+ A•üi ãó€^RItRRltR#)éNc óÜa€SfRp M\S4'dSp MV3Rlp Vf\P!V4MVP4p \PP V4p \V4'dW!V 4, p MWP V 4, p \PP V 4p WÓ8gWÔV ,8dV #V !V 4pVP4p\P!WÎ4p\V4EFFpV P4p\V4'd V!V4pMVP V4pV\P!VV4, pV VV,, p V VV,,p \PP V 4p Ve V!W WWÍ4WÓ8gWÔV ,8dV u#V !V 4pV'd=\P!V V, V4V, p\P!WÎ4pM(RV, p\P!WÎ4pVV,pVV,pWþ, pEKI \RV,4h)a$Solves a system of linear equations :math:`Ax=b` using conjugate gradient descent :cite:`hestenes1952methods` Parameters ---------- A: scipy.sparse.csr_matrix Square matrix b: numpy.ndarray Vector describing the right-hand side of the system x0: numpy.ndarray Initialization, if `None` then :code:`x=np.zeros_like(b)` atol: float Absolute tolerance. The loop terminates if the :math:`||r||` is smaller than `atol`, where :math:`r` denotes the residual of the current iterate. rtol: float Relative tolerance. The loop terminates if :math:`{||r||}/{||b||}` is smaller than `rtol`, where :math:`r` denotes the residual of the current iterate. callback: function Function :code:`callback(A, x, b, norm_b, r, norm_r)` called after each iteration, defaults to `None` M: function or scipy.sparse.csr_matrix Function that applies the preconditioner to a vector. Alternatively, `M` can be a matrix describing the precondioner. reorthogonalize: boolean Whether to apply reorthogonalization of the residuals after each update, defaults to `False` Returns ------- x: numpy.ndarray Solution of the system Example ------- >>> from pymatting import * >>> import numpy as np >>> A = np.array([[3.0, 1.0], [1.0, 2.0]]) >>> M = jacobi(A) >>> b = np.array([4.0, 3.0]) >>> cg(A, b, M=M) array([1., 1.]) có€V#©N©)Úxs&ÚQ/var/www/html/photoedit/myenv/lib/python3.14/site-packages/pymatting/solver/cg.pyÚ preconditionÚcg..precondition6s€ØˆHócó&<€SPV4#r)Údot)rÚMs&€rr r =sø€Ø—5‘5˜“8ˆOr gð?z@Conjugate gradient descent did not converge within %d iterations) ÚcallableÚnpÚ zeros_likeÚcopyÚlinalgÚnormr ÚinnerÚrangeÚ ValueError)ÚAÚbÚx0ÚatolÚrtolÚmaxiterÚcallbackrÚreorthogonalizer rÚnorm_bÚrÚnorm_rÚzÚpÚrzÚ iterationÚr_oldÚApÚalphaÚbetas&&&&&&&f& rÚcgr+sÔø€ð` ‚yó ô !ŠØ‰ õ ðšJŒ Š aÔ¨B¯G©G«I€Aä Y‰Y^‰^˜AÓ €Fä‡{‚{Ø !“H‰à —‘a“Lˆä Y‰Y^‰^˜AÓ €Fà „}˜¨¥Ô.؈áQ‹€AØ ‰‹€AÜ Š!‹€Bä˜7—^ˆ Ø—‘“ˆä A;Š;Ù1“‰Bà—‘q“ˆBà”R—X’X˜a “_Õ$ˆØ ˆUQYˆØ ˆURZˆä—‘—‘ Ó"ˆà Ò Ù Q˜1 aÔ 0à Œ=˜F¨F¥]Ô2ØŠHá ˜‹Oˆç Ü—8’8˜A I qÓ)¨BÕ.ˆDÜ—’˜!“‰Bà˜•8ˆDÜ—’˜!“ˆBØ BJˆDà ˆT ˆØ ‹ñ?$ôB ØJÈWÕTó ðr )NggH¯¼šò×z>i'NNF)Únumpyrr+rr rÚr-sðÛöqr