torch.svd_lowrank — PyTorch 2.7 documentation (original) (raw)
torch.svd_lowrank(A, q=6, niter=2, M=None)[source][source]¶
Return the singular value decomposition (U, S, V) of a matrix, batches of matrices, or a sparse matrix AA such thatA≈Udiag(S)VHA \approx U \operatorname{diag}(S) V^{\text{H}}. In case MM is given, then SVD is computed for the matrix A−MA - M.
Note
The implementation is based on the Algorithm 5.1 from Halko et al., 2009.
Note
For an adequate approximation of a k-rank matrixAA, where k is not known in advance but could be estimated, the number of QQ columns, q, can be choosen according to the following criteria: in general,k<=q<=min(2∗k,m,n)k <= q <= min(2*k, m, n). For large low-rank matrices, take q=k+5..10q = k + 5..10. If k is relatively small compared to min(m,n)min(m, n), choosingq=k+0..2q = k + 0..2 may be sufficient.
Note
This is a randomized method. To obtain repeatable results, set the seed for the pseudorandom number generator
Note
In general, use the full-rank SVD implementationtorch.linalg.svd() for dense matrices due to its 10x higher performance characteristics. The low-rank SVD will be useful for huge sparse matrices thattorch.linalg.svd() cannot handle.
Args::
A (Tensor): the input tensor of size (∗,m,n)(*, 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
(∗,m,n)(*, m, 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 atarXiv).
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