torch.svd_lowrank

torch.svd_lowrank(A, q=6, niter=2, M=None)

Return the singular value decomposition (U, S, V) of a matrix, batches of matrices, or a sparse matrix $A$ such that $A \approx U diag(S) V^T$. In case $M$ is given, then SVD is computed for the matrix $A - M$.

Note

The implementation is based on the Algorithm 5.1 from Halko et al, 2009.

Note

To obtain repeatable results, reset the seed for the pseudorandom number generator

Note

The input is assumed to be a low-rank matrix.

Note

In general, use the full-rank SVD implementation torch.linalg.svd() for dense matrices due to its 10-fold higher performance characteristics. The low-rank SVD will be useful for huge sparse matrices that torch.linalg.svd() cannot handle.

Args::

A (Tensor): the input tensor of size $(*, m, n)$

q (int, optional): a slightly overestimated rank of A.

niter (int, optional): the number of subspace iterations to

conduct; niter must be a nonnegative integer, and defaults to 2

M (Tensor, optional): the input tensor’s mean of size

$(*, 1, n)$, which will be broadcasted to the size of A in this function.

References::

• Nathan Halko, Per-Gunnar Martinsson, and Joel Tropp, Finding structure with randomness: probabilistic algorithms for constructing approximate matrix decompositions, arXiv:0909.4061 [math.NA; math.PR], 2009 (available at arXiv).

Return type

Tuple[Tensor, Tensor, Tensor]