_-Ph*+rdZddlmZddlZddlmZddlmZdZ dd Z dd Z d Z ddZ dZdZdZdZdS)zAlgorithms related to graphs.)warnN)sparse)amg_corectj|s(tj|stj|}|jd|jdkrt d|S)z!Return (square) matrix as sparse.rrzexpected square matrix)risspmatrix_csrisspmatrix_csc csr_matrixshape ValueError)Gs K/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/pyamg/graph.pyasgraphr sb  !! $ $!(=a(@(@!  a wqzQWQZ1222 Hserialc  t|}|jd}tj|d}d|dd<||dkr(tj}|||j|jddd|n|dkrGtj}|||j|jddd|tj |d nWtd |d tj }|||j|j||tj |d|S) aCompute a maximal independent vertex set for a graph. Parameters ---------- G : sparse matrix Symmetric matrix, preferably in sparse CSR or CSC format The nonzeros of G represent the edges of an undirected graph. algo : {'serial', 'parallel'} Algorithm used to compute the MIS * serial : greedy serial algorithm * parallel : variant of Luby's parallel MIS algorithm Returns ------- S : array S[i] = 1 if vertex i is in the MIS S[i] = 0 otherwise Notes ----- Diagonal entries in the G (self loops) will be ignored. Luby's algorithm is significantly more expensive than the greedy serial algorithm. rintcdtypeNrrparallelzUnknown algorithm ()) rr npemptyrmaximal_independent_set_serialindptrindices maximal_independent_set_parallelrandomrandr "maximal_independent_set_k_parallel)r algokNmisfns rmaximal_independent_setr's6  A  A (1F # # #C CFy 8  8B Bq!(AIr1a 5 5 5 5 Z  :B Bq!(AIr1abinnQ6G6G L L L L:4:::;; ;  8 1ah 1c29>>!+<+->???? 5  ) 1ah 8RY^^A->->????5F555666 Orct|}|jd}|jdkr,|jdkrt d|jtkrt dtj |d}tj |tj |j}d||<tj |dd}|||<tj ||j|j|j||||fS)a6Bellman-Ford iteration. Parameters ---------- G : sparse matrix Directed graph with positive weights. seeds : list Starting seeds Returns ------- distances : array Distance of each point to the nearest seed nearest_seed : array Index of the nearest seed Notes ----- This should be viewed as the transpose of Bellman-Ford in scipy.sparse.csgraph. Here, bellman_ford is used to find the shortest path from any point *to* the seeds. In csgraph, bellman_ford is used to find "the shortest distance from point i to point j". So csgraph.bellman_ford could be run `for seed in seeds`. Also note that `test_graph.py` tests against `csgraph.bellman_ford(G.T)`. See Also -------- scipy.sparse.csgraph.bellman_ford rz2Bellman-Ford is defined only for positive weights.z.Bellman-Ford is defined only for real weights.rrr)rr nnzdataminr rcomplexrasarrayfullinfr bellman_fordrr)r seedsr$ distances nearest_seeds rr:r:ss<  A  Auqyy 6::< >>>??? yy{{a> >>>???x(((H!'***IQ ""ZZ\\ q!(AIqv"5zz9h G G G Z  $ $ & &  E  g~~ BCCC x ''rc0t|}|jd}tj||jj}tj||jj}d|dd<t j}||j|jt|||||fS)aBreadth First search of a graph. Parameters ---------- G : csr_matrix, csc_matrix A sparse NxN matrix where each nonzero entry G[i,j] is the distance between nodes i and j. seed : int Index of the seed location Returns ------- order : int array Breadth first order level : int array Final levels Examples -------- 0---2 | / | / 1---4---7---8---9 | /| / | / | / 3/ 6/ | | 5 >>> import numpy as np >>> import pyamg >>> import scipy.sparse as sparse >>> edges = np.array([[0,1],[0,2],[1,2],[1,3],[1,4],[3,4],[3,5], ... [4,6], [4,7], [6,7], [7,8], [8,9]]) >>> N = np.max(edges.ravel())+1 >>> data = np.ones((edges.shape[0],)) >>> A = sparse.coo_matrix((data, (edges[:,0], edges[:,1])), shape=(N,N)) >>> c, l = pyamg.graph.breadth_first_search(A, 0) >>> print(l) [0 1 1 2 2 3 3 3 4 5] >>> print(c) [0 1 2 3 4 5 6 7 8 9] rrN) rr rrrrrbreadth_first_searchrint)r seedr$orderlevelBFSs rrRrRsZ  A  A HQ ' 'E HQ ' 'EE!!!H  'CC!)SYYu555 %<rct|}|jd}tj||jj}t j}|||j|j||S)aCompute the connected components of a graph. The connected components of a graph G, which is represented by a symmetric sparse matrix, are labeled with the integers 0,1,..(K-1) where K is the number of components. Parameters ---------- G : symmetric matrix, preferably in sparse CSR or CSC format The nonzeros of G represent the edges of an undirected graph. Returns ------- components : ndarray An array of component labels for each vertex of the graph. Notes ----- If the nonzero structure of G is not symmetric, then the result is undefined. Examples -------- >>> from pyamg.graph import connected_components >>> print(connected_components( [[0,1,0],[1,0,1],[0,1,0]] )) [0 0 0] >>> print(connected_components( [[0,1,0],[1,0,0],[0,0,0]] )) [0 0 1] >>> print(connected_components( [[0,0,0],[0,0,0],[0,0,0]] )) [0 1 2] >>> print(connected_components( [[0,1,0,0],[1,0,0,0],[0,0,0,1],[0,0,1,0]] )) [0 0 1 1] r) rr rrrrrconnected_componentsr)r r$ componentsr&s rrYrY&sXF  A  A!QX^,,J  &BBq!(AIz*** rcjt|\}}}|ddd}||ddfdd|fS)a Symmetric Reverse Cutthill-McKee. Parameters ---------- A : sparse matrix Sparse matrix Returns ------- B : sparse matrix Permuted matrix with reordering Notes ----- Get a pseudo-peripheral node, then call BFS Examples -------- >>> from pyamg import gallery >>> from pyamg.graph import symmetric_rcm >>> n = 200 >>> density = 1.0/n >>> A = gallery.sprand(n, n, density, format='csr') >>> S = A + A.T >>> # try the visualizations >>> # import matplotlib.pyplot as plt >>> # plt.figure() >>> # plt.subplot(121) >>> # plt.spy(S,marker='.') >>> # plt.subplot(122) >>> # plt.spy(symmetric_rcm(S),marker='.') See Also -------- pseudo_peripheral_node Nr)pseudo_peripheral_node)A dummy_rootrU dummy_levelps r symmetric_rcmraTsFL&%>"J{ ddd A QT7111a4=rc|jd}tj|j}t tj|z}d} t||\}}|}tj ||kd}||} | } tj | | kdd} || } || |kr | }|| }n|||fS)a(Find a pseudo peripheral node. Parameters ---------- A : sparse matrix Sparse matrix Returns ------- x : int Location of the node order : array BFS ordering level : array BFS levels Notes ----- Algorithm in Saad r) r rdiffrrSrr rRrHwherer5) r]nvalencexdeltarUrVmaxlevel lastnodeslastnodesvalenceminlastnodesvalenceys rr\r\s,  AgahG BINN  q !!A E#+Aq11 u99;;HUh.//2 "9-.2244 H%)<< = =a @ C aL 8e  A!HEEeU? "##r)rN)r()r>)__doc__warningsrnumpyrscipyrrrr'r1r:rKrRrYrar\rrrts##   ....b****Z1%1%1%hB(B(B(B(J777t+++\***Z/#/#/#/#/#r