Source code for pina.model.layers.orthogonal
"""Module for OrthogonalBlock."""
import torch
from ...utils import check_consistency
[docs]
class OrthogonalBlock(torch.nn.Module):
"""
Module to make the input orthonormal.
The module takes a tensor of size :math:`[N, M]` and returns a tensor of
size :math:`[N, M]` where the columns are orthonormal. The block performs a
Gram Schmidt orthogonalization process for the input, see
`here <https://en.wikipedia.org/wiki/Gram%E2%80%93Schmidt_process>` for
details.
"""
def __init__(self, dim=-1, requires_grad=True):
"""
Initialize the OrthogonalBlock module.
:param int dim: The dimension where to orthogonalize.
:param bool requires_grad: If autograd should record operations on
the returned tensor, defaults to True.
"""
super().__init__()
# store dim
self.dim = dim
# store requires_grad
check_consistency(requires_grad, bool)
self._requires_grad = requires_grad
[docs]
def forward(self, X):
"""
Forward pass of the OrthogonalBlock module using a Gram-Schmidt
algorithm.
:raises Warning: If the dimension is greater than the other dimensions.
:param torch.Tensor X: The input tensor to orthogonalize. The input must
be of dimensions :math:`[N, M]`.
:return: The orthonormal tensor.
"""
# check dim is less than all the other dimensions
if X.shape[self.dim] > min(X.shape):
raise Warning(
"The dimension where to orthogonalize is greater"
" than the other dimensions"
)
result = torch.zeros_like(X, requires_grad=self._requires_grad)
X_0 = torch.select(X, self.dim, 0).clone()
result_0 = X_0 / torch.linalg.norm(X_0)
result = self._differentiable_copy(result, 0, result_0)
# iterate over the rest of the basis with Gram-Schmidt
for i in range(1, X.shape[self.dim]):
v = torch.select(X, self.dim, i).clone()
for j in range(i):
vj = torch.select(result, self.dim, j).clone()
v = v - torch.sum(v * vj, dim=self.dim, keepdim=True) * vj
# result_i = torch.select(result, self.dim, i)
result_i = v / torch.linalg.norm(v)
result = self._differentiable_copy(result, i, result_i)
return result
def _differentiable_copy(self, result, idx, value):
"""
Perform a differentiable copy operation on a tensor.
:param torch.Tensor result: The tensor where values will be copied to.
:param int idx: The index along the specified dimension where the
value will be copied.
:param torch.Tensor value: The tensor value to copy into the
result tensor.
:return: A new tensor with the copied values.
:rtype: torch.Tensor
"""
return result.index_copy(
self.dim, torch.tensor([idx]), value.unsqueeze(self.dim)
)
@property
def dim(self):
"""
Get the dimension along which operations are performed.
:return: The current dimension value.
:rtype: int
"""
return self._dim
@dim.setter
def dim(self, value):
"""
Set the dimension along which operations are performed.
:param value: The dimension to be set, which must be 0, 1, or -1.
:type value: int
:raises IndexError: If the provided dimension is not in the
range [-1, 1].
"""
# check consistency
check_consistency(value, int)
if value not in [0, 1, -1]:
raise IndexError(
"Dimension out of range (expected to be in "
f"range of [-1, 1], but got {value})"
)
# assign value
self._dim = value
@property
def requires_grad(self):
"""
Indicates whether gradient computation is required for operations
on the tensors.
:return: True if gradients are required, False otherwise.
:rtype: bool
"""
return self._requires_grad