+ &j)zRtRR.t^RIt^RIHtHt^RIHtHtRRRllt RRR llt RR R llt RR R llt R#)zBImplement various linear algebra algorithms for low rank matrices. svd_lowrank pca_lowrankN) _linalg_utilsTensor)handle_torch_functionhas_torch_functionc pV^8dQhR\R\R\R,R\R,R\/#)AqniterNMreturn)rint)formats"f/Users/jameslopez/projects/CWCArchive/cwc-podcast/.venv/lib/python3.14/site-packages/torch/_lowrank.py __annotate__r sIG G  G  G  :G } G  G cVf^MTpVP4'g\P!V4M VPp\Pp\ P !VPR,WVPR7pV!W4pVeWu!W64, p\ PPV4Pp\V4Fp V!VPV4pVeWu!VPV4, p\ PPV4PpV!W4pVeWu!W84, p\ PPV4PpK V#)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 &&&& rget_approximate_basisr( sbAEE01 F % %a (AGGE ]]F AGGBKAA q A} q  A 5\ 144O =F144O#A LLOOA   1L =F1L A LLOOA   Hrc V^8dQhR\R\R,R\R,R\R,R\\\\3,/#r r r Nr r rrrtuple)rs"rrrUsR=2=2 =2 Tz=2 :=2} =2  666 !" =2rc @\PP4'goW3p\\ \ V44P \P\ R434'g%\V4'd\\W@WVR7#\WW#R7#)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 `_). N)r r r ) rjit is_scriptingsetmaptypeissubsetrrrr _svd_lowrank)r r r r tensor_opss&&&& rrrUs~j 99 ! ! # #V 3tZ()22 \\4: &   ,,(Za  e 11rc V^8dQhR\R\R,R\R,R\R,R\\\\3,/#r*r+)rs"rrrsR  Tz :}   666 !" rcVf^MTpVPRRwrE\PpVe VPVP 44pWE8dVP pVe VP p\ WW#R7pV!VP V4pVeW!VP V4, p\PPVRR7wrp V P p VPV 4p WE8dYrWV 3#)Nr r F) full_matrices) rrr broadcast_tosizer$r(rr svd) r r r r mnrr"BUSVhVs &&&& rr4r4sYAA 7723`_). )r rFr Nzq(=z>) must be non-negative integer and not greater than min(m, n)=zniter(=z) must be non-negative integerr8z8pca_lowrank input is expected to be 2-dimensional tensor)dimrT)rIkeepdimr:)r:)rr.r/r2rrrrrmin ValueErrorrrr4 is_sparselensparsesumindiceszerosrrsparse_coo_tensorvaluesonesmmmTmean)r r rFr r>r?rccolumn_indicesrQC_t ones_m1_tr Cs&&&& rrrs D 99 ! ! # # 7%,, &+=qd+C+C(aT1& WWRS\FQy 1L1fc!i!RSVWXS\R] ^   QJ75')GHII  % %a (E A66  qww<1 WX X LL  QE  *Q .Q++   &&!((   $ %% XXZ!QuXX JJqwws|q!f4E((S LLOOC + . .A33 FFudF +AE1T::r)r N)r N)NTr ) __doc____all__rrrrtorch.overridesrrr(rr4rrrrcs<H - ( 1EG T=2@Dn;n;r