%% Figure 8 -- figure supplement 2
% Generates data for panels A, B and C.
% figure8supp2.XLSX data file must be in the same directory (experimental data
% are read for angle and tension PDFS
% Function can be switched to behave like a script ('true'), assigning but
% not returning values, or in a standard way ('false'). No input is
% implicit 'true'.
%   ===================================================================

%% The calling the 'script' function
% =====================================================================
function [varargout] = figure8supp2_source_code(scriptlike)
% if called with scriptlike==true, function behaves like a script, returns
% nothing and copies results directly into the base workspace

    if nargin == 0; % without input, function behaves like a script
        scriptlike = true;
    end
    
% =======================================================================
    % Panel A
    % read angle and tension measured distributions
    disp('Reading data from XLSX file');
    if ~exist('figure8supp2.xlsx','file')
        error(strjoin({'File ''figure8supp2.xlsx'' cannot be found.'...
            'This file contains source data for this code. Please make sure'...
            'the file is accessible and try again'}));
    end
    tensionPDF = xlsread('figure8supp2.xlsx',2,'C2:D2001','basic');
    anglePDF   = xlsread('figure8supp2.xlsx',2,'A2:B2001','basic');

    % estimate adhesion parameter S by seeking maximal correlation between data
    % angle PDF and angle PDF transformed from tension PDF
    disp(strcat('Estimating adhesion parameter S by maximal correlation between data',...
    ' angle PDF and angle PDF transformed from tension PDF (corresponds to panel A)'));
    [ transAnglePDF,~,S] = tensionAngleTransform( tensionPDF, anglePDF );
    transAnglePDF(:,1) = transAnglePDF(:,1)*180/pi; % consistently in degrees
    transAnglePDF(:,2) = transAnglePDF(:,2)*pi/180;

    if scriptlike
        disp('Angle PDF obtained by transforming tension PDF was saved as ''transAnglePDF''.');
        disp('Estimated adhesion parameter S [pN] was saved in variable ''S''');
    end;
    
    S=1000*S;   % to piconewtons

    % calculate joint distribution and use it to obtain adhesion distribution
    % of S;
    disp(strcat('Estimating adhesion parameter S based on joint PDF of angle and tension (corresponds to panel B and C)'));
    [AFM, ASM, ADM, ~, ~, adhesionPDF, quantile, jointPDF] = getAdhesionDistribution(anglePDF, tensionPDF, 20);

    disp(strcat('Mean adhesion is:', num2str(AFM),' pN'));
    disp(strcat('Adhesion median is:', num2str(quantile(10)), ' pN'));
    disp(strcat('Adhesion mode is:', num2str(ADM), ' pN'));
    disp(strcat('Adhesion inetrquartile range is:', '[', num2str(quantile(5)),',',num2str(quantile(15)),'] pN'));

    if scriptlike
        disp('Joint PDF was saved (in reduced form) in variable ''jointPDF''');
        disp('A contourplot can be generated typing ''contour(jointPDF)''');
        disp('Adhesion PDF was saved in variable ''adhesionPDF''');
    end
        
    % to mimic behaviour of a script; force variables into base workspace
    if scriptlike
        assignin('base','tensionPDF',tensionPDF);
        assignin('base','anglePDF',anglePDF);
        assignin('base','transAnglePDF',transAnglePDF);
        assignin('base','adhesionPDF',adhesionPDF);
        assignin('base','jointPDF',jointPDF);
        assignin('base','S',S);
        assignin('base','AFM',AFM);
        assignin('base','ASM',ASM);
        assignin('base','ADM',ADM);
        assignin('base','quantile',quantile);
    else
        varargout{1} = tensionPDF;
        varargout{2} = anglePDF;
        varargout{3} = transAnglePDF;
        varargout{4} = adhesionPDF;
        varargout{5} = jointPDF;
        varargout{6} = S;
        varargout{7} = AFM;
        varargout{8} = ASM;
        varargout{9} = ADM;
        varargout{10}= quantile;
    end
end



%% The methods section, called by the first 'script' function 
% ====================================================================

function [ angDst, angDataDst, adh ] = tensionAngleTransform( tenDst, angDataDst )
%TENSIONANGLETRANSFORM Transformation from distribution of tension to
%   distribution of angles according to a prescribed function 
%   T = ADH/(2(1-cos(ang/2))); The transformation from tensions to angles is
%   first calculated (transforming coordinates, transforming density using
%   Jacobian). Then, it is re-binned to conform with experimental angles
%   distribution (angDataDst), error is calculated, and minimum search run
%   to find the optimal adhesion parameter.
% 
%   tenDst = tension PDF
%   angDataDst = measured angle PDF
%   angDst = angle PDF as a transform of tension PDF
%   adh    = adhesion parameter estimated by max. correl. of angDataDst and
%            angDst
%   ====================================================================

    adh = 0.1; % initial adhesion guess

    % normalize inputs, if not normalized
    tenDst(:,1) = tenDst(:,1)/1000; % in nanonewtons
    tenDstSum = sum(tenDst(:,2)) * (max(tenDst(:,1)-min(tenDst(:,1))))/numel(tenDst(:,1));
    tenDst(:,2) = tenDst(:,2)/tenDstSum;
    angDataDst(:,1) = angDataDst(:,1)*pi/180;   % in radians
    angDataDstSum = sum(angDataDst(:,2)) * (max(angDataDst(:,1))-min(angDataDst(:,1)))/numel(angDataDst(:,1));
    angDataDst(:,2) = angDataDst(:,2)/angDataDstSum;    % experimental angles distribution; normalized
    s=size(tenDst,1);       % tension data vector length -> calculated angles dist length
    ds = size(angDataDst,1);% angle data vector length

    % relAT = @(a) (0.5*adh/(1-cos(a/2)));    % angle to tension relation;

    model = @distDiff;  % model for min-search
    est = fminsearch(model,adh,optimset('MaxIter',100));    % min seach, max 100 iterations

        % transforms tension distribution into angle distribution using
        % equation with single parameter (adhesion), which is optimized by
        % compating the resulting angle distribution with a real distribution
        % of angles in culture -- order of magnitude estimate    
        function [err,angDst] = distDiff(par)
            persistent itr;     % number of iterations
            if isempty(itr);itr=0;end;

            angVar = zeros(s,1);
            angJac = zeros(s,1);
            angDst = zeros(s,2);
            angDstSum = 0;
            relTA = @(t) (2*acos(max(0,1-0.5*par/t)));     % tension to angle relation
            angJ  = @(a) (0.25*par * sqrt(2*(1-cos(a/2))-(1-cos(a/2))^2) / (1-(cos(a/2))^2) );  % jacobian

            for i=1:s
                angVar(i) = relTA( tenDst(i,1) );   % get angle corresponding to the given tension
                angJac(i) = angJ( angVar(i) );      % get jacobian at the given point
                angDst(i,:) = [angVar(i), tenDst(i,2) * angJac(i)];
                if i>1; angDstSum = angDstSum + angDst(i-1,2) * abs(angDst(i-1,1)-angDst(i,1)); end;
            end
            angDst(:,2) = angDst(:,2)/angDstSum;    % normalize; ang distribution calculated from tension with given adh

            angDstCopy = angDst(:,1);       % copy the angles corresponding to the tensions
            angDataDst(:,3) = zeros(ds,1);  % create one more collumn for the calculated ang data

            for d=2:size(angDataDst,1)  % angle increases; equidistant angle values
                bin = [angDataDst(d-1,1),angDataDst(d,1)];
                for b=numel(angDstCopy):-1:1    % angle increases (inverse ordering) -- from the end so it can be cropped each iteration

                    dot=angDstCopy(b);  % angle value at particular coordinate
                    if in(bin,dot)      % if the value belongs to the designated bit
                        angDstCopy(b:numel(angDstCopy)) = []; % delete all smaller angles (out of scope)
                        angDataDst(d,3) = angDataDst(d,3) + angDst(b,2);
                        break;
                    end;
                end
            end

            itr = itr+1;
            CC = corrcoef(angDataDst(:,2), angDataDst(:,3));
            err = (1 - CC(1,2))^2;
            %err = sum(( angDataDst(:,2) - angDataDst(:,3) ).^2);    % get error
            %disp(strcat('Iteration:',num2str(itr),...
            %    ',adhesion estimate is:',num2str(par),' nN,with correlation:',num2str(CC(1,2))));

        end

        % checks if 'dot' belongs into a 'bin'; bin(1) < bin(2)
        function [is] = in(bin,dot)
            if dot>=bin(1)&& dot <=bin(2);
                is=true;
            else
                is=false;
            end           
        end

    [err,angDst] = model(est);  % generate the output
    disp(strcat('The adhesion estimate is:',num2str(est),' nN, with correlation:',num2str(1-sqrt(err)))); % display what was converget to

    adh=est;

    % plot the results
    plot(angDst(:,1)*180/pi,angDst(:,2)*pi/180,'r-', 'LineWidth',2);
    xlim([0,180]);
    hold on;
    plot(angDataDst(:,1)*180/pi,angDataDst(:,2)*pi/180,'b-','LineWidth',2 );
    lh = legend('Transformed distribution','Experimental data');
    lh.Box = 'off';
    lh.Location = 'northeast';
    title('Angle $$\beta$$ distribution','Interpreter','latex');
    xlabel('angle $$\beta$$ [$$^{\circ}$$]','Interpreter','latex');
    ylabel('PDF($$\beta$$)','Interpreter','latex');
    ha = gca;
    set(ha,'LineWidth',2,'FontSize',18);
    text(80,0.04,strjoin({'Adhesion estimate: $$S=$$',num2str(round(est*1000)),'pN',...
                      char(10),'distribution correlation:',num2str(round(1-sqrt(err),3))}),'Interpreter','latex','FontSize',18);

    angDataDst(:,3) = [];

end

function [AFM, ASM, ADM, ADMindex, DFM, adhHist, quantile, adhDistReduced] = getAdhesionDistribution(angleDist, tensionDist, quantiles)
% Calculates the adhesion parameter and it's distribution
% Cosiders angle distribution and tension distribution independent, which
% they aren't, but since we have no information on their correlation, it is
% the best we can do.
% angleDist = distribution of angles, first column are angle values in degrees, second
% the probabilities.
% tensionDist = distribution of tensions, the first column are tension
% values, the second their probabilities.
% quantiles = number of qunatiles to calculate

% returns adhesive parameter:   AFM - 1st moment, ASM - standard deviation, 
%                               ADM - mode, adhDistReduced - distribution 
%                               DFM - angle and tension first moments
%                               adhHist - adhesion PDF
%                               quantile - values for 20 quantiles
%   ========================================================================

    adhDist = zeros(numel(angleDist(:,1)), numel(tensionDist(:,1)));
    AFM = 0;
    ASM = 0;
    dt = 1;
    dA = 0.1;     % distribution is normalized by a sum, not integral. Otherwise, dA = 0.1
    DFM = [0,0];

    % approximate the joint probability distribution
    for a=1:numel(angleDist(:,1))
        for t=1:numel(tensionDist(:,1))
            adhDist(a,t) = angleDist(a,2) * tensionDist(t,2);
        end
    end

    % average - distribution first moment
    for a=1:numel(angleDist(:,1))
        for t=1:numel(tensionDist(:,1))
            DFM(2) = DFM(2) + tensionDist(t,1) * adhDist(a,t) * dA * dt;
            DFM(1) = DFM(1) + angleDist(a,1) * adhDist(a,t) * dA * dt;
        end
    end

    % calculate the adhesion coefficient
    for a=1:numel(angleDist(:,1))
        for t=1:numel(tensionDist(:,1))
            AFM = AFM + 2*tensionDist(t,1)*(1-cos(angleDist(a,1) * pi/360)) * adhDist(a,t) * dt * dA;
        end
    end

    % calculate the variance
    for a=1:numel(angleDist(:,1))
        for t=1:numel(tensionDist(:,1))
            ASM = ASM + (2*tensionDist(t,1)*(1-cos(angleDist(a,1) * pi/360))-AFM)^2 * adhDist(a,t) * dt * dA;
        end
    end

    ASM = sqrt(ASM);

    [maxVal,maxInd] = max(adhDist,[],1);
    [~,ind] = max(maxVal);

    ADMindex = [maxInd(ind),ind];

    % calculate the mode of adhesion
    ADM = (2*tensionDist(ADMindex(2),1)*(1-cos(angleDist(ADMindex(1),1) * pi/360)));

    adhHist = zeros(4001,2);
    adhHist(:,1) = (1:1:4001)';
    
    % calculate adhesion histohram
    for a=1:numel(angleDist(:,1))
        for t=1:numel(tensionDist(:,1))
            Si = 2*tensionDist(t,1)*(1-cos(angleDist(a,1) * pi/360)); 
            adhHist( round(Si)+1,2 ) = adhHist( round(Si)+1,2 ) + adhDist(a,t) * dA * dt;
        end
    end

    P = 0;
    n = quantiles;
    quantile = zeros(1,n);
    a = 1;
    for i=1:4000
        P = P + adhHist(i,2);
        if P > a/n && quantile(a)==0
            quantile(a) = i-1;
            a = a+1;
        end
    end
    quantile(n) = 4000;

    adhDistReduced = zeros( round(size(adhDist,1)/10), round(size(adhDist,2)/10));
    %downsample the distribution so it can be visualized
    for a=1:size(adhDistReduced,1)
        for t=1:size(adhDistReduced,2)
            adhDistReduced(a,t) =  sum(sum(adhDist(1+(a-1)*10:a*10, 1+(t-1)*10:t*10)));
        end
    end

end