from typing import Optional, Tuple
import torch
from torch import Tensor
from torch_geometric.utils.coalesce import coalesce
[docs]def grid(
height: int,
width: int,
dtype: Optional[torch.dtype] = None,
device: Optional[torch.device] = None,
) -> Tuple[Tensor, Tensor]:
r"""Returns the edge indices of a two-dimensional grid graph with height
:attr:`height` and width :attr:`width` and its node positions.
Args:
height (int): The height of the grid.
width (int): The width of the grid.
dtype (:obj:`torch.dtype`, optional): The desired data type of the
returned position tensor.
dtype (:obj:`torch.device`, optional): The desired device of the
returned tensors.
:rtype: (:class:`LongTensor`, :class:`Tensor`)
Example:
>>> (row, col), pos = grid(height=2, width=2)
>>> row
tensor([0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3])
>>> col
tensor([0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3])
>>> pos
tensor([[0., 1.],
[1., 1.],
[0., 0.],
[1., 0.]])
"""
edge_index = grid_index(height, width, device)
pos = grid_pos(height, width, dtype, device)
return edge_index, pos
def grid_index(
height: int,
width: int,
device: Optional[torch.device] = None,
) -> Tensor:
w = width
kernel = [-w - 1, -1, w - 1, -w, 0, w, -w + 1, 1, w + 1]
kernel = torch.tensor(kernel, device=device)
row = torch.arange(height * width, dtype=torch.long, device=device)
row = row.view(-1, 1).repeat(1, kernel.size(0))
col = row + kernel.view(1, -1)
row, col = row.view(height, -1), col.view(height, -1)
index = torch.arange(3, row.size(1) - 3, dtype=torch.long, device=device)
row, col = row[:, index].view(-1), col[:, index].view(-1)
mask = (col >= 0) & (col < height * width)
row, col = row[mask], col[mask]
edge_index = torch.stack([row, col], dim=0)
edge_index = coalesce(edge_index, None, height * width)
return edge_index
def grid_pos(
height: int,
width: int,
dtype: Optional[torch.dtype] = None,
device: Optional[torch.device] = None,
) -> Tensor:
dtype = torch.float if dtype is None else dtype
x = torch.arange(width, dtype=dtype, device=device)
y = (height - 1) - torch.arange(height, dtype=dtype, device=device)
x = x.repeat(height)
y = y.unsqueeze(-1).repeat(1, width).view(-1)
return torch.stack([x, y], dim=-1)