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    filename: bipartite_matching.m
    path of file: ./repos/deep-photo-styletransfer/gen_laplacian/gaimc
    
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% BIPARTITE_MATCHING Solve a maximum weight bipartite matching problem
%
% [val m1 m2]=bipartite_matching(A) for a rectangular matrix A 
% [val m1 m2 mi]=bipartite_matching(x,ei,ej,n,m) for a matrix stored
% in triplet format.  This call also returns a matching indicator mi so
% that val = x'*mi.
%
% The maximum weight bipartite matching problem tries to pick out elements
% from A such that each row and column get only a single non-zero but the
% sum of all the chosen elements is as large as possible.
%
% This function is slightly atypical for a graph library, because it will
% be primarily used on rectangular inputs.  However, these rectangular
% inputs model bipartite graphs and we take advantage of that stucture in
% this code.  The underlying graph adjency matrix is 
%   G = spaugment(A,0); 
% where A is the rectangular input to the bipartite_matching function.
%
% Matlab already has the dmperm function that computes a maximum
% cardinality matching between the rows and the columns.  This function
% gives us the maximum weight matching instead.  For unweighted graphs, the
% two functions are equivalent.
%
% Note: If ei and ej contain duplicate edges, the results of this function

    
function [val m1 m2 mi]=bipartite_matching(varargin)
% BIPARTITE_MATCHING Solve a maximum weight bipartite matching problem
%
% [val m1 m2]=bipartite_matching(A) for a rectangular matrix A 
% [val m1 m2 mi]=bipartite_matching(x,ei,ej,n,m) for a matrix stored
% in triplet format.  This call also returns a matching indicator mi so
% that val = x'*mi.
%
% The maximum weight bipartite matching problem tries to pick out elements
% from A such that each row and column get only a single non-zero but the
% sum of all the chosen elements is as large as possible.
%
% This function is slightly atypical for a graph library, because it will
% be primarily used on rectangular inputs.  However, these rectangular
% inputs model bipartite graphs and we take advantage of that stucture in
% this code.  The underlying graph adjency matrix is 
%   G = spaugment(A,0); 
% where A is the rectangular input to the bipartite_matching function.
%
% Matlab already has the dmperm function that computes a maximum
% cardinality matching between the rows and the columns.  This function
% gives us the maximum weight matching instead.  For unweighted graphs, the
% two functions are equivalent.
%
% Note: If ei and ej contain duplicate edges, the results of this function
% are incorrect.
%
% See also DMPERM
%
% Example:
%   A = rand(10,8); % bipartite matching between random data
%   [val mi mj] = bipartite_matching(A);
%   val

% David F. Gleich and Ying Wang
% Copyright, Stanford University, 2008-2009
% Computational Approaches to Digital Stewardship

% 2008-04-24: Initial coding (copy from Ying Wang matching_sparse_mex.cpp)
% 2008-11-15: Added triplet input/output
% 2009-04-30: Modified for gaimc library
% 2009-05-15: Fixed error with empty inputs and triple added example.

[rp ci ai tripi n m] = bipartite_matching_setup(varargin{:});

if isempty(tripi)
    error(nargoutchk(0,3,nargout,'struct'));
else    
    error(nargoutchk(0,4,nargout,'struct'));
end