_-Phd$ dZddlmZddlZddlmZmZddlm Z ddl m Z ddl m Z mZmZmZmZmZmZdd lmZdd lmZmZmZmZmZd d lmZmZmZm Z m!Z!d d l"m#Z#ddddfdddifdddddfdddd ddd dfddddf dZ$dZ%dS) z"Approximate idealkrestriction AMG.)deepcopyN)isspmatrix_csrisspmatrix_bsr)MultilevelSolver)change_smoothers) classical_strength_of_connection symmetric_strength_of_connection evolution_strength_of_connectiondistance_strength_of_connectionalgebraic_distanceaffinity_distance#energy_based_strength_of_connection)filter_matrix_rows)direct_interpolationclassical_interpolationinjection_interpolationone_point_interpolation local_air)RSPMISPMIScCLJPCLJPc)CR classicalg333333?min)thetanormr second_passT one_pointairg?)rdegree fc_jacobig?F)omega iterationswithrho f_iterations c_iterationsc >|}|jd|jdkrtdtj|jrtdt jg} || d_t| |krc| djjd| krGt| |||||| } | rn/t| |kr| djjd| kGt | fi| }t||||S)uF Create a multilevel solver using approximate ideal restriction (AIR) AMG. Parameters ---------- A : csr_matrix Square (non)symmetric matrix in CSR format strength : ['symmetric', 'classical', 'evolution', 'distance', 'algebraic_distance','affinity', 'energy_based', None] Method used to determine the strength of connection between unknowns of the linear system. Method-specific parameters may be passed in using a tuple, e.g. strength=('symmetric',{'theta' : 0.25 }). If strength=None, all nonzero entries of the matrix are considered strong. CF : {string} : default 'RS' with second pass Method used for coarse grid selection (C/F splitting) Supported methods are RS, PMIS, PMISc, CLJP, CLJPc, and CR. interpolation : {string} : default 'one_point' Options include 'direct', 'classical', 'inject' and 'one-point'. restrict : {string} : default distance-2 AIR, with theta = 0.05. Option is 'air' for local approximate ideal restriction (lAIR), with inner options specifying degree, strength tolerance, etc. presmoother : {string or dict} : default None Method used for presmoothing at each level. Method-specific parameters may be passed in using a tuple. postsmoother : {string or dict} Postsmoothing method with the same usage as presmoother. postsmoother=('fc_jacobi', ... ) with 2 F-sweeps, 1 C-sweep is default. filter_operator : (bool, tol) : default None Remove small entries in operators on each level if True. Entries are considered "small" if |a_ij| < tol |a_ii|. max_levels: {integer} : default 20 Maximum number of levels to be used in the multilevel solver. max_coarse: {integer} : default 20 Maximum number of variables permitted on the coarse grid. keep: {bool} : default False Flag to indicate keeping strength of connection matrix (C) in hierarchy. Returns ------- ml : multilevel_solver Multigrid hierarchy of matrices and prolongation operators Examples -------- >>> from pyamg.gallery import poisson >>> from pyamg import air_solver >>> A = poisson((10,),format='csr') >>> ml = air_solver(A,max_coarse=3) Notes ----- "coarse_solver" is an optional argument and is the solver used at the coarsest grid. The default is a pseudo-inverse. Most simply, coarse_solver can be one of ['splu', 'lu', 'cholesky, 'pinv', 'gauss_seidel', ... ]. Additionally, coarse_solver 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. See [2001TrOoSc]_ for additional details. References ---------- [1] Manteuffel, T. A., Münzenmaier, S., Ruge, J., & Southworth, B. S. (2019). Nonsymmetric reduction-based algebraic multigrid. SIAM Journal on Scientific Computing, 41(5), S242-S268. [2] Manteuffel, T. A., Ruge, J., & Southworth, B. S. (2018). Nonsymmetric algebraic multigrid based on local approximate ideal restriction (lAIR). SIAM Journal on Scientific Computing, 40(6), A4105-A4130. See Also -------- aggregation.smoothed_aggregation_solver, multilevel_solver, aggregation.rootnode_solver, ruge_stuben_solver rrzexpected square matrixz,AIR solver not verified for complex matrices) asfptypeshape ValueErrornp iscomplexobjdatarLevelAlenextend_hierarchyr)r5strengthCF interpolationrestrict presmoother postsmootherfilter_operator max_levels max_coarsekeepkwargslevelsbottommls S/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/pyamg/classical/air.py air_solverrGs#t AwqzQWQZ1222 qvIGHHH$&& 'FF2JL f++ " "vbz|'9!'.unpack_args/ a   Q41: "u rHNrrr-T)diagonallump symmetricrdistance)ode evolution energy_basedr affinityz,Unrecognized strength of connection method: rrrrrrzUnknown C/F splitting method directr"injectzUnknown interpolation method r#zUnknown restriction method )(r6rr5rnnzr/r r r r rr rr0rrrrrrr1sumrrrrrCastypebool splittingPRrtocsrrtobsrappendrr4)rCr8r9r:r;r>rArNr5fnrBr[r^num_fptsr_r`s rFr7r7s #/!*<*A*A v;;!  &&AAr A1oa04oVWFXYYYYY 2JL u qH%%JB [ ,Q 9 9& 9 9 {   ,Q 9 9& 9 9 z   +A 8 8 8 8 # # # ,Q 9 9& 9 9 ~   / < >>vi  HC NN""A qM**JB [ #Aq) > >v > > x Ay ; ;F ; ; {   #Aq) > >v > > x #Ay ; ;F ; ;===>>>H%%JB U{{ a - -f - -;r;;<<< r $++D11F2JF2JLF2JL A A q>!#4#4 GGII   ^A%6%6 GGII MM"(**+++F2JL 1rH)&__doc__copyrnumpyr1 scipy.sparserr multilevelrrelaxation.smoothingrr8r r r r r rr util.utilsrclassical.interpolaterrrrrsplitrrrrrcrrrGr7rHrFrqs((77777777))))))333333PPPPPPPPPPPPPPPPPP,+++++000000000000000/////////////%U&C&CD-./($! < <=(Cq6;Q;<+>+>? $kkkk\j j j j j rH