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function [p,q,r,s,cc,rr] = cs_dmspy (A,res,seed)
%CS_DMSPY plot the Dulmage-Mendelsohn decomposition of a matrix.
% [p,q,r,s,cc,rr] = cs_dmspy(A) computes [p,q,r,s,cc,rr] = cs_dmperm(A),
% does spy(A(p,q)), and then draws boxes around the coarse and fine
% decompositions. A 2nd input argument (cs_dmspy(A,res)) changes the
% resolution of the image to res-by-res (default resolution is 256).
% If res is zero, spy is used instead of cspy. If the resolution is low, the
% picture of the blocks in the figure can overlap. They do not actually
% overlap in the matrix. With 3 arguments, cs_dmspy(A,res,seed),
% cs_dmperm(A,seed) is used, where seed controls the randomized algorithm
% used by cs_dmperm.
%
% Example:
% Prob = ssget ('HB/arc130') ; cs_dmspy (Prob.A) ;
%
% See also CS_DMPERM, CS_DMSOL, DMPERM, SPRANK, SPY.
% CXSparse, Copyright (c) 2006-2022, Timothy A. Davis. All Rights Reserved.
% SPDX-License-Identifier: LGPL-2.1+
if (~issparse (A))
A = sparse (A) ;
end
if (nargin < 2)
res = 256 ;
end
if (nargin < 3)
seed = 0 ;
end
% Dulmage-Mendelsohn permutation
[p1,q,r,s,cc,rr] = cs_dmperm (A,seed) ;
if (nargout > 0)
p = p1 ;
end
nb = length (r)-1 ;
% plot the result
S = A (p1,q) ;
if (res == 0)
spy (S) ;
e = 1 ;
else
e = cspy (S,res) ;
end
hold on
title (sprintf ( ...
'%d-by-%d, sprank: %d, fine blocks: %d, coarse blocks: %d-by-%d\n', ...
size (A), rr(4)-1, nb, length (find (diff (rr))), ...
length (find (diff (cc))))) ;
drawboxes (nb, e, r, s) ;
[m n] = size (A) ;
drawbox (1,m+1,1,n+1,'k',1,e) ;
drawbox (rr(1), rr(2), cc(1), cc (2), 'r', 2, e) ;
drawbox (rr(1), rr(2), cc(2), cc (3), 'r', 2, e) ;
drawbox (rr(2), rr(3), cc(3), cc (4), 'k', 2, e) ;
drawbox (rr(3), rr(4), cc(4), cc (5), 'r', 2, e) ;
drawbox (rr(4), rr(5), cc(4), cc (5), 'r', 2, e) ;
hold off
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