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function [G_coarse, A_coarse, map] = coarsen (G, O, A) %#ok
%COARSEN coarsen a graph unsafely but quickly.
% coarsen(G) computes a matching of vertices in the graph G and then coarsens
% the graph by combining all matched vertices into supervertices. It assumes
% that the matrix G provided has an all zero diagonal, is symmetric, and has
% all positive edge weights. With no option struct specified, the coarsening
% is done using a combination of heavy-edge matching and other more
% aggressive techniques to avoid stalling. An optional vertex weight vector A
% can also be specified. Note that mongoose_coarsen_mex does NOT check to
% see if the supplied matrix is of the correct form, and may provide
% erroneous results if used incorrectly.
%
% [G_coarse, A_coarse, map] = coarsen(G) coarsens a graph represented with
% sparse adjacency matrix G. G_coarse is the coarsened adjacency matrix,
% A_coarse is the coarsened array of vertex weights, and map is a mapping of
% original vertices to coarsened vertices.
%
% [G_coarse, A_coarse, map] = coarsen(G, O) uses the option struct O to
% specify coarsening options (e.g. matching strategies).
%
% [G_coarse, A_coarse, map] = coarsen(G, O, A) uses the array A as vertex
% weights, such that A(i) is the vertex weight of vertex i. If A is not
% specified, A is assumed to be an array of all ones (all weights are one).
%
% Example:
% Prob = ssget('DNVS/troll'); A = Prob.A;
% G = sanitize(A);
% G_coarse = coarsen(G);
% subplot(1,2,1); spy(G); subplot(1,2,2); spy(G_coarse);
%
% See also SAFE_COARSEN, EDGECUT_OPTIONS.
% Copyright (c) 2018, N. Yeralan, S. Kolodziej, T. Davis, W. Hager
error ('coarsen mexFunction not found') ;
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