Ei)0SrSS/rSSKrSSKJrJr SSKJrJr SS\S\ S \ S-S \S-S \4 S jjr SS\S\ S-S \ S-S \S-S \ \\\44 S jjr SS\S\ S-S \ S-S \S-S \ \\\44 Sjjr SS\S\ S-S\S \ S \ \\\44 Sjjrg)zBImplement various linear algebra algorithms for low rank matrices. svd_lowrank pca_lowrankN) _linalg_utilsTensor)handle_torch_functionhas_torch_functionAqniterMreturncUcSOUnUR5(d[R"U5O URn[Rn[ R "URSXURS9nU"X5nUb Xu"X65- n[ RRU5Rn[U5Hn U"URU5nUbXu"URU5- n[ RRU5RnU"X5nUb Xu"X85- n[ RRU5RnM U$)aReturn tensor :math:`Q` with :math:`q` orthonormal columns such that :math:`Q Q^H A` approximates :math:`A`. If :math:`M` is specified, then :math:`Q` is such that :math:`Q Q^H (A - M)` approximates :math:`A - M`. without instantiating any tensors of the size of :math:`A` or :math:`M`. .. note:: The implementation is based on the Algorithm 4.4 from Halko et al., 2009. .. note:: For an adequate approximation of a k-rank matrix :math:`A`, where k is not known in advance but could be estimated, the number of :math:`Q` columns, q, can be chosen according to the following criteria: in general, :math:`k <= q <= min(2*k, m, n)`. For large low-rank matrices, take :math:`q = k + 5..10`. If k is relatively small compared to :math:`min(m, n)`, choosing :math:`q = k + 0..2` may be sufficient. .. note:: To obtain repeatable results, reset the seed for the pseudorandom number generator Args:: A (Tensor): the input tensor of size :math:`(*, m, n)` q (int): the dimension of subspace spanned by :math:`Q` columns. niter (int, optional): the number of subspace iterations to conduct; ``niter`` must be a nonnegative integer. In most cases, the default value 2 is more than enough. M (Tensor, optional): the input tensor's mean of size :math:`(*, m, n)`. References:: - Nathan Halko, Per-Gunnar Martinsson, and Joel Tropp, Finding structure with randomness: probabilistic algorithms for constructing approximate matrix decompositions, arXiv:0909.4061 [math.NA; math.PR], 2009 (available at `arXiv `_). dtypedevice) is_complex_utilsget_floating_dtypermatmultorchrandnshaperlinalgqrQrangemH) r r r r rrRXr_s K/home/mande/repo/quber/.venv/lib/python3.13/site-packages/torch/_lowrank.pyget_approximate_basisr$ sbAEE01 F % %a (AGGE ]]F AGGBKAA q A} q  A 5\ 144O =F144O#A LLOOA   1L =F1L A LLOOA   Hc .[RR5(diX4n[[ [ U55R [R[ S545(d [U5(a[[X@XUS9$[XX#S9$)a*Return the singular value decomposition ``(U, S, V)`` of a matrix, batches of matrices, or a sparse matrix :math:`A` such that :math:`A \approx U \operatorname{diag}(S) V^{\text{H}}`. In case :math:`M` is given, then SVD is computed for the matrix :math:`A - 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 matrix :math:`A`, where k is not known in advance but could be estimated, the number of :math:`Q` columns, q, can be chosen according to the following criteria: in general, :math:`k <= q <= min(2*k, m, n)`. For large low-rank matrices, take :math:`q = k + 5..10`. If k is relatively small compared to :math:`min(m, n)`, choosing :math:`q = 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 implementation :func:`torch.linalg.svd` for dense matrices due to its 10x higher performance characteristics. The low-rank SVD will be useful for huge sparse matrices that :func:`torch.linalg.svd` cannot handle. Args:: A (Tensor): the input tensor of size :math:`(*, 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 :math:`(*, 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 at `arXiv `_). 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