_-PhddZddlZddlmZddlZddlmZddlmZddl m Z ddl m Z  d d Z dS) z/Conjugate Gradient, Normal Error Krylov solver.N)warn)sparse)aslinearoperator)norm) make_systemh㈵>rrc tj|r|j} n8t t j|j} t||||\}}} }} |j d} tj ddd} |(tt j d| zdz}nT|d krtd |d| zkr6td tt j d| zdz}||| zz }t!|}||z}| |z}t j||}||g|dd<t!|}|d krd }|dkr||z}n|dkrtj|jrt!|jj}nUt+|jt jr't!t j|j}ntd||t j| z|zz}nY|dkr't!|}t!||z}||z}n,|dkrt j|}|}ntd||kr | | dfSd} |t j||z }| ||zz } t j|| r|dkr ||||zzz}n||| zz }||z}t j||}||z }|}||z}|| |zz }|d z }t j|}|||| || |dkr||z}nf|dkr)||t j| z|zz}n7|dkrt!|}||z}n|dkrt j|}|}||kr | | dfS||kr | | |fS)a Conjugate Gradient, Normal Error algorithm. Applies CG to the normal equations, A A.H x = b. Left preconditioning is supported. Note that unless A is well-conditioned, the use of CGNE is inadvisable 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|| 'rMr': ^1/2 < tol 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 A.H 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 cgne >>> 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) = cgne(A,b, maxiter=2, tol=1e-8) >>> print(f'{norm(b - A*x):.6}') 46.1547 References ---------- .. [1] Yousef Saad, "Iterative Methods for Sparse Linear Systems, Second Edition", SIAM, pp. 276-7, 2003 http://www-users.cs.umn.edu/~saad/books.html ralwayszpyamg.krylov._cgne)moduleNg?rz%Number of iterations must be positivezOmaximum allowed inner iterations (maxiter) are the 130% timesthe number of dofsgg?r zrr+z5Unable to use ||A||_F with the current matrix format.MrMrrMrzInvalid stopping criteria.)r isspmatrixT conjugaternpasarrayconjrshapewarningsfilterwarningsintceil ValueErrorrrinnerissparseAdata isinstancendarrayravellinalgsqrtmodappend)r bx0tolcriteriamaxiterMcallback residualsAHx postprocessn recompute_rrnormrzpold_zrnormbrtolnormAnormMbitalphanew_zrbetas R/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/pyamg/krylov/_cgne.pycgnerD sV6 S]]__bjmm00224 5 5*!QA66Aq!Q   A H-ABBBBK bgc!enn%%) 1@AAA CE   " # # #bgc!enn%%) AE A GGE AA QA XakkmmQ ' 'Fw !!!  GGE ||4U{ U   ?13   VNNEE RZ ( ( V!#''EETUU UebinnQ///%78 V  Qa!eV| U  5666 t|| A"" B3(!++--333 UQY 6"k " " rAvv !a% AAAE A E!++--++ T  R!V  a q!!    U # # #   HQKKK t  ;DD   %").."3"33e;
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