_-PhXdZddlZddlmZddlZddlmZddlmZddl m Z  d d Z dS) z!Conjugate Residual Krylov solver.N)warn)sparse)norm) make_systemh㈵>rrc t||||\}}} }} tjdd|#tdt |zdz}n|dkrt d||| zz } || z} | } tj| | }tj | }||g|dd<t|}|d krd }|d kr||z}n|d krtj |jrt|jj}nUt!|jtjr'ttj|j}nt d ||tj | z|zz}nA|dkr,tj|}t||z}||z}nt d||kr | | dfSd}|| z}tj| |}|| z}d} |}|tj| |z }| || zz } tj||r|dkr | ||zz} n||| zz } || z} || z}tj| |}||z }| |z} | | z } ||z}||z }|dz }tj| | }tj | }|||| || |d kr||z}nI|d kr)||tj | z|zz}n|dkrt| }||z}||kr | | dfS|d krt-d| | dfS||kr | | |fS)aO Conjugate Residual algorithm. Solves the linear system Ax = b. Left preconditioning is supported. The matrix A must be Hermitian symmetric (but not necessarily definite). Parameters ---------- A : array, matrix, sparse matrix, LinearOperator n x n, linear system to solve b : array, matrix right hand side, shape is (n,) or (n,1) x0 : array, matrix initial guess, default is a vector of zeros tol : float Tolerance for stopping criteria criteria : string Stopping criteria, let r=r_k, x=x_k 'rr': ||r|| < tol ||b|| 'rr+': ||r|| < tol (||b|| + ||A||_F ||x||) 'MrMr': ||M r|| < tol ||M b|| if ||b||=0, then set ||b||=1 for these tests. maxiter : int maximum number of iterations allowed M : array, matrix, sparse matrix, LinearOperator n x n, inverted preconditioner, i.e. solve M A x = M b. callback : function User-supplied function is called after each iteration as callback(xk), where xk is the current solution vector residuals : list residual history in the 2-norm, including the initial residual Returns ------- (xk, info) xk : an updated guess after k iterations to the solution of Ax = b info : halting status == ======================================= 0 successful exit >0 convergence to tolerance not achieved, return iteration count instead. <0 numerical breakdown, or illegal input == ======================================= Notes ----- The LinearOperator class is in scipy.sparse.linalg. Use this class if you prefer to define A or M as a mat-vec routine as opposed to explicitly constructing the matrix. Examples -------- >>> from pyamg.krylov import cr >>> from pyamg.util.linalg import norm >>> import numpy as np >>> from pyamg.gallery import poisson >>> A = poisson((10,10)) >>> b = np.ones((A.shape[0],)) >>> (x,flag) = cr(A,b, maxiter=2, tol=1e-8) >>> print(f'{norm(b - A*x):.6}') 6.54282 References ---------- .. [1] Yousef Saad, "Iterative Methods for Sparse Linear Systems, Second Edition", SIAM, pp. 262-67, 2003 http://www-users.cs.umn.edu/~saad/books.html alwayszpyamg.krylov._cr)moduleNg?rz%Number of iterations must be positivegg?r zrr+z5Unable to use ||A||_F with the current matrix format.MrMrzInvalid stopping criteria.rTz< Singular preconditioner detected in CR, ceasing iterations )rwarningsfilterwarningsintlen ValueErrorcopynpinner conjugatelinalgrrissparseAdata isinstancendarrayravelsqrtmodappendr)rbx0tolcriteriamaxiterMcallback residualsx postprocessrzpzznormrnormbrtolnormAnormMb recompute_rAzrAzApitrAz_oldalphabetas P/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/pyamg/krylov/_cr.pycrr@ s.P*!QA66Aq!Q  H-?@@@@c#a&&j//A% 1@AAA AE A AA A !++-- # #B INN1  Ew !!!  GGE ||4U{ U   ?13   VNNEE RZ ( ( V!#''EETUU UebinnQ///%78 V   a!eV|5666 t|| A""K QB (1;;==" % %C QB B7(bhr||~~r222 UQY 6"k " " rAvv OAAAE A E Uhq{{}}b))7{ T  Q d  b a XakkmmQ ' ' q!!    U # # #   HQKKK t  ;DD   %").."3"33e;
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