# Source code for torch_geometric.transforms.linear_transformation

```from typing import Union

import torch
from torch import Tensor

from torch_geometric.data import Data, HeteroData
from torch_geometric.data.datapipes import functional_transform
from torch_geometric.transforms import BaseTransform

[docs]@functional_transform('linear_transformation')
class LinearTransformation(BaseTransform):
r"""Transforms node positions :obj:`data.pos` with a square transformation
matrix computed offline (functional name: :obj:`linear_transformation`)

Args:
matrix (Tensor): Tensor with shape :obj:`[D, D]` where :obj:`D`
corresponds to the dimensionality of node positions.
"""
def __init__(self, matrix: Tensor):
if not isinstance(matrix, Tensor):
matrix = torch.tensor(matrix)
assert matrix.dim() == 2, (
'Transformation matrix should be two-dimensional.')
assert matrix.size(0) == matrix.size(1), (
f'Transformation matrix should be square (got {matrix.size()})')

# Store the matrix as its transpose.
# We do this to enable post-multiplication in `forward`.
self.matrix = matrix.t()

def forward(
self,
data: Union[Data, HeteroData],
) -> Union[Data, HeteroData]:
for store in data.node_stores:
if not hasattr(store, 'pos'):
continue

pos = store.pos.view(-1, 1) if store.pos.dim() == 1 else store.pos
assert pos.size(-1) == self.matrix.size(-2), (
'Node position matrix and transformation matrix have '
'incompatible shape')
# We post-multiply the points by the transformation matrix instead
# of pre-multiplying, because `pos` attribute has shape `[N, D]`,
# and we want to preserve this shape.
store.pos = pos @ self.matrix.to(pos.device, pos.dtype)

return data

def __repr__(self) -> str:
return f'{self.__class__.__name__}(\n{self.matrix.cpu().numpy()}\n)'
```