VpfZ"dZddlmZddlmZddlZddlZddlmZddl Z ddl m Z ddl m Z ddl mZeje jd  dddZeje jd  dddZdS) uA JIT-compatible library for QDWH-based singular value decomposition. QDWH is short for QR-based dynamically weighted Halley iteration. The Halley iteration implemented through QR decompositions is numerically stable and does not require solving a linear system involving the iteration matrix or computing its inversion. This is desirable for multicore and heterogeneous computing systems. References: Nakatsukasa, Yuji, and Nicholas J. Higham. "Stable and efficient spectral divide and conquer algorithms for the symmetric eigenvalue decomposition and the SVD." SIAM Journal on Scientific Computing 35, no. 3 (2013): A1325-A1349. https://epubs.siam.org/doi/abs/10.1137/120876605 Nakatsukasa, Yuji, Zhaojun Bai, and François Gygi. "Optimizing Halley's iteration for computing the matrix polar decomposition." SIAM Journal on Matrix Analysis and Applications 31, no. 5 (2010): 2700-2720. https://epubs.siam.org/doi/abs/10.1137/090774999 ) annotations)SequenceN)Any)lax)core))static_argnumsar hermitianbool compute_uvmax_iterationsintsubset_by_indextuple[int, int] | NonereturnAny | Sequence[Any]ctj|||\}}}}tj||d\}} t j| d} t j| d} | | } |s| S|dd| f} || z} dtt j|j j }| d |j d |z| d zk}d }fd }tj ||| |f\} }| | | fS)abSingular value decomposition for m x n matrix and m >= n. Args: a: A matrix of shape `m x n` with `m >= n`. hermitian: True if `a` is Hermitian. compute_uv: Whether to also compute `u` and `v` in addition to `s`. max_iterations: The predefined maximum number of iterations of QDWH. Returns: A 3-tuple (`u`, `s`, `v`), where `u` is a unitary matrix of shape `m x n`, `s` is vector of length `n` containing the singular values in the descending order, `v` is a unitary matrix of shape `n x n`, and `a = (u * s) @ v.T.conj()`. For `compute_uv=False`, only `s` is returned. ) is_hermitianrF)rsort_eigenvaluesgT) descendingNctj|d\}}|tjtjtj|dkddz}|S)NF full_matricesrr)rlinalgqrjnpdiagwhere)u_outrs P/var/www/html/nettyfy-visnx/env/lib/python3.11/site-packages/jax/_src/lax/svd.pycorrect_rank_deficiencyz;_svd_tall_and_square_input..correct_rank_deficiencyesQz}}U%}88HE1 CHSYsx{{a'7B??@@ @E Lrrrc|dS)Nrargss r&z,_svd_tall_and_square_input..ls Qr(c*|ddfS)NrFr*)r,r's r&r-z,_svd_tall_and_square_input..ms00a995Ar() rrqdwheighr!maximumargsortfloatfinfodtypeepsshape while_loop)r rrrru_ph_vssort_idxs_outv_outr$r6 do_correctioncond_fbody_fr's @r&_svd_tall_and_square_inputrD1s>.i!,#q!Q 5   $!Q  k!S![t , , ,( H+%  L AAAxK.% +% ci  $%%#)qwqzC/%(::-  & A A A A& ^FFUM,B C C(%  r()rr r r TF rctjt|d}tjt|d}tjt|d}tjt|d}|t |dkrt dt j|dt j|d f}|d|d krt d |ddkrt d |j\}}||kr|n|}|d |krt d |r|d|fkrt d ||d z ||dz f}|j\}}d} ||kr%|j }|j\}}d} d} |rQtj |d\} } | ddd|f} | dd|df}| d|ddf}d} n/|d|zkr&tj |d\} }d} |s?tjd5t!|||||cdddS#1swxYwYtjd5t!|||||\| r| zdddn #1swxYwY|rt#j|ft#jt#j|}d}fd}tj|||f\}| rj fSj fS)a#Singular value decomposition. Args: a: A matrix of shape `m x n`. full_matrices: If True, `u` and `vh` have the shapes `m x m` and `n x n`, respectively. If False, the shapes are `m x k` and `k x n`, respectively, where `k = min(m, n)`. compute_uv: Whether to also compute `u` and `v` in addition to `s`. hermitian: True if `a` is Hermitian. max_iterations: The predefined maximum number of iterations of QDWH. subset_by_index: Optional 2-tuple [start, end] indicating the range of indices of singular components to compute. For example, if ``subset_by_index`` = [0,2], then ``svd`` computes the two largest singular values (and their singular vectors if `compute_uv` is true. Returns: A 3-tuple (`u`, `s`, `vh`), where `u` and `vh` are unitary matrices, `s` is vector of length `k` containing the singular values in the non-increasing order, and `k = min(m, n)`. The shapes of `u` and `vh` depend on the value of `full_matrices`. For `compute_uv=False`, only `s` is returned. zbThe `full_matrices` argument must be statically specified to use `svd` within JAX transformations.z_The `compute_uv` argument must be statically specified to use `svd` within JAX transformations.z^The `hermitian` argument must be statically specified to use `svd` within JAX transformations.zcThe `max_iterations` argument must be statically specified to use `svd` within JAX transformations.Nr z*subset_by_index must be a tuple of size 2.rrz)Got empty index range in subset_by_index.z0Indices in subset_by_index must be non-negative.z0Index in subset_by_index[1] exceeds matrix size.z8full_matrices and subset_by_index cannot be both be set.FTrgffffff?float32c6tj|dS)Nr)r! logical_notr+s r&r-zsvd..sQ00r(ctjdtjtjtjtjtjtjfS)NT)r!array full_likenan)r,r?r$r@s r&r-zsvd..sH ioo mE37## mE37## mE37## r()rconcrete_or_errorrrlen ValueErroroperatorindexr7Tconjrrr jaxdefault_matmul_precisionrDr!hstackallisfiniter8)r rrrrrmnrankis_flipreduce_to_squareq_fulla_fullq u_out_null is_finiterBrCr;r?r$r@s @@@r&svdreqsb>( M;<<-% J;<<*$ ;)) ;.  ?q  C D DD q)**q)**Oq_Q/// B C CCqA I J JJ 7DAqA111DqD  I J JJQI55  D   oa00$9K2KLO $!Q 'UU  A 7DAqG Z]]1D]99NFFqqq"1"u A122Jrr111u A 4!8|| Z]]1E] 2 2da  %i 0 0 ' Y NO  #I..4 9j./E5%%ie , Jz* + +Egcl1oo&&) 0 0&      & > fy%6!UE5 * 5%',,.. ))   ''s$3III2JJ!$J!)N) r rrrrrrrrrrr)TFrFN)r rrrrrrrrrrrrr)__doc__ __future__rcollections.abcr functoolsrRtypingrrVrjax._srcr jax.numpynumpyr!partialjitrDrer*r(r&rps4*#"""""$$$$$$ 37<888 /3 ====98=~37?;;;.2 A(A(A(A(<;A(A(A(r(