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function [p, q, r, s] = cs_scc2 (A, bipartite)
%CS_SCC2 cs_scc, or connected components of a bipartite graph.
% [p,q,r,s] = cs_scc2(A) finds a permutation p so that A(p,q) is permuted into
% block upper triangular form (if A is square). In this case, r=s, p=q and
% the kth diagonal block is given by A (t,t) where t = r(k):r(k)+1.
% The diagonal of A is ignored. Each block is one strongly connected
% component of A.
%
% If A is not square (or for [p,q,r,s] = cs_scc2(A,1)), then the connected
% components of the bipartite graph of A are found. A(p,q) is permuted into
% block diagonal form, where the diagonal blocks are rectangular. The kth
% block is given by A(r(k):r(k+1)-1,s(k):s(k+1)-1). A can be rectangular.
%
% Example:
% Prob = ssget ('HB/arc130') ; A = Prob.A ; [p q r s] = cs_scc2 (A) ;
% cspy (A (p,q)) ;
% Prob = ssget ('HB/wm1') ; A = Prob.A ; [p q r s] = cs_scc2 (A) ;
% cspy (A (p,q)) ;
%
% See also CS_DMPERM, DMPERM, CS_SCC, CCSPY.
% CXSparse, Copyright (c) 2006-2022, Timothy A. Davis. All Rights Reserved.
% SPDX-License-Identifier: LGPL-2.1+
[m n] = size (A) ;
if (nargin < 2)
bipartite = 0 ;
end
if (m ~= n | bipartite) %#ok
% find the connected components of [I A ; A' 0]
S = spaugment (A) ;
[psym,rsym] = cs_scc (S) ;
p = psym (find (psym <= m)) ; %#ok
q = psym (find (psym > m)) - m ; %#ok
nb = length (rsym) - 1 ;
r = zeros (1,nb+1) ;
s = zeros (1,nb+1) ;
krow = 1 ;
kcol = 1 ;
for k = 1:nb
% find the rows and columns in the kth component
r (k) = krow ;
s (k) = kcol ;
ksym = psym (rsym (k):rsym (k+1)-1) ;
krow = krow + length (find (ksym <= m)) ;
kcol = kcol + length (find (ksym > m)) ;
end
r (nb+1) = m+1 ;
s (nb+1) = n+1 ;
else
% find the strongly connected components of A
[p,r] = cs_scc (A) ;
q = p ;
s = r ;
end
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