_-PhdZddlmZddlZddlmZmZmZm Z ddl m Z ddl m Z ddlmZmZdd lmZd d d d dfdddifdddifddfdZdZdS)z+Support for pairwise-aggregation-based AMG.)warnN) csr_matrixisspmatrix_csrisspmatrix_bsrSparseEfficiencyWarning)MultilevelSolver)change_smoothers) get_blocksize levelize_strength_or_aggregation)pairwise_aggregationpairwiseg?min)thetanorm matchingsblock_gauss_seidelsweep symmetric c t|sWt|sH t|}tdtn"#t $r}t d|d}~wwxYw|}|jd|jdkrtdtj |j rtdt|||\}}}g}|tj||d_t%||krt'|djjdt)|djz |krgt+||t%||krDt'|djjdt)|djz |kgt|fi|} t-| ||| S) a Create a multilevel solver using Pairwise Aggregation. Parameters ---------- A : {csr_matrix, bsr_matrix} Sparse NxN matrix in CSR or BSR format aggregate : {tuple, string, list} : default ('pairwise', {'theta': 0.25, 'norm':'min', 'matchings': 2}) Method choice must be 'pairwise'; inner pairwise options including matchings, theta, and norm can be modified, presmoother : {tuple, string, list} : default ('block_gauss_seidel', {'sweep':'symmetric'}) Defines the presmoother for the multilevel cycling. The default block Gauss-Seidel option defaults to point-wise Gauss-Seidel, if the matrix is CSR or is a BSR matrix with blocksize of 1. See notes below for varying this parameter on a per level basis. postsmoother : {tuple, string, list} Same as presmoother, except defines the postsmoother. max_levels : {integer} : default 10 Maximum number of levels to be used in the multilevel solver. max_coarse : {integer} : default 500 Maximum number of variables permitted on the coarse grid. Other Parameters ---------------- coarse_solver : ['splu', 'lu', 'cholesky, 'pinv', 'gauss_seidel', ... ] Solver used at the coarsest level of the MG hierarchy. Optionally, may be a tuple (fn, args), where fn is a string such as ['splu', 'lu', ...] or a callable function, and args is a dictionary of arguments to be passed to fn. Returns ------- ml : multilevel_solver Multigrid hierarchy of matrices and prolongation operators See Also -------- multilevel_solver, classical.ruge_stuben_solver, aggregation.smoothed_aggregation_solver Examples -------- >>> from pyamg import pairwise_solver >>> from pyamg.gallery import poisson >>> from scipy.sparse.linalg import cg >>> import numpy as np >>> A = poisson((100, 100), format='csr') # matrix >>> b = np.ones((A.shape[0])) # RHS >>> ml = pairwise_solver(A) # AMG solver >>> M = ml.aspreconditioner(cycle='V') # preconditioner >>> x, info = cg(A, b, tol=1e-8, maxiter=30, M=M) # solve with CG References ---------- [0] Notay, Y. (2010). An aggregation-based algebraic multigrid method. Electronic transactions on numerical analysis, 37(6), 123-146. zImplicit conversion of A to CSRzSArgument A must have type csr_matrix or bsr_matrix, or be convertible to csr_matrixNrr zexpected square matrixz1Pairwise solver not verified for complex matrices)rrrrr Exception TypeErrorasfptypeshape ValueErrornp iscomplexobjdatar appendrLevelAlenintr _extend_hierarchyr ) r% aggregate presmoother postsmoother max_levels max_coarsekwargselevelsmls Z/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/pyamg/aggregation/pairwise.pypairwise_solverr3sN 1  F!2!2F F1 A 24K L L L L F F F>??DE F F AwqzQWQZ1222 qvNLMMM )J KK&J IF MM"(**+++F2JL f++ " " r "1%mF2JL&A&AA B BZ O O&),,, f++ " " r "1%mF2JL&A&AA B BZ O O & + +F + +BRl333 Is$A A$AA$cd}|dj}||t|dz \}}t|fi|ddid}|j}t |r|}||d_||d_| tj ||z|z}||d_dS)zExtend the multigrid hierarchy.cTt|tr|d|dfS|ifS)Nrr ) isinstancetuple)vs r2 unpack_argz%_extend_hierarchy..unpack_argzs/ a   Q41: "u rr compute_PTrN) r%r&r T conjugatertocsrPRr#rr$)r0r)r9r%_r.r?r@s r2r(r(xs r A 9S[[]344IAvQ99&99D999!rJs)11.-----777777LLLLLLLL++++++ *T',1,>,>?!5");!7!9"6#*K"8":!bffffRr: