a j-@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. cCs6zt||_Wn"ty0tt||_Yn0dSN)rA TypeErrornpZasarray)selfrr?E:\soccer\ml_env\Lib\site-packages\scipy/sparse/linalg/_svdp.py__init__:s z_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 |jjWSty8|jt|jjdjYS0dS)Nr)rdtypeAttributeErrorrrzerosr#r$rrrr%Js  z _AProd.dtypeN) __name__ __module__ __qualname____doc__rr"propertyr#r%rrrrr3s rrTFMb`?c+ Cst|}|}|dvr td|s4|dkr4tdt|}|jj}zt|}t|}WnPtyt t j d|drt t j}n t t j}t|}t|}Yn0|j\}}|dks|t||krtd|d urd |}|d urd }t|d|d|}||kr"td |d |d|r,dnd}|r:dnd}t j||dfd|d}t j||fd|d}|d ur|j|d|d d df<t t j d|dr|d d dfd|j|d7<n8z||d d df<Wn"tytd|Yn0| d urt t |j} | d ur6t |jd} |rt j| | | |f|d}|d urh||}|t||||krtdn|dkrtdnt j| | | f|d}t jtt| tt|fdd}d}|s|r8||d|d||dtd||d|d|t||} d|}!nB||d|d ||dt||d|d} d |d}!t j | |d}"t j |!t jd}#t j d|d}$t j dt jd}%|rt j ||d!||d}&|"|&|#f}'n|"|#f}'|rB|t|||||||||||| g |'|||$|%R\}}(})}}*n:|||||||||| g |'|||$|%R\}}(})}}*|*dkrtd"|*d#n |*dkrtd$|d%|d&|d d d |f|(|d d d |fj|)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 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``. 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``. >rrz#`which` must be either 'LM' or 'SM'rz#`which`='SM' requires irl_mode=Truer)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) rupper ValueErrorrr%char_lansvd_irl_dict _lansvd_dictKeyErrorrZ iscomplexobjemptycomplexfloatr#minr'uniformsqrtZfinfoepsarraylowerintboolmaxZint32isupper_which_converterrZconjT)+rkwhichZirl_modeZkmaxZ compute_uZ compute_vZv0Z full_outputZtoldeltaetaZanormZcgsZelrZ min_relgapZshiftsmaxiterZ random_stateZaprodtypZ lansvd_irlZlansvdrrZjobuZjobvuvZdoptionZioption blocksizeZlworkZliworkZworkZiworkZdparmr!ZzworkZworkssigmabndinforrrrRs_       &      "     6        )rTNTTNFrNNrFTr-NNN)r+__all__numpyrZscipy._lib._utilrZscipy.sparse.linalgrZ scipy.linalgrZ_propackrrr r ZslansvdZdlansvdZclansvdZzlansvdr?Z slansvd_irlZ dlansvd_irlZ clansvd_irlZ zlansvd_irlr>rNrrrrrrs8