_-Ph6,^dZddlZddlmZmZmZddlmZddl m Z dZ dd Z d Z ddZdS)zSolve an arbitrary system.N)isspmatrix_csrisspmatrix_bsr csr_matrix)smoothed_aggregation_solver) ishermitiancDt|sQt|sB t|}tdn"#t$r}t d|d}~wwxYw|jd|jdkrt d|}|S)a^ Convert A to CSR, if A is not a CSR or BSR matrix already. Parameters ---------- A : array, matrix, sparse matrix (n x n) matrix to convert to CSR Returns ------- A : csr_matrix, bsr_matrix If A is csr_matrix or bsr_matrix, then do nothing and return A. Else, convert A to CSR if possible and return. Examples -------- >>> from pyamg.gallery import poisson >>> from pyamg.blackbox import make_csr >>> A = poisson((40,40),format='csc') >>> Acsr = make_csr(A) Implicit conversion of A to CSR in pyamg.blackbox.make_csr z:Implicit conversion of A to CSR in pyamg.blackbox.make_csrzSArgument A must have type csr_matrix or bsr_matrix, or be convertible to csr_matrixNrrzArgument A must be a square)rrrprint Exception TypeErrorshapeasfptype)Aes N/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/pyamg/blackbox.pymake_csrr s2 1  R!2!2R R1 A N O O O O R R RJKKPQ R R wqzQWQZ5666 A Hs? A AATct|}i}t|drd|d<|rtdnd|d<|rtd|ddkr!dd d d d d f|d<ddddf|d<ddddf|d<n ddd d d d f|d<ddd df|d<ddd df|d<|t|r|jddkrn|jd}t jt jt|j d|z df|j t j ||d<nt j|j ddf|j |d<nt|t j rt|j dkr|dd}|j d|j dks|j ddkrt!dt j||j |d<nt!d|ddkrd|d<n|d|d<dd d d!d"f|d#<d$|d%<d&|d'<d(|d)<d*|d+<d,|d-<|S).aGenerate a dictionary of SA parameters for an arbitrary matrix A. Parameters ---------- A : array, matrix, csr_matrix, bsr_matrix (n x n) matrix to invert, CSR or BSR format preferred for efficiency B : None, array Near null-space modes used to construct the smoothed aggregation solver If None, the constant vector is used If (n x m) array, then B is passed to smoothed_aggregation_solver verb : bool If True, print verbose output during runtime Returns ------- config : dict A dictionary of solver configuration parameters that one uses to generate a smoothed aggregation solver Notes ----- The config dictionary contains the following parameter entries: symmetry, smooth, presmoother, postsmoother, B, strength, max_levels, max_coarse, coarse_solver, aggregate, keep. See smoothed_aggregtion_solver for each parameter's description. Examples -------- >>> from pyamg.gallery import poisson >>> from pyamg import solver_configuration >>> A = poisson((40,40),format='csr') >>> solver_config = solver_configuration(A,verb=False) T) fast_check hermitiansymmetryz Detected a Hermitian matrix nonsymmetricz! Detected a non-Hermitian matrixenergycglocal)krylovmaxiterdegree weightingsmoothblock_gauss_seidel symmetricr)sweep iterations presmoother postsmoothergmresgauss_seidel_nrNrdtypeBz9Invalid dimensions of B, B.shape[0] must equal A.shape[0]z Invalid BBH evolutionl2g@)k proj_typeepsilonstrength max_levelsi max_coarsepinv coarse_solverstandard aggregateFkeep)rrr r blocksizenpkrononesintr r+eye isinstancendarraylenreshaper arraycopy)rr,verbconfigbsizes rsolver_configurationrL4sH  A F1&&&7(z  3 1 2 2 2+z  7 5 6 6 6j[(($!12'J'JKx!5+6a!H!H!J}"6,7q"I"I"K~%Q12'J'JKx!2+6a!H!H!J}"3,7q"I"I"K~ y !   BQ!!3!3KNE'"'3qwqzE/A+B+BA*F01#9#9#9:<&--IIF3KK'171:q/AAAF3KK Arz " " % qw<<1   "a  A GAJ!'!* $ $!'!*//WXX Xhq000s  $$$ j[((t c{''))t &QT36(8(89F:F<F<$F?$F;F6N Mc.t|} t||d|d|d|d|d|d|d|d|d |d |d |d  S#t$r}td|d}~wwxYw)aGenerate an SA solver given matrix A and a configuration. Parameters ---------- A : array, matrix, csr_matrix, bsr_matrix Matrix to invert, CSR or BSR format preferred for efficiency config : dict A dictionary of solver configuration parameters that is used to generate a smoothed aggregation solver Returns ------- ml : smoothed_aggregation_solver smoothed aggregation hierarchy Notes ----- config must contain the following parameter entries for smoothed_aggregation_solver: symmetry, smooth, presmoother, postsmoother, B, strength, max_levels, max_coarse, coarse_solver, aggregate, keep Examples -------- >>> from pyamg.gallery import poisson >>> from pyamg import solver_configuration,solver >>> A = poisson((40,40),format='csr') >>> config = solver_configuration(A,verb=False) >>> ml = solver(A,config) r,r.r!r4r6r7r9rr;r&r'r<) r,r.r!r4r6r7r9rr;r&r'r<z-Failed generating smoothed_aggregation_solverN)rrr r )rrJrs rsolverrOs@  AP '*0++1$Fc t|}|#t|d|} t|| }n;|jdjjd|jdkrt d|jdjjdkrd} nd} |Ctj tj |jd|j }|r0tj d td |d fd } nd} |||| ||| | } |r|||zz } ||| zz }|}tjtjtj|| z| }tjtjtj||z|}td|dd|dtj|dkr||z }td|d|r| |j|fS| |jS)aSolve Ax=b. Solve the arbitrary system Ax=b with the best out-of-the box choice for a solver. The matrix A can be non-Hermitian, indefinite, Hermitian positive-definite, complex, etc... Generic and robust settings for smoothed_aggregation_solver(..) are used to invert A. Parameters ---------- A : array, matrix, csr_matrix, bsr_matrix Matrix to invert, CSR or BSR format preferred for efficiency b : array Right hand side. x0 : array Initial guess (default random vector) tol : float Stopping criteria: relative residual r[k]/r[0] tolerance maxiter : int Stopping criteria: maximum number of allowable iterations return_solver : bool True: return the solver generated existing_solver : smoothed_aggregation_solver If instance of a multilevel solver, then existing_solver is used to invert A, thus saving time on setup cost. verb : bool If True, print verbose output during runtime residuals : list List to contain residual norms at each iteration. The preconditioned norm is used, namely ||r||_M = (M r, r)^(1/2) = (r, r)^(1/2) Returns ------- x : array Solution to Ax = b ml : MultilevelSolver Optional return of the multilevel structure used for the solve Notes ----- If calling solve(...) multiple times for the same matrix, A, solver reuse is easy and efficient. Set "return_solver=True", and the return value will be a tuple, (x,ml), where ml is the solver used to invert A, and x is the solution to Ax=b. Then, the next time solve(...) is called, set "existing_solver=ml". Examples -------- >>> import numpy as np >>> from pyamg import solve >>> from pyamg.gallery import poisson >>> from pyamg.util.linalg import norm >>> A = poisson((40,40),format='csr') >>> b = np.array(np.arange(A.shape[0]), dtype=float) >>> x = solve(A,b,verb=False) >>> print(f'{norm(b - A*x)/norm(b):1.2e}') 6.28e-06 N)r,rIrz_Argument existing_solver must have level 0 matrix of same size as Arrr(r*)rz maxiter = cR|ddz|d<td|ddS)Nrrz iteration )r )_x iterations rcallbackzsolve..callback-s5$Q.callback21s8Ay)) )rM)x0acceltolrrV residualsz# Residuals ||r_k||_M, ||r_0||_M = z1.2ez, gV瞯rGrandomrandr+zerosr solveaspreconditionersqrtinner conjugateabsrF)rbr[r]r return_solverexisting_solverrIr^rJr\rZrYr0rkMnr0nrkratiorVrUs @@rrcrcs~  A&a4d;;; F++  !! $ & ,Q /171: = =011 1a "+{:: z XbinnQWQZ11 A A A HTNN  (w(())) 3 3 3 * * * * * * *  aBeg'0I  G GA N RZ QY  , , . .gbhr|AF33R8899gbhr|AF33R8899 JCJJJJJJKKK 6#;;  #IE LLLL M M M5 !'""O44 99QW  rM)NT)NrPrQFNTN)__doc__numpyr> scipy.sparserrr aggregationr util.linalgrrrLrOrcrXrMrrws CCCCCCCCCC444444$$$$$$& & & RccccL3P3P3Pl?D59wwwwwwrM