_-Ph&zdZddlmZddlZddlmZddlmZm Z m Z ddl m Z ddl mZmZd Z ddZddZdZdS)zCompatible Relaxation.)deepcopyN)norm) isspmatrixspdiagsisspmatrix_csr)amg_core) gauss_seidelgauss_seidel_indexedc|jd}tj|f}t|dddf} d| |<t | } d} d} |dvrt d|dkrt || |d d| |<n|d krt|| ||d | } t | } | }| | z } | dz } | d |zkrn!t| |z | z d kr| |krn| | fS) a9Perform CR sweeps on a target vector. Internal function called by CR. Performs habituated or concurrent relaxation sweeps on target vector. Stops when either (i) very fast convergence, CF < 0.1*thetacr, are observed, or at least a given number of sweeps have been performed and the relative change in CF < 0.1. Parameters ---------- A : csr_matrix B : array like Target near null space mode Findex : array like List of F indices in current splitting Cindex : array like List of C indices in current splitting nu : int minimum number of relaxation sweeps to do thetacr Desired convergence factor Returns ------- rho : float Convergence factor of last iteration e : array like Smoothed error vector rNgT) habituated concurrentz4method not recognized: need habituated or concurrentr) iterationsr)indicesrg?) shapenpzerosrrNotImplementedErrorr r abs)ABFindexCindexnuthetacrmethodnzeenormrhokit enorm_oldrhok_olds R/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/pyamg/classical/cr.py_CRsweepr' sC<  A !A111a4AAfI GGE D B 5 5 5%'677 7 \ ! ! AqQ / / / /AfII | # # Aq&Q G G G G Qy  a #-    ! !D (C / /bBhh -0 7Nrffffff?autoFc |jd}|dkrnt|tr|n$t|trt|}t j|dkst j|dkrtd|dks|dkrtdt|std|j tkrtd|t j|df}|jdkr$|t#|df}|dddf} t j|fd } t j|dzfd } || d<t jd|d | dd<| dd} t jd d } t j|f}t+||| | ||| \}}t-d|D]}|dkrd|z }n/|d }t#|dkr|t0j}||j|j| || | ||| d}| d|dz} | |dzd} t+||| | ||| \}}|r$t9d|d|d|| dz |z ||krn| S)aUse Compatible Relaxation to compute a C/F splitting. Parameters ---------- A : csr_matrix sparse matrix (n x n) usually matrix A of Ax=b method : {'habituated','concurrent'} Method used during relaxation: - concurrent: GS relaxation on F-points, leaving e_c = 0 - habituated: full relaxation, setting e_c = 0 B : array like Target algebraically smooth vector used in CR. If multiple vectors passed in, only first one is used. If B=None, the constant vector is used. nu : int Number of smoothing iterations to apply each CR sweep. thetacr : float Desired convergence factor of relaxations, 0 < thetacr < 1. thetacs : list, float, 'auto' Threshold value, 0 < thetacs < 1, to consider nodes from candidate set for coarse grid. If e[i] > thetacs for relaxed error vector, e, node i is considered for the coarse grid. Can be passed in as float to be used for every iteration, list of floats to be used on progressive iterations, or as string 'auto,' wherein each iteration thetacs = 1 - rho, for convergence factor rho from most recent smoothing. maxiter : int Maximum number of CR iterations (updating of C/F splitting) to do. verbose : bool If true, print iteration number, convergence factor and coarsening factor after each iteration. Returns ------- splitting : array C/F list of 1's (coarse pt) and 0's (fine pt) (n x 1) References ---------- [1] Brannick, James J., and Robert D. Falgout. "Compatible relaxation and coarsening in algebraic multigrid." SIAM Journal on Scientific Computing 32.3 (2010): 1393-1416. Examples -------- >>> from pyamg.gallery import poisson >>> from pyamg.classical.cr import CR >>> A = poisson((20,20),format='csr') >>> splitting = CR(A) rr+r zMust have 0 < thetacs < 1zMust have 0 < thetacr < 1zexpecting csr sparse matrix Acomplex A not implementedNintc)dtype)r)rz CR Iteration z CF = z, Coarsening factor = )r isinstancelistreversefloatrmaxmin ValueErrorr TypeErrorr0complexronesndimreshapelenrarangeemptyr'rangepopr cr_helperindptrrprint)rrrrrthetacsmaxiterverbosertarget splittingrrrgammarhor r#tcsfnnum_Fs r&CRrPNs=l  A& gt $ $ $ OO      ' ' $7mmG F7OOq bfWoo&:&:899 91 'Q,,4555 !  97888w'!"=>>> y GQFOOv{{ IIs1vvqk " " qqq!tWF!V,,,Ih!vV,,,GGAJ)Aq///GABBK QRR[F Xd& ) ) )F HaTNNEaFFB G G GFCAw$$ f  C%CC"+C7||a   18 9         E!G%%'$!QGFKKKQ  ? >">>C>>,-gajL!+;>> ? ? ? == E  r(h㈵> ct|std|jtkrt d|jd}d}t j|df}| | }| }||z}d|z t j ||z} t||} | |kr||krtd|D]]} |dz || z} |dz || || || zz z} ||  || z|| zd|| z|| zz|| zz }| dkrtd|cSd|z| t j| | zd |z| zz z z }||| z }|j| }|j| dz}t j ||j|||j||}| d|z |z||| z|| |zzzz} ||j||xx||j||zz cc<||| <_t||} |dz }| |kr||kt j|}t)|dg||}||z|z}|}| |d }t jd|z t j|z}d|z |zS) aBinormalize matrix A. Attempt to create unit l_1 norm rows. Parameters ---------- A : csr_matrix sparse matrix (n x n) tol : float tolerance x : array guess at the diagonal maxiter : int maximum number of iterations to try Returns ------- C : csr_matrix diagonally scaled A, C=DAD Notes ----- - Goal: Scale A so that l_1 norm of the rows are equal to 1: - B = DAD - want row sum of B = 1 - easily done with tol=0 if B=DA, but this is not symmetric - algorithm is O(N log (1.0/tol)) Examples -------- >>> from pyamg.gallery import poisson >>> from pyamg.classical.cr import binormalize >>> A = poisson((10,),format='csr') >>> C = binormalize(A) References ---------- .. [1] Livne, Golub, "Scaling by Binormalization" Tech Report SCCM-03-12, SCCM, Stanford, 2003 http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.3.1679 zexpecting sparse matrix Ar.rr ?r g+=z&warning: A nearly un-binormalizable...)axis)rr9r0r:rrrr;ravelmultiplytocscdiagonaldot rowsum_stdevrArEsqrtrDrdatartocsrsum)rtolrGrr#xrdbetabetabarstdevic2c1c0xnewdxiiiiidot_BcolDCscales r& binormalizerssAR a==53444w'!"=>>>  A B AA 1 A A q5D1uq$'G D ! !E #++"w,,q!  AA#qtBA#Q!A$qt)+,BA$qtAaD1T!W9QqT>1AgI=BsU{{>???bDB3B2b!9!99:D!B!B(1Q3-Cva "S& 12AF2c6NCCHQ HtAw,>1b,H IIG 2c6" # # #r!&C.'8 8 # # #AaDDQ%% a9 #++"w,,>  A A31%%A A A  A ::a==  !  $ $D GSUbfTll* + +E eGQ;r(c |j}d|z tj||z}tjd|z tjtjtj|||z dz}||z S)aiCompute row sum standard deviation. Compute for approximation x, the std dev of the row sums s(x) = ( 1/n \sum_k (x_k beta_k - betabar)^2 )^(1/2) with betabar = 1/n dot(beta,x) Parameters ---------- x : array beta : array Returns ------- s(x)/betabar : float Notes ----- equation (7) in Livne/Golub rTr )sizerr[r]r`powerrX)rbrdrrerfs r&r\r\?sm* AQw"&D//)G GS1Wrx At0D0Dw0NPQ'R'R S SS T TE 7?r()rNr)r*r+r,F)rQrR)__doc__copyrnumpyr scipy.linalgr scipy.sparserrrpyamgrrelaxation.relaxationr r r'rPrsr\r(r&rs<<<<<<<<<<FFFFFFFF???D69,1IIIIXbbbbJr(