(ph+JSrS/rSSKrSSKJr SSKJr SSKJ r SSKJ r SS KJ r SS KJ r \ R\ R\ R\ R S .r\ R$\ R&\ R(\ R*S .rS S S.r"SS5rSSjrg)a Python wrapper for PROPACK -------------------------- PROPACK is a collection of Fortran routines for iterative computation of partial SVDs of large matrices or linear operators. Based on BSD licensed pypropack project: http://github.com/jakevdp/pypropack Author: Jake Vanderplas PROPACK source is BSD licensed, and available at http://soi.stanford.edu/~rmunk/PROPACK/ _svdpN)aslinearoperator) LinAlgError) _spropack) _dpropack) _cpropack) _zpropack)fdFDLS)LMSMcD\rSrSrSrSrSr\S5r\S5r Sr g) _AProd2z| Wrapper class for linear operator The call signature of the __call__ method matches the callback of the PROPACK routines. c[U5Ulg![a' [[R"U55Ulgf=fN)rA TypeErrornpasarray)selfrs L/var/www/html/venv/lib/python3.13/site-packages/scipy/sparse/linalg/_svdp.py__init___AProd.__init__9s6 5%a(DF 5%bjjm4DF 5s.AAcUS:XaURRU5USS&gURRU5USS&g)Nn)rmatvecrmatvec)rtransamr!xysparmiparms r__call___AProd.__call__?s5 S=66==#AaD66>>!$AaDc.URR$r)rshapers rr. _AProd.shapeEsvv||r,cURR$![aS URR[R "URR S55Rs$f=f)Nr)rdtypeAttributeErrorr"rzerosr.r/s rr2 _AProd.dtypeIsU B66<<  B66==$&&,,q/!:;AA A BsAA54A5)rN) __name__ __module__ __qualname____firstlineno____doc__rr*propertyr.r2__static_attributes__r,rrr2s; 5 % BBr,rc Uc [S5eUR5nUS;a [S5eU(dUS:Xa [S5e[U5nURRn[ Un[ UnURunnUS :dU[UU5:a [S 5eUcS U-nUcS n[US -US -U5nXA:a[S USUS35eU(aSOSnU(aSOSn[R"UUS -4SUS9n[R"UU4SUS9nUcfUR!US9USS2S4'[R"[R"SUS95(a!USS2S4==SUR!US9-- ss'O UUSS2S4'U c4[R""[R$"U5R&5n U c#[R$"U5R&S-n U(a][R("XX4UR+5S9nUcXA- nU[UU- UU5:a [S5eUS:a [S5eO%[R("XU 4UR+5S9n[R("[-[/U 55[-[/U554SS9nSnU(dU(aFUU-SU--SU-U--S-[1SU-U-SU--S-U[1UU5-5-n S U-n!O5UU-SU--S!U-U--S-[1UU-SU-S-5-n S!U-S -n![R"U UR+5S9n"[R"U![R2S9n#[R"S UR+5S9n$[R"S [R2S9n%UR55(a$[R"UU-S"U--US9n&U"U&U#4n'OU"U#4n'U(a*U"[6UUUUUUUUUUUU / U'QUPUPU$PU%P76unn(n)nn*OU"UUUUUUUUU / U'QUPUPU$PU%P76unn(n)nn*U*S:a[9S#U*S$35eU*S:a[9S%US&US'35eUSS2SU24U(USS2SU24R;5R<U)4$![a [R"[R"SUS95(a%[R"[5RnO$[R"[5Rn[ Un[ UnGNf=f![a [SU35ef=f)(a4 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>rrz#`which` must be either 'LM' or 'SM'rz#`which`='SM' requires irl_mode=Truer)r2rz.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'r!r )orderr2)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) ValueErrorupperrr2char_lansvd_irl_dict _lansvd_dictKeyErrorr iscomplexobjemptycomplexfloatr.minr4uniformsqrtfinfoepsarraylowerintboolmaxint32isupper_which_converterrconjT)+rkwhichirl_modekmax compute_u compute_vv0 full_outputtoldeltaetaanormcgselr min_relgapshiftsmaxiterrngaprodtyp lansvd_irllansvdr%r!jobujobvuvdoptionioption blocksizelworkliworkworkiworkdparmr)zworkworkssigmabndinfos+ rrrQsr {UVV KKME L >??  >?? 1IE ++  C #%c* c" ;;DAq A1s1ay=IJJ |!t q1ua!eT "D x gaS +, , 3D3D !TAXc5A !T#S1A  z++1+%!Q$ ??288AS1 2 2 adGrCKKQK// /G :AadG  } ))* {hhsm4'((E:#))+N >XF s4&=!Q' '<= = aZ34 4((E.ciikBhhDIDI7sCGIIA$4,q03 dF4K!D& 1 $ c!Qi 4!!4A$4,q03q1uafqj3II4! 88E -D HHV288 ,E HHQciik *E HHQbhh 'E {{}}QAS1eU"e !+,rs  )0$                              BB>15JK8<;?d3r,