vlinalg¶

torchvectorized.vlinalg.vSymEig(inputs: torch.Tensor, eigenvectors=False, flatten_output=False, descending_eigenvals=False)¶

Compute the eigendecomposition $\mathbf{M} = \mathbf{U} \mathbf{\Sigma} \mathbf{U}^{\top}$ of every voxel in a volume of flattened 3x3 symmetric matrices of shape Bx9xDxHxW.

Parameters:	inputs (torch.Tensor) – The input tensor of shape Bx9xDxHxW, where the 9 channels represent flattened 3x3 symmetric matrices. eigenvectors (bool) – If `True`, computes the eigenvectors. flatten_output (bool) – If `True` the eigenvalues are returned as: *(BDHW)x3 and the eigenvectors as (BDHW)x3x3* otherwise they are returned with shapes Bx3xDxHxW and Bx3x3xDxHxW respectively. descending_eigenvals (bool) – If `True`, return the eigenvvalues in descending order
Returns:	Return the eigenvalues and the eigenvectors as tensors.
Return type:	tuple[torch.Tensor, None]

Example:

import torch
from torchvectorized.utils import sym
from torchvectorized.vlinalg import vSymEig

b, c, d, h, w = 1, 9, 32, 32, 32
inputs = sym(torch.rand(b, c, d, h, w))
eig_vals, eig_vecs = vSymEig(inputs, eigenvectors=True)

torchvectorized.vlinalg.vExpm(inputs: torch.Tensor, replace_nans=False)¶

Compute the matrix exponential $\mathbf{M} = \mathbf{U} exp(\mathbf{\Sigma}) \mathbf{U}^{\top}$ of every voxel in a volume of flattened 3x3 symmetric matrices of shape Bx9xDxHxW.

Parameters:	inputs (torch.Tensor) – The input tensor of shape Bx9xDxHxW, where the 9 channels represent flattened 3x3 symmetric matrices. replace_nans (bool) – If `True`, replace nans by 0
Returns:	Return a tensor with shape Bx9xDxHxW where every voxel is the matrix exponential of the inpur matrix at the same spatial location.
Return type:	torch.Tensor

Example:

import torch
from torchvectorized.utils import sym
from torchvectorized.vlinalg import vExpm

b, c, d, h, w = 1, 9, 32, 32, 32
inputs = sym(torch.rand(b, c, d, h, w))
output = vExpm(inputs)

torchvectorized.vlinalg.vLogm(inputs: torch.Tensor, replace_nans=False)¶

Compute the matrix logarithm $\mathbf{M} = \mathbf{U} log(\mathbf{\Sigma}) \mathbf{U}^{\top}$ of every voxel in a volume of flattened 3x3 symmetric matrices of shape Bx9xDxHxW.

Parameters:	inputs (torch.Tensor) – The input tensor of shape Bx9xDxHxW, where the 9 channels represent flattened 3x3 symmetric matrices. replace_nans (bool) – If `True`, replace nans by 0
Returns:	Return a tensor with shape Bx9xDxHxW where every voxel is the matrix logarithm of the inpur matrix at the same spatial location.
Return type:	torch.Tensor

Example:

import torch
from torchvectorized.utils import sym
from torchvectorized.vlinalg import vLogm

b, c, d, h, w = 1, 9, 32, 32, 32
inputs = sym(torch.rand(b, c, d, h, w))
output = vLogm(inputs)

torchvectorized.vlinalg.vTrace(inputs: torch.Tensor)¶

Compute the trace of every voxel in a volume of flattened 3x3 symmetric matrices of shape Bx9xDxHxW.

Parameters:	inputs (torch.Tensor) – The input tensor of shape Bx9xDxHxW, where the 9 channels represent flattened 3x3 symmetric matrices.
Returns:	Return a tensor with shape Bx1xDxHxW where every voxel is the trace of the inpur matrix at the same spatial location.
Return type:	torch.Tensor

Example:

import torch
from torchvectorized.utils import sym
from torchvectorized.vlinalg import vTrace

b, c, d, h, w = 1, 9, 32, 32, 32
inputs = sym(torch.rand(b, c, d, h, w))
output = vTrace(inputs)

torchvectorized.vlinalg.vDet(inputs: torch.Tensor)¶

Compute the determinant of every voxel in a volume of flattened 3x3 symmetric matrices of shape Bx9xDxHxW.

Parameters:	inputs (torch.Tensor) – The input tensor of shape Bx9xDxHxW, where the 9 channels represent flattened 3x3 symmetric matrices.
Returns:	Return a tensor with shape Bx1xDxHxW where every voxel is the determinant of the inpur matrix at the same spatial location.
Return type:	torch.Tensor

Example:

import torch
from torchvectorized.utils import sym
from torchvectorized.vlinalg import vDet

b, c, d, h, w = 1, 9, 32, 32, 32
inputs = sym(torch.rand(b, c, d, h, w))
output = vDet(inputs)