U Gv f=-@sdZdgZddlZddlmZddlmZddlm Z ddl m Z dd l m Z dd l m Z dd l mZe je je jejd Ze je je jejd Zd ddZGdddZdddZdS)a Python wrapper for PROPACK -------------------------- PROPACK is a collection of Fortran routines for iterative computation of partial SVDs of large matrices or linear operators. Based on BSD licensed pypropack project: http://github.com/jakevdp/pypropack Author: Jake Vanderplas PROPACK source is BSD licensed, and available at http://soi.stanford.edu/~rmunk/PROPACK/ _svdpN)check_random_state)aslinearoperator) LinAlgError) _spropack) _dpropack) _cpropack) _zpropack)fdFDLS)LMSMc@s8eZdZdZddZddZeddZedd Zd S) _AProdz Wrapper class for linear operator The call signature of the __call__ method matches the callback of the PROPACK routines. cCs8zt||_Wn$tk r2tt||_YnXdSN)rA TypeErrornpZasarray)selfrr=/tmp/pip-unpacked-wheel-96ln3f52/scipy/sparse/linalg/_svdp.py__init__:sz_AProd.__init__cCs6|dkr|j||dd<n|j||dd<dS)Nn)rmatvecZrmatvec)rZtransamrxyZsparmiparmrrr__call__@sz_AProd.__call__cCs|jjSr)rshaperrrrr#Fsz _AProd.shapec Cs@z |jjWStk r:|jt|jjdjYSXdS)Nr)rdtypeAttributeErrorrrzerosr#r$rrrr%Js z _AProd.dtypeN) __name__ __module__ __qualname____doc__rr"propertyr#r%rrrrr3s rrTFMb`?c+ Cst|r"tdjdkr"tdt|}|}|dkrBtd|sV|dkrVtdt|}|j j }zt |}t |}WnRt k rttjd|drt tj }n t tj }t |}t |}YnX|j\}}|d ks|t||krtd |d krd |}|d krd }t|d |d |}||krJtd|d|d|rTdnd}|rbdnd}tj||d fd|d}tj||fd|d}|d kr|j|d|d d df<ttjd|dr*|d d dfd|j|d7<n:z||d d df<Wn$tk r(td|YnX| d krFtt|j} | d kr`t|jd} |rtj| | | |f|d}|d kr||}|t||||krtdn|dkrtdntj| | | f|d}tjtt| tt|fdd}d}|s|rb||d|d||dtd ||d|d|t||} d|}!nB||d|d!||dt||d|d} d!|d }!tj| |d}"tj|!tjd}#tjd |d}$tjd tjd}%|rtj||d"||d}&|"|&|#f}'n|"|#f}'|rd|t|||||||||||| f |'|||$|%f\}}(})}}*n2|||||||||| f |'|||$|%f\}}(})}}*|*dkrt d#|*d$n |*dkrt d%|d&|d'|d d d |f|(|d d d |f!j"|)fS)(a; 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 singluar 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 degredation. 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``. random_state : {None, int, `numpy.random.Generator`, `numpy.random.RandomState`}, optional Pseudorandom number generator state used to generate resamples. If `random_state` is ``None`` (or `np.random`), the `numpy.random.RandomState` singleton is used. If `random_state` is an int, a new ``RandomState`` instance is used, seeded with `random_state`. If `random_state` is already a ``Generator`` or ``RandomState`` instance then that instance is used. 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``. rzBPROPACK complex-valued SVD methods not available for 32-bit builds>rrz#`which` must be either 'LM' or 'SM'rz#`which`='SM' requires irl_mode=True)r%rz.k must be positive and not greater than m or nN iz3kmax must be greater than or equal to k, but kmax (z) < k ()r rr )orderr%)sizey?zv0 must be of length g?z0shifts must satisfy k <= min(kmax-shifts, m, n)!zshifts must be >= 0!i  z#An invariant subspace of dimension z was found.zk=z0 singular triplets did not converge within kmax=z iterations)#rZ iscomplexobjZintpitemsizerrupper ValueErrorrr%char_lansvd_irl_dict _lansvd_dictKeyErroremptycomplexfloatr#minr'uniformsqrtZfinfoZepsarraylowerintboolmaxZint32isupper_which_converterrZconjT)+rkwhichZirl_modeZkmaxZ compute_uZ compute_vZv0Z full_outputZtoldeltaetaZanormZcgsZelrZ min_relgapZshiftsmaxiterZ random_stateZaprodtypZ lansvd_irlZlansvdrrZjobuZjobvuvZdoptionZioption blocksizeZlworkZliworkZworkZiworkZdparmr!ZzworkZworkssigmaZbndinforrrrRsa        &      "     6       )rTNTTNFrNNrFTr-NNN)r+__all__ZnumpyrZscipy._lib._utilrZscipy.sparse.linalgrZ scipy.linalgrZ_propackrrr r ZslansvdZdlansvdZclansvdZzlansvdr@Z slansvd_irlZ dlansvd_irlZ clansvd_irlZ zlansvd_irlr?rNrrrrrrsN