_-Ph>;vdZddlmZddlZddlmZddlmZddl m Z ddl m Z d Z d Z ddZddZddZdS)zAggregation methods.)warnN)sparse)amg_core) lloyd_cluster) classical_strength_of_connectionctj|std|jd|jdkrt d|jj}|jd}tj||}tj||}tj }|||j|j ||}|d|}|dkr.tj |dfdtj g|fS||f}|dkr{|dk}tj|||} ||} tjt#| d} tj| | | ff| |fStj|dz|} tjt#|d} tj | || f| |fS) aCompute the sparsity pattern of the tentative prolongator. Parameters ---------- C : csr_matrix strength of connection matrix Returns ------- AggOp : csr_matrix aggregation operator which determines the sparsity pattern of the tentative prolongator Cpts : array array of Cpts, i.e., Cpts[i] = root node of aggregate i Examples -------- >>> from scipy.sparse import csr_matrix >>> from pyamg.gallery import poisson >>> from pyamg.aggregation.aggregate import standard_aggregation >>> A = poisson((4,), format='csr') # 1D mesh with 4 vertices >>> A.toarray() array([[ 2., -1., 0., 0.], [-1., 2., -1., 0.], [ 0., -1., 2., -1.], [ 0., 0., -1., 2.]]) >>> standard_aggregation(A)[0].toarray() # two aggregates array([[1, 0], [1, 0], [0, 1], [0, 1]], dtype=int8) >>> A = csr_matrix([[1,0,0],[0,1,1],[0,1,1]]) >>> A.toarray() # first vertex is isolated array([[1, 0, 0], [0, 1, 1], [0, 1, 1]]) >>> standard_aggregation(A)[0].toarray() # one aggregate array([[0], [1], [1]], dtype=int8) See Also -------- amg_core.standard_aggregation expected csr_matrixrexpected square matrixdtypeNint8shape)risspmatrix_csr TypeErrorr ValueErrorindptrrnpemptyrstandard_aggregationindices csr_matrixarrayminarangeoneslen coo_matrixtocsr)C index_typenum_rowsTjCptsfnnum_aggregatesrmaskrowcoldataTpTxs [/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/pyamg/aggregation/aggregate.pyrr s^   # #/-...wqzQWQZ1222JwqzH (* - - -B 8HJ / / /D  &BR!(AIr4@@N  D (Af=== HRz * * *+ +~ &E vvxx2~~Rxi 333D9hws3xxv... $c !35AAAGGII4OO 8A:Z 0 0 0B R ' ' 'B  b"b\ 7 7 7 ==ctj|std|jd|jdkrt d|jj}|jd}tj||}tj||}tj }|||j|j ||}|d|}|dz }|dkrtj |dfd|fS||f}tj |dz|}tjt|d} tj | ||f||fS) a.Compute the sparsity pattern of the tentative prolongator. Parameters ---------- C : csr_matrix strength of connection matrix Returns ------- AggOp : csr_matrix aggregation operator which determines the sparsity pattern of the tentative prolongator Cpts : array array of Cpts, i.e., Cpts[i] = root node of aggregate i Examples -------- >>> from scipy.sparse import csr_matrix >>> from pyamg.gallery import poisson >>> from pyamg.aggregation.aggregate import naive_aggregation >>> A = poisson((4,), format='csr') # 1D mesh with 4 vertices >>> A.toarray() array([[ 2., -1., 0., 0.], [-1., 2., -1., 0.], [ 0., -1., 2., -1.], [ 0., 0., -1., 2.]]) >>> naive_aggregation(A)[0].toarray() # two aggregates array([[1, 0], [1, 0], [0, 1], [0, 1]], dtype=int8) >>> A = csr_matrix([[1,0,0],[0,1,1],[0,1,1]]) >>> A.toarray() # first vertex is isolated array([[1, 0, 0], [0, 1, 1], [0, 1, 1]]) >>> naive_aggregation(A)[0].toarray() # two aggregates array([[1, 0], [0, 1], [0, 1]], dtype=int8) See Also -------- amg_core.naive_aggregation Notes ----- Differs from standard aggregation. Each dof is considered. If it has been aggregated, skip over. Otherwise, put dof and any unaggregated neighbors in an aggregate. Results in possibly much higher complexities than standard aggregation. r rr r r Nrr)rrrrrrrrrrnaive_aggregationrrrrr ) r#r$r%r&r'r(r)rr.r/s r0r3r3bsJl   # #/-...wqzQWQZ1222JwqzH (* - - -B 8HJ / / /D  #BR!(AIr4@@N  D aB (Af===tCC ~ &E 8A:Z 0 0 0B R ' ' 'B  b"b\ 7 7 7 ==r1?rFc tj|sftj|sR |}t dtjn"#t $r}td|d}~wwxYw|jj }|}d}d} td|D]} tj|rt||d|} nt||d|} | j d} tj| |} tj| |}tj}|| | j| j| j| |}| |d|} n| |d|} | d z } |dkr(tj| d fd }t d n| |f}tj| d z|}tj|s=tjt-| d }tj|| |f| }n|d|jdz|d |jd zf}tjt-| tj|jdgzd }tj|| |f|j| }| dkr|}nCtj|rtj||z}ntj||z}|dkrnM| |d z krBtj|r!|j|z|z}|j|z|z}|r||j d}|| fS)aCompute the sparsity pattern of the tentative prolongator. Parameters ---------- A : csr_matrix or bsr_matrix level matrix matchings : int, default 2 number of times to perform pairwise aggregation; each matching increases coarsening factor by about two. theta : float, default 0.25 Strength tolerance used in computing classical SOC. norm : string, default 'min' Norm type used in computing classical SOC. compute_P : bool; default False Compute pairwise interpolation directly; if False, return integer aggregation matrix for smoothed_aggregation_solver. If True, return float interpolation P, converting to BSR form with identity of size bsize x bsize on each aggregate if A is BSR. Examples -------- >>> from scipy.sparse import csr_matrix >>> from pyamg.gallery import poisson >>> from pyamg.aggregation.aggregate import pairwise_aggregation >>> A = poisson((4,), format='csr') # 1D mesh with 4 vertices >>> A.toarray() array([[ 2., -1., 0., 0.], [-1., 2., -1., 0.], [ 0., -1., 2., -1.], [ 0., 0., -1., 2.]]) >>> pairwise_aggregation(A, matchings=1)[0].toarray() # two aggregates array([[1, 0], [1, 0], [0, 1], [0, 1]], dtype=int8) >>> pairwise_aggregation(A, matchings=2)[0].toarray() # one aggregate array([[1], [1], [1], [1]], dtype=int8) See Also -------- amg_core.pairwise_aggregation References ---------- [0] Notay, Y. (2010). An aggregation-based algebraic multigrid method. Electronic transactions on numerical analysis, 37(6), 123-146. zImplicit conversion of A to csrz(Invalid matrix type, must be CSR or BSR.NrT)AthetablocknormFr r rz$No pairwise aggregates found, T = 0.r) blocksizer)copy)risspmatrix_bsrrr"rSparseEfficiencyWarning Exceptionrrrrangerrrrrpairwise_aggregationrr-rrrr r:ridentity bsr_matrixTastype)r6 matchingsr7r9 compute_Per$AcrCr'ir#r%r&new_cptsr(r)T_temprr.r/s r0r@r@sn  !! $ $O(=a(@(@O O A 2F4R S S S S O O OFGGQ N OJ B A D1i 7,7,   # # \02U$UYZZZAA02U%VZ[[[A71: Xhj 1 1 18HJ777  *Hah 162xPP <O^O,DD.12D !V Q  &!}FCCCF 7 8 8 8 8~.E8A:Z888B(++ ]WSWWF333*BB2IJXc"ggr{1;q>'B'B&CC6RRR*BB<1;V[\\\ 66AA$Q'' 2%a&j11%a&j11 Q   E !  $V,, ,X^^%%*V3X]V+* HHQW5H ) ) d7Ns.A A8#A33A8Q?unit c |dks|dkrtdtj|s#tj|st d|dkr2t j|jt}n|dkrt|j}nf|dkrdt|jz }nH|d kr|j}n:|d kr"|j|j z }ntd ||j tkrt j|}| dksJ|||j|jf|j }t'tt)||jdzd|jd}t+||| \}}} |dkd} || } t jt1| d}tj|| | ff|jd|f } | | fS)abAggregate nodes using Lloyd Clustering. Parameters ---------- C : csr_matrix strength of connection matrix ratio : scalar Fraction of the nodes which will be seeds. distance : ['unit','abs','inv',None] Distance assigned to each edge of the graph G used in Lloyd clustering For each nonzero value C[i,j]: ======= =========================== 'unit' G[i,j] = 1 'abs' G[i,j] = abs(C[i,j]) 'inv' G[i,j] = 1.0/abs(C[i,j]) 'same' G[i,j] = C[i,j] 'sub' G[i,j] = C[i,j] - min(C) ======= =========================== maxiter : int Maximum number of iterations to perform Returns ------- AggOp : csr_matrix aggregation operator which determines the sparsity pattern of the tentative prolongator seeds : array array of Cpts, i.e., Cpts[i] = root node of aggregate i See Also -------- amg_core.standard_aggregation Examples -------- >>> from scipy.sparse import csr_matrix >>> from pyamg.gallery import poisson >>> from pyamg.aggregation.aggregate import lloyd_aggregation >>> A = poisson((4,), format='csr') # 1D mesh with 4 vertices >>> A.toarray() array([[ 2., -1., 0., 0.], [-1., 2., -1., 0.], [ 0., -1., 2., -1.], [ 0., 0., -1., 2.]]) >>> lloyd_aggregation(A)[0].toarray() # one aggregate array([[1], [1], [1], [1]], dtype=int8) >>> # more seeding for two aggregates >>> Agg = lloyd_aggregation(A,ratio=0.5)[0].toarray() rr zratio must be > 0.0 and <= 1.0!expected csr_matrix or csc_matrixrMabsinvg?samerzUnrecognized value distance=r)maxiterrr )rrrisspmatrix_cscrr ones_liker-rDfloatrQrrcomplexreal __class__rrrintmaxrnonzerorr r!r") r#ratiodistancerTr-G num_seeds_clustersseedsr+r,AggOps r0lloyd_aggregationrf9s,r zzUQYY9:::  !! $ $=(=a(@(@=;<<<6|AF##**511 U  16{{ U  3qv;; V  v U  v $BBBCCCw'wt}} 88::???? T19ah/qw ??ACEAGAJ.22AGAJ??@@I&q)WEEEAx q= ! ! # #A &C 3-C 73s886 * * *D  tc3Z0%&WQZ$; = = ==BUWW %<r1c |t|jddz }|dks||jdkrtdtj|s#tj|st d|jdkrtd|j tkrtj |j}n|j}| ||j|jf|j}|jd}tj|d|}|tj}tj|j j}|tj||j z}d||<d tj|tj z}|||<t/j||j|j|j|||||} tjt5|} tjt5| tj }tj|| | ff|jd|f} | |fS) aAggregate nodes using Balanced Lloyd Clustering. Parameters ---------- C : csr_matrix strength of connection matrix with positive weights num_clusters : int Number of seeds or clusters expected (default: C.shape[0] / 10) Returns ------- AggOp : csr_matrix aggregation operator which determines the sparsity pattern of the tentative prolongator seeds : array array of Cpts, i.e., Cpts[i] = root node of aggregate i See Also -------- amg_core.standard_aggregation Examples -------- >>> import pyamg >>> from pyamg.aggregation.aggregate import balanced_lloyd_aggregation >>> data = pyamg.gallery.load_example('unit_square') >>> G = data['A'] >>> xy = data['vertices'][:,:2] >>> G.data[:] = np.ones(len(G.data)) >>> np.random.seed(787888) >>> AggOp, seeds = balanced_lloyd_aggregation(G) NrrNr z$num_clusters must be between 1 and nrPzpositive edge weights requiredrr r)r[rrrrrUrr-rrrXrrYrZrrrandom permutationrDint32finfor\rrlloyd_cluster_exactrr r!r") r# num_clustersr-r` num_nodesrdmvdcmr,r+res r0balanced_lloyd_aggregationrrs2F171:?++ a @ @ @@E %<r1)rr4rF)rLrMrN)N)__doc__warningsrnumpyrscipyrrgraphrstrengthrrr3r@rfrrr1r0r{s!!!!!!777777S>S>S>lP>P>P>f04/4AAAAH\\\\~JJJJJJr1