function Pairs = call_plex(square)
% function Pairs = call_plex(square)
% Author -  Deepti Pachauri 
%           Department of Computer Sciences 
%           University of Wisconsin - Madison
% Construct persistent homology given flat map of signal (square).
% INPUT -
%     square - flat map of cortical signal.
% Output -
%       Pairs - Persistent homology in degree 0 stored as cell array.


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% addpath where Plex is installed. For example
% addpath(genpath('/home/Plex/plex-2.5'));
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Pairs = cell(1,1);
[lmax, lmin] = figure_extrema(square);
X = [lmin.J; lmax.J];
Y = [lmin.I; lmax.I];
tri = delaunay(X,Y);
C = attach(plex,tri');
figure, imagesc(square)
hold on
plot(X,Y,'k+')
figure, plot3complex(C,[X,Y]')

%filtration specification for persistence
f = [lmin.value lmax.value];
filtrationDirection = 1;
F = {filtrationDirection * f};

F1 = extend(C, F);
F1(1,4) = {[]};
disp('calculating persistence...\n')
I = persistence(C, F1); % calculate the persistent homology
Pairs{1,1} = I{1,1};