with its log in a numerically stable way.
Given a value tensor :attr:`src`, this function first groups the values
along the first dimension based on the indices specified in :attr:`index`,
and then proceeds to compute the softmax individually for each group.
Args:
src (Tensor): The source tensor.
index (LongTensor): The indices of elements for applying the softmax.
num_nodes (int, optional): The number of nodes, *i.e.*
:obj:`max_val + 1` of :attr:`index`. (default: :obj:`None`)
:rtype: :class:`Tensor`
"""
num_nodes = maybe_num_nodes(index, num_nodes)
shifted = src - scatter_max(src, index, dim=0,
dim_size=num_nodes)[0][index]
exp_shifted = shifted.exp()
exp_sum = scatter_add(exp_shifted, index, dim=0, dim_size=num_nodes)[index]
scores = exp_shifted / (exp_sum + 1e-16)
return scores, shifted - (exp_sum + 1e-16).log()
def to_undirected(edge_index, num_nodes=None):
r"""Converts the graph given by :attr:`edge_index` to an undirected graph,
so that :math:`(j,i) \in \mathcal{E}` for every edge :math:`(i,j) \in
\mathcal{E}`.
Args:
edge_index (LongTensor): The edge indices.
num_nodes (int, optional): The number of nodes, *i.e.*
:obj:`max_val + 1` of :attr:`edge_index`. (default: :obj:`None`)
:rtype: :class:`LongTensor`
"""
num_nodes = maybe_num_nodes(edge_index, num_nodes)
row, col = edge_index
value_ori = torch.full([row.size(0)], 2)
value_add = torch.full([col.size(0)], 1)
row, col = torch.cat([row, col], dim=0), torch.cat([col, row], dim=0)
edge_attr = torch.cat([value_ori, value_add], dim=0)
edge_index = torch.stack([row, col], dim=0)
edge_index, edge_attr = coalesce(edge_index, edge_attr, num_nodes,
num_nodes)
return edge_index, edge_attr.view(-1, 1).type(torch.float32)
def topk_softmax(src, index, k, num_nodes=None):
r"""Computes a sparsely evaluated softmax using only top-k values.
Given a value tensor :attr:`src`, this function first groups the values
along the first dimension based on the indices specified in :attr:`index`,
and then select top-k values for each group, compute the softmax individually.
The output of not selected indices will be zero.
Args:
src (Tensor): The source tensor.
index (LongTensor): The indices of elements for applying the softmax.
k (int): The number of indexes to select from each group.
num_nodes (int, optional): The number of nodes, *i.e.*
:obj:`max_val + 1` of :attr:`index`. (default: :obj:`None`)
:rtype: :class:`Tensor`
"""
num_nodes = maybe_num_nodes(index, num_nodes)
# Create mask the topk values of which are 1., otherwise 0.
out = src.clone()
topk_mask = torch.zeros_like(out)
for _ in range(k):
v_max = scatter_max(out, index, dim=0, dim_size=num_nodes)[0]
i_max = (out == v_max[index])
topk_mask[i_max] = 1.
out[i_max] = float("-Inf")
out = src - scatter_max(src, index, dim=0, dim_size=num_nodes)[0][index]
out = out.exp()
# Mask except topk values
out = out * topk_mask
out = out / (scatter_add(out, index, dim=0, dim_size=num_nodes)[index] +
1e-16)
return out
