Symmetric matrix - full SVD

Implementation taken from https://arxiv.org/abs/1903.09650 which follows derivation given in https://people.maths.ox.ac.uk/gilesm/files/NA-08-01.pdf

class linalg.svd_symeig.SVDSYMEIG

static backward(self, dU, dS, dV)

Defines a formula for differentiating the operation.

This function is to be overridden by all subclasses.

It must accept a context ctx as the first argument, followed by as many outputs did forward() return, 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.

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(self, A)

Parameters

A (torch.tensor) – square symmetric matrix

Returns

left singular vectors U, singular values S, and right singular vectors V

Return type

torch.tensor, torch.tensor, torch.tensor

Computes SVD of a matrix M, where M is symmetric \(M=M^T\), through symmetric decomposition \(M= UDU^T\).