_-PhBXdZddlZddlmZddlZddlmZddlmZddl m Z  d d Z dS) z#Steepest Descent projection method.N)warn)sparse)norm) make_systemh㈵>rrc t||||\}}} }} tjdd|tt |}n|dkrt d||| zz } || z} t j| | } t j | }||g|dd<t|}|dkrd}|d kr||z}n|d krtj |j rt|j j}nUt|j t jr'tt j|j }nt d ||t j | z|zz}nY|d kr't| }t||z}||z}n,|d krt j| }|}nt dd}d} || z}t j| |}|dkrt'd| | dfS| |z }| || zz} |dz }t j||r|dkr ||| zz } n| ||zz } || z} t j| | } | dkrt'd| | dfSt| }|||| || |d kr||z}nf|d kr)||t j | z|zz}n7|d krt| }||z}n|d krt j| }|}||kr | | dfS| dkrt'd| | dfS||kr | | |fS)a| Steepest descent algorithm. Solves the linear system Ax = b. Left preconditioning is supported. 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 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 of cg == ======================================= 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. See Also -------- _minimal_residual Examples -------- >>> from pyamg.krylov import steepest_descent >>> 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) = steepest_descent(A,b, maxiter=2, tol=1e-8) >>> print(f'{norm(b - A*x):.6}') 7.89436 References ---------- .. [1] Yousef Saad, "Iterative Methods for Sparse Linear Systems, Second Edition", SIAM, pp. 137--142, 2003 http://www-users.cs.umn.edu/~saad/books.html alwayszpyamg.krylov._steepest_descent)moduleNz%Number of iterations must be positivegg?r zrr+z5Unable to use ||A||_F with the current matrix format.MrMrrMrzInvalid stopping criteria.2rTz: Indefinite matrix detected in steepest descent, aborting zC Indefinite preconditioner detected in steepest descent, stopping. zA Singular preconditioner detected in steepest descent, stopping. )rwarningsfilterwarningsintlen ValueErrornpinner conjugatelinalgrrissparseAdata isinstancendarrayravelsqrtrmodappend)rbx0tolcriteriamaxiterMcallback residualsx postprocessrzrznormrnormbrtolnormAnormMb recompute_ritqzAzalphas ^/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/pyamg/krylov/_steepest_descent.pysteepest_descentr< sX*!QA66Aq!Q  H-MNNNNc!ff++ 1@AAA AE A AA !++-- # #B INN1  Ew !!!  GGE ||4U{ U   ?13   VNNEE RZ ( ( V!#''EETUU UebinnQ///%78 V  Qa!eV| U   5666K B5( Ehq{{}}a(( 99 O P P PKNNB' 'S  M a 6"k " " rAvvAE AAEAI A E XakkmmQ ' ' 88 X Y Y YKNNB' 'Q    U # # #   HQKKK t  ;DD   %").."3"33e;
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