bip( dgZddlZddlmZddlmZddlmZejejejejdZ ejejej ej"dZdddZGd d Z d d Zy) _svdpN)aslinearoperator) LinAlgError)_propack)fdFD)LMSMc<eZdZdZdZdZedZedZy)_AProdz Wrapper class for linear operator The call signature of the __call__ method matches the callback of the PROPACK routines. c t||_y#t$r&ttj||_YywxYwN)rA TypeErrornpasarray)selfrs T/home/cdr/jupyterlab/.venv/lib/python3.12/site-packages/scipy/sparse/linalg/_svdp.py__init__z_AProd.__init__(s6 5%a(DF 5%bjjm4DF 5s,AAc|dk(r|jj||ddy|jj||ddy)Nr)rmatvecrmatvec)rtransamnxys r__call__z_AProd.__call__.s5 Q;66==#AaD66>>!$AaDc.|jjSr)rshapers rr$z _AProd.shape4svv||r"c |jjS#t$rR|jjt j |jj djcYSwxYw)Nr)rdtypeAttributeErrorrrzerosr$r%s rr'z _AProd.dtype8sU B66<<  B66==$&&,,q/!:;AA A BsAA32A3N) __name__ __module__ __qualname____doc__rr!propertyr$r'r"rrr!s; 5 % BBr"rcB | td|j}|dvr td|s|dk(r tdt|}|jj} t |}t |}|j\}}|d ks|t||kDr td |d |z}|d}t|d z|d z|}||krtd|d|d|rd nd}|rd nd}tj||d zfd|}tj||fd|}tj|d|j}tj|d|j}|h|j||dddf<tjtjd|r/|dddfxxd|j|zz cc<n ||dddf<| 2tj tj"|j$} | "tj"|j$dz} |r^tj&| | | |f|j}|||z }|t||z ||kDr td|dkr3tdtj&| | | f|j}tj&t)t+| t)t+|fd} d}!|s|rH||zd|dzzzd|zzdz}"|"t-d |dzzd|zzdz|!t-||zz }"d!|z}#n5||zd|zzd|dzzzdzt-||zd|zdzz}"d|zdz}#tj|"|j}$tj|#tj.}%tjd |j}&tjd tj.}'|j1r#tj||z|z|}(|$|(|%f})n|$|%f})|j3dtj4tj6j,dtj8"}*|r(|t:||||||||| |||||g|)|| |&|'|*}+n|||||||| |||||g |)|| |&|'|*}+|+dkDrt=d#|+d$|+dkrt=d%|d&|d'|ddd|f||ddd|fj?j@|fS#t$rEtjtjd|rd }nd }t |}t |}YwxYw#t$rtd|wxYw)(ax Compute the singular value decomposition of a linear operator using PROPACK Parameters ---------- A : array_like, sparse matrix, or LinearOperator Operator for which SVD will be computed. If `A` is a LinearOperator object, it must define both ``matvec`` and ``rmatvec`` methods. k : int Number of singular values/vectors to compute which : {"LM", "SM"} Which singular triplets to compute: - 'LM': compute triplets corresponding to the `k` largest singular values - 'SM': compute triplets corresponding to the `k` smallest singular values `which='SM'` requires `irl_mode=True`. Computes largest singular values by default. irl_mode : bool, optional If `True`, then compute SVD using IRL (implicitly restarted Lanczos) mode. Default is `True`. kmax : int, optional Maximal number of iterations / maximal dimension of the Krylov subspace. Default is ``10 * k``. compute_u : bool, optional If `True` (default) then compute left singular vectors, `u`. compute_v : bool, optional If `True` (default) then compute right singular vectors, `v`. tol : float, optional The desired relative accuracy for computed singular values. If not specified, it will be set based on machine precision. v0 : array_like, optional Starting vector for iterations: must be of length ``A.shape[0]``. If not specified, PROPACK will generate a starting vector. full_output : bool, optional If `True`, then return sigma_bound. Default is `False`. delta : float, optional Level of orthogonality to maintain between Lanczos vectors. Default is set based on machine precision. eta : float, optional Orthogonality cutoff. During reorthogonalization, vectors with component larger than `eta` along the Lanczos vector will be purged. Default is set based on machine precision. anorm : float, optional Estimate of ``||A||``. Default is ``0``. cgs : bool, optional If `True`, reorthogonalization is done using classical Gram-Schmidt. If `False` (default), it is done using modified Gram-Schmidt. elr : bool, optional If `True` (default), then extended local orthogonality is enforced when obtaining singular vectors. min_relgap : float, optional The smallest relative gap allowed between any shift in IRL mode. Default is ``0.001``. Accessed only if ``irl_mode=True``. shifts : int, optional Number of shifts per restart in IRL mode. Default is determined to satisfy ``k <= min(kmax-shifts, m, n)``. Must be >= 0, but choosing 0 might lead to performance degradation. Accessed only if ``irl_mode=True``. maxiter : int, optional Maximum number of restarts in IRL mode. Default is ``1000``. Accessed only if ``irl_mode=True``. rng : `numpy.random.Generator`, optional Pseudorandom number generator state. When `rng` is None, a new `numpy.random.Generator` is created using entropy from the operating system. Types other than `numpy.random.Generator` are passed to `numpy.random.default_rng` to instantiate a ``Generator``. Returns ------- u : ndarray The `k` largest (``which="LM"``) or smallest (``which="SM"``) left singular vectors, ``shape == (A.shape[0], 3)``, returned only if ``compute_u=True``. sigma : ndarray The top `k` singular values, ``shape == (k,)`` vt : ndarray The `k` largest (``which="LM"``) or smallest (``which="SM"``) right singular vectors, ``shape == (3, A.shape[1])``, returned only if ``compute_v=True``. sigma_bound : ndarray the error bounds on the singular values sigma, returned only if ``full_output=True``. Nz:`rng` must be a normalized numpy.random.Generator instance>r r z#`which` must be either 'LM' or 'SM'r z#`which`='SM' requires irl_mode=Truer)r'r r rz.k must be positive and not greater than m or n iz3kmax must be greater than or equal to k, but kmax (z) < k ()r )orderr')sizey?zv0 must be of length g?z0shifts must satisfy k <= min(kmax-shifts, m, n)!zshifts must be >= 0!i  )lowhighr4r'z#An invariant subspace of dimension z was found.zk=z0 singular triplets did not converge within kmax=z iterations)! 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QtQwY4'!+RAq \::4A$47*Q.QUAdFQJ1GG4! 88E -D HHV288 ,E HHQciik *E HHQbhh 'E {{}QS1eU"e  "(();)?)?"#2996I*5141fa#E3<49<;B<"<$)<+0<2;< dD!Q4eQsAII%I'.I05I7<I>GI ax1${ CE E 6 &' ' QU8UAa!eHMMO--s 22w # ??288AS1 2CC%c* c"#Z :4QC89 9 :s!T5 V5A VVV)r TNTTNFrNNrFTgMb`?NNN)__all__numpyrscipy.sparse.linalgr scipy.linalgrrslansvddlansvdclansvdzlansvdrC slansvd_irl dlansvd_irl clansvd_irl zlansvd_irlrBrWrrr/r"rrs )0$                             BB>15JK8<;?c3r"