torchbox.linalg package

Submodules

torchbox.linalg.decomposition module

class torchbox.linalg.decomposition.MatrixSquareRoot(*args, **kwargs)

Bases: torch.autograd.function.Function

Square root of a positive definite matrix.

NOTE: matrix square root is not differentiable for matrices with

zero eigenvalues.

static backward(ctx, grad_output)

Defines a formula for differentiating the operation with backward mode automatic differentiation (alias to the vjp function).

This function is to be overridden by all subclasses.

It must accept a context ctx as the first argument, followed by as many outputs as the forward() returned (None will be passed in for non tensor outputs of the forward function), and it should return as many tensors, as there were inputs to forward(). Each argument is the gradient w.r.t the given output, and each returned value should be the gradient w.r.t. the corresponding input. If an input is not a Tensor or is a Tensor not requiring grads, you can just pass None as a gradient for that input.

The context can be used to retrieve tensors saved during the forward pass. It also has an attribute ctx.needs_input_grad as a tuple of booleans representing whether each input needs gradient. E.g., backward() will have ctx.needs_input_grad[0] = True if the first input to forward() needs gradient computated w.r.t. the output.

static forward(ctx, input)

This function is to be overridden by all subclasses. There are two ways to define forward:

Usage 1 (Combined forward and ctx):

@staticmethod
def forward(ctx: Any, *args: Any, **kwargs: Any) -> Any:
    pass

  • It must accept a context ctx as the first argument, followed by any number of arguments (tensors or other types).

  • See combining-forward-context for more details

Usage 2 (Separate forward and ctx):

@staticmethod
def forward(*args: Any, **kwargs: Any) -> Any:
    pass

@staticmethod
def setup_context(ctx: Any, inputs: Tuple[Any, ...], output: Any) -> None:
    pass

  • The forward no longer accepts a ctx argument.

  • Instead, you must also override the torch.autograd.Function.setup_context() staticmethod to handle setting up the ctx object. output is the output of the forward, inputs are a Tuple of inputs to the forward.

  • See extending-autograd for more details

The context can be used to store arbitrary data that can be then retrieved during the backward pass. Tensors should not be stored directly on ctx (though this is not currently enforced for backward compatibility). Instead, tensors should be saved either with ctx.save_for_backward() if they are intended to be used in backward (equivalently, vjp) or ctx.save_for_forward() if they are intended to be used for in jvp.

torchbox.linalg.decomposition.eig(A, cdim=None, dim=(- 2, - 1), keepdim=False)

Computes the eigenvalues and eigenvectors of a square matrix.

Parameters

  • A (Tensor) – any size tensor, both complex and real representation are supported. For real representation, the real and imaginary dimension is specified by cdim or caxis.

  • cdim (int or None, optional) – if A and B are complex tensors but represented in real format, cdim or caxis should be specified (Default is None).

  • dim (tulpe or list) – dimensions for multiplication (default is (-2, -1))

  • keepdim (bool) – keep dimensions? (include complex dim, defalut is False)

torchbox.linalg.decomposition.eigvals(A, cdim=None, dim=(- 2, - 1), keepdim=False)

Computes the eigenvalues of a square matrix.

Parameters

  • A (Tensor) – any size tensor, both complex and real representation are supported. For real representation, the real and imaginary dimension is specified by cdim or caxis.

  • cdim (int or None, optional) – if A and B are complex tensors but represented in real format, cdim or caxis should be specified (Default is None).

  • dim (tulpe or list) – dimensions for multiplication (default is (-2, -1))

  • keepdim (bool) – keep dimensions? (include complex dim, defalut is False)

torchbox.linalg.decomposition.svd_rank(A, svdr='auto')

compute rank of the truncated Singular Value Decomposition

Gavish, Matan, and David L. Donoho, The optimal hard threshold for singular values is, IEEE Transactions on Information Theory 60.8 (2014): 5040-5053.

Parameters

  • A (Tensor) – The input matrix

  • svdr (str or int, optional) – the rank for the truncation, 'auto' for automatic computation, by default 'auto'

torchbox.linalg.orthogonalization module

torchbox.linalg.orthogonalization.orth(x)

Orthogonalization

A function like MATLAB’s orth. After orthogonalizing, each column is a orthogonal basis.

Parameters

x (Tensor) – The matrix to be orthogonalized.

Examples

code:

x = th.tensor([[1, 2.], [3, 4], [5, 6]])
y = orth(x)
print(x)
print(y)
print((y[0, :] * y[1, :] * y[2, :]).sum())
print((y[:, 0] * y[:, 1]).sum())

result:

tensor([[1., 2.],
        [3., 4.],
        [5., 6.]])
tensor([[-0.2298,  0.8835],
        [-0.5247,  0.2408],
        [-0.8196, -0.4019]])
tensor(-0.1844)
tensor(-1.7881e-07)

Module contents