ukiU)dZddlmZddlmZddlZddlZddlmZddl Z ddl m Z ddl m Z ddl mZdd l mZdd l mZdd l m Zdd lmZdd lmZddlmZej4e j6d d ddZej4e j6d d ddZdddZdddZej@ejBey)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)api)config)core)dtypes)lax)numpy)mlir)linalg)qdwh))static_argnumsctj|||\}}}}tj||d\}} t j | d} t j | d} | | } |s| S|dd| f} || z} dttj|jj}| d |jd |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_hermitianmax_iterationsF)subset_by_indexsort_eigenvaluesgT) descendingNctj|d\}}|tjtjtj|dk\ddz}|S)NF) full_matricesrr) lax_linalgqrjnpdiagwhere)u_outrs R/home/cdr/jupyterlab/.venv/lib/python3.12/site-packages/jax/_src/tpu/linalg/svd.pycorrect_rank_deficiencyz;_svd_tall_and_square_input..correct_rank_deficiencylsH}}U%8HE1 CHHSYYsxx{a'7B?@ @E Lrrrc |dS)Nrargss r$z,_svd_tall_and_square_input..ss Qr&c|ddfS)NrFr()r*r%s r$r+z,_svd_tall_and_square_input..ts0a95Ar&)tpu_qdwhrreighrmaximumargsortfloatr finfodtypeepsshaper while_loop)a hermitian compute_uvrru_ph_vssort_idxs_outv_outr"r4 do_correctioncond_fbody_fr%s @r$_svd_tall_and_square_inputrE8s.i,#q!Q 5 $!Q  kk!S![[t ,( H+%  L AxK.% +% fll177#''(#)qwwqzC/%(::- & A& ^^FFUM,B C(%  r&)rrrrctjt|d}tjt|d}tjt|d}tjt|d}|t |dk7r t dt j|dt j|d f}|d|d k\r t d |ddkr t d |j\}}||kr|n|}|d |kDr t d |r|d|fk7r t d ||d z ||dz f}|j\}}d} ||kr+|jj}|j\}}d} d} |rD||kDr?tj|dd\} } | ddd|f} | dd|df}| d|ddf}d} n%|d|zkDrtj|dd\} }d} |s.tjd5t|||||cdddStjd5t|||||\| r zddd|r||kDrt!j"ft!j$t!j&|}d}fd}t)j*|||f\}| rjjfSjjfS#1swYxYw#1swYxYw)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.Nrz*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.FT)pivotingrgffffff?float32c2tj|dS)Nr)r logical_notr)s r$r+zsvd..sQ0r&ctjdtjtjtjtjtjtjfS)NT)rarray full_likenpnan)r*r@r"rAs r$r+zsvd..sK iio mmE266" mmE266" mmE266" r&)rconcrete_or_errorboolintlen ValueErroroperatorindexr5Tconjrrrdefault_matmul_precisionrErhstackallisfiniter r6)r7rr9r8rrmnrankis_flipreduce_to_squareq_fulla_fullq u_out_null is_finiterCrDr<r@r"rAs @@@r$svdrhysS>(( M;<-%% J;<*$$ ;))) ;.  ?q C DD q)*q)*Oq_Q// B CCqA I JJ 77DAqA11DqD I JJQI5  D  oa00$9K2KLO $!Q 'U  A 77DAqGq1u]]1uDINFFq"1"u A12Jrr1u A 4!8| ]]1uE Bda   ( ( 3 ' Y NO &&y14 9j./E5%%ie q1u JJz* +Eggcll1o&) 0& & >> fy%6!UE5 5%'',,. ))   ''= s8K5&L5K>L ) algorithmcF|(|tjjk7r td|jdd}t j t|||}tt|D]}tj|}|r||\}} } | || gS||} | gS)Nz6The SVD algorithm parameter is not implemented on TPU.rr9r) r SvdAlgorithmDEFAULTNotImplementedErrorr5 functoolspartialrhrangerTrvmap) r7rr9rri batch_dimsfnr<ur>vhs r$_svd_tpurxsyJ,C,C,K,KK @ BBwws|* !% " Z !a "B!uHAq" q": 1A 3Jr&c|j\}|jdd\}}|A|tjjtjj fvr t d|dk(s|dk(r/tjtjd||||Stjtd|||||S)NrkzPOnly the POLAR (which is also DEFAULT on TPU) SVD algorithm is supported on TPU.rT)multiple_results)rr9rl) avals_inr5rrmrnPOLARror lower_fun _empty_svdrx) ctxoperandrr9rri operand_avalr^r_s r$_svd_tpu_lowering_rulers,,-,   BC $!Qy%%##1     !VqAv G4>>*//$ G #   94 8  !%  r&)N) r7rr8rRr9rRrrSrtuple[int, int] | NonereturnAny | Sequence[Any])TF N)r7rrrRr9rRr8rRrrSrrrr)"__doc__ __future__rcollections.abcrrprVtypingrr rOjax._srcrrrr r rjax._src.interpretersr jax._src.laxr rjax._src.tpu.linalgrr-rqjitrErhrxrregister_loweringsvd_pr(r&r$rsR*#$!&-0377<8 /3 = === = , =  =9=@377?;.2 A( A(A(A( A(  A( , A(A(<A(HJN0LP>z'')?@r&