%Written by Anna Grosberg and Nancy Drew
%
%Created on: April 8, 2013
%updated:
%
%Synthetic data for COOP

%This code will create the plots to compare the synthetic data with
%alanlytical predictions for the most correlated and the uncorelated COOP

close all
clear all

%Mean angle for constructs A (Figure synthetic data paper COOP)
A_m = 0.75*pi();
%A_m = 0;
%Mean angle for constructs B (Figure synthetic data paper COOP)
B_m = 0.25*pi();
%B_m=0;

%Specify the standard deviation for the Gaussian distributions of P and Q.
%Remember that in this formulation we always assume that P has better (or
%the same) organization as Q.
P_sigma = [0,0,0,0,0,0.1,0.5,0.5];
%P_sigma=0;
P_mean = [A_m,B_m,B_m,B_m,A_m,A_m,A_m,B_m];
P_color = ['b','r','r','r','b','b','b','r'];
Q_sigma = [0,0.1,0.5,100,0.5,0.5,0.5,100];
%Q_sigma=0;
Q_mean = [B_m,A_m,A_m,A_m,B_m,B_m,B_m,A_m];
Q_color = ['r','b','b','b','r','r','r','b'];
P_Ylim = [1,1,1,1,1,0.08,0.08,0.08];
Q_Ylim = [1,0.08,0.08,0.08,0.08,0.08,0.08,0.08];
F_Ylim = [1,0.08,0.08,0.08,0.08,0.08,1,0.08];

%Number of points (i.e. pseudo vectors to make)
N_points = 10^8;

%Number of cases
N_cases = length(P_sigma);

%initilize figure number
Fig_Num = 0;
%cycle through each case
for case_num=1:N_cases
    if Q_sigma(case_num) < P_sigma(case_num)
        disp(['Error p is less organized than q in run ', case_num]);
    else
        if P_sigma(case_num) == 100 %check if P is random
            %generate random distribution
            alpha = (pi()).*rand(N_points,1) + (P_mean(case_num) - 0.5*pi());
        else
            %generate a distribution with a standard deviation P_sigma(i)
            alpha = normrnd(P_mean(case_num),P_sigma(case_num),[N_points,1]);
        end
        %Specify distribution for the Uncorrelated case
        if Q_sigma(case_num) == 100 %check if Q is random
            %generate random distribution
            beta_u = (pi()).*rand(N_points,1) + (Q_mean(case_num) - 0.5*pi());
        else
            %generate a distribution with a standard deviation Q_sigma(i)
            beta_u = normrnd(Q_mean(case_num),Q_sigma(case_num),[N_points,1]);
        end
        %Specify distribution for the Correlated case
        if Q_sigma(case_num) == 100 %check if Q is random
            %generate random distribution
            theta = pi().*(rand(N_points,1)-0.5); %randomely distributed theta, shifted to have mean at 0            
        else
            F_sigma = sqrt((Q_sigma(case_num))^2 - (P_sigma(case_num))^2); %stdandard deviation of theta
            %generate a distribution with a standard deviation F_sigma            
            theta = normrnd(0,F_sigma,[N_points,1]); %theta distributed randomely
        end
        %beta is the sum of theta and alpha and we move the average
        beta_c = alpha + theta+(Q_mean(case_num) - P_mean(case_num));
        
        
       %===============================Code OOP for component 1=================
        u(1,:) = cos(alpha(:));
        u(2,:) = sin(alpha(:));
        for i=1:2
            for j=1:2
                OOT_All(i,j,:)=u(i,:).*u(j,:);
                OOT_Mean(i,j) = mean(OOT_All(i,j,:));
            end
        end
        OOT = 2.*OOT_Mean-eye(2);
        [directions,orient_parameters]=eig(OOT);
        [Orientation_order_parameter,I] = max(max(orient_parameters));
        Orientation_order_parameter_1(case_num)=Orientation_order_parameter
        OOP1hist=mod(atan2(u(2,:),u(1,:)),pi().*ones(size(u(1,:))));
        Fig_Num = Fig_Num +1;
        figure(Fig_Num)
        num_bins = 180;
        angle_vec_dist = 0:(pi/(num_bins-1)):pi;
        [n,xout] = hist(OOP1hist,angle_vec_dist);
        bar(xout,n./sum(n),'hist');
        h = findobj(gca,'Type','patch');
        set(h,'FaceColor',P_color(case_num),'EdgeColor',P_color(case_num))
        title(['Orientation for First Component P_\sigma = ', num2str(P_sigma(case_num)),' rad, P_\rho = ', num2str(P_mean(case_num)),' rad, OOP = ',num2str(Orientation_order_parameter_1(case_num)) ],'FontName','Arial','FontSize',8,'FontWeight','bold');
        xlabel('Orientation Angle (rad)','FontName','Arial','FontSize',8,'FontWeight','bold');
        ylabel('Normalized Occurence','FontName','Arial','FontSize',8,'FontWeight','bold');
        xlim([0 pi]);
        %y_max = max(n./sum(n));
        ylim([0 P_Ylim(case_num)]);
        set(gca,'XTick',0:pi/4:pi)
        set(gca,'XTickLabel',{'0','pi/4','pi/2','3pi/4','pi'},'FontSize',8)
        saveas(figure(Fig_Num),['UOrientationFirstComponent_case_num',num2str(case_num),'rad.fig']);
        saveas(figure(Fig_Num),['UOrientationFirstComponent_case_num',num2str(case_num),'rad.pdf']);
        
        %===============================Code OOP for component 2 Uncor=================
        v_u(1,:) = cos(beta_u(:));
        v_u(2,:) = sin(beta_u(:));
        for i=1:2
            for j=1:2
                OOT_All(i,j,:)=v_u(i,:).*v_u(j,:);
                OOT_Mean(i,j) = mean(OOT_All(i,j,:));
            end
        end
        OOT = 2.*OOT_Mean-eye(2);
        [directions,orient_parameters]=eig(OOT);
        [Orientation_order_parameter,I] = max(max(orient_parameters));
        Orientation_order_parameter_2_u(case_num)=Orientation_order_parameter
        OOP1hist=mod(atan2(v_u(2,:),v_u(1,:)),pi().*ones(size(u(1,:))));
        Fig_Num = Fig_Num +1;
        figure(Fig_Num)
        num_bins = 180;
        angle_vec_dist = 0:(pi/(num_bins-1)):pi;
        [n,xout] = hist(OOP1hist,angle_vec_dist);
        bar(xout,n./sum(n),'hist');
        h = findobj(gca,'Type','patch');
        set(h,'FaceColor',Q_color(case_num),'EdgeColor',Q_color(case_num))
        title(['Orientation for Second Component (Uncorrelated) Q_\sigma = ', num2str(Q_sigma(case_num)),' rad, Q_\rho = ', num2str(Q_mean(case_num)),' rad, OOP = ',num2str(Orientation_order_parameter_2_u(case_num))],'FontName','Arial','FontSize',8,'FontWeight','bold');
        xlabel('Orientation Angle (rad)','FontName','Arial','FontSize',8,'FontWeight','bold');
        ylabel('Normalized Occurence','FontName','Arial','FontSize',8,'FontWeight','bold');
        xlim([0 pi]);
        %y_max = max(n./sum(n));
        ylim([0 Q_Ylim(case_num)]);
        set(gca,'XTick',0:pi/4:pi)
        set(gca,'XTickLabel',{'0','pi/4','pi/2','3pi/4','pi'},'FontSize',8)
        saveas(figure(Fig_Num),['UOrientationSecondComponent_case_num',num2str(case_num),'rad.fig']);
        saveas(figure(Fig_Num),['UOrientationSecondComponent_case_num',num2str(case_num),'rad.pdf']);
        %===============================Code OOP for component 2 Cor=================
        v_c(1,:) = cos(beta_c(:));
        v_c(2,:) = sin(beta_c(:));
        for i=1:2
            for j=1:2
                OOT_All(i,j,:)=v_c(i,:).*v_c(j,:);
                OOT_Mean(i,j) = mean(OOT_All(i,j,:));
            end
        end
        OOT = 2.*OOT_Mean-eye(2);
        [directions,orient_parameters]=eig(OOT);
        [Orientation_order_parameter,I] = max(max(orient_parameters));
        Orientation_order_parameter_2_c(case_num)=Orientation_order_parameter
        OOP1hist=mod(atan2(v_c(2,:),v_c(1,:)),pi().*ones(size(u(1,:))));
        Fig_Num = Fig_Num +1;
        figure(Fig_Num)
        num_bins = 180;
        angle_vec_dist = 0:(pi/(num_bins-1)):pi;
        [n,xout] = hist(OOP1hist,angle_vec_dist);
        bar(xout,n./sum(n),'hist');
        h = findobj(gca,'Type','patch');
        set(h,'FaceColor',Q_color(case_num),'EdgeColor',Q_color(case_num))
        title(['Orientation for Second Component (Correlated) Q_\sigma = ', num2str(Q_sigma(case_num)),' rad, Q_\rho = ', num2str(Q_mean(case_num)),' rad, OOP = ',num2str(Orientation_order_parameter_2_c(case_num))],'FontName','Arial','FontSize',8,'FontWeight','bold');
        xlabel('Orientation Angle (rad)','FontName','Arial','FontSize',8,'FontWeight','bold');
        ylabel('Normalized Occurence','FontName','Arial','FontSize',8,'FontWeight','bold');
        xlim([0 pi]);
        %y_max = max(n./sum(n));
        ylim([0 Q_Ylim(case_num)]);
        set(gca,'XTick',0:pi/4:pi)
        set(gca,'XTickLabel',{'0','pi/4','pi/2','3pi/4','pi'},'FontSize',8)
        saveas(figure(Fig_Num),['OrientationSecondComponent_case_num',num2str(case_num),'rad.fig']);
        saveas(figure(Fig_Num),['OrientationSecondComponent_case_num',num2str(case_num),'rad.pdf']);
        %========================Code COOP (Uncor)======================
        nonzero_co_orientation=[alpha beta_u];
        f(1,:) = u(1,:).*v_u(1,:)+u(2,:).*v_u(2,:);
        f(2,:) = u(1,:).*v_u(2,:)-u(2,:).*v_u(1,:);
        for i=1:2
            for j=1:2
                OOT_All(i,j,:)=f(i,:).*f(j,:);
                OOT_Mean(i,j) = mean(OOT_All(i,j,:));
            end
        end
        OOT = 2.*OOT_Mean-eye(2);
        [directions,orient_parameters]=eig(OOT);
        [Orientation_order_parameter,I] = max(max(orient_parameters));
        COOP_Uncor(case_num)=Orientation_order_parameter
        fs(1,:)=sign(f(2,:)).*f(1,:);
        fs(2,:)=sign(f(2,:)).*f(2,:);
        COOPhist=mod(atan2(fs(2,:),fs(1,:)),pi().*ones(size(u(1,:))));
        [n,xout] = hist(COOPhist,angle_vec_dist);
        Fig_Num = Fig_Num +1;
        figure(Fig_Num)
        bar(xout,n./sum(n),'hist');
        h = findobj(gca,'Type','patch');
        set(h,'FaceColor','g','EdgeColor','m')
        title(['Co-Orientation (Uncorrelated) P_sigma=',num2str(P_sigma(case_num)),', Q_sigma=',num2str(Q_sigma(case_num)),'COOP=',num2str(COOP_Uncor(case_num))],'FontName','Arial','FontSize',8,'FontWeight','bold');
        xlabel('Co-Orientation Angle (rad)','FontName','Arial','FontSize',8,'FontWeight','bold');
        ylabel('Normalized Occurence','FontName','Arial','FontSize',8,'FontWeight','bold');
        xlim([0 pi]);
        %y_max = max(n./sum(n));
        ylim([0 F_Ylim(case_num)]);
        set(gca,'XTick',0:pi/4:pi)
        set(gca,'XTickLabel',{'0','pi/4','pi/2','3pi/4','pi'},'FontSize',8)
        saveas(figure(Fig_Num), ['UCOOP_case_num',num2str(case_num),'.fig']);
        saveas(figure(Fig_Num), ['UCOOP_case_num',num2str(case_num),'.pdf']);
        %========================Code COOP (Cor)======================
        nonzero_co_orientation=[alpha beta_c];
        f(1,:) = u(1,:).*v_c(1,:)+u(2,:).*v_c(2,:);
        f(2,:) = u(1,:).*v_c(2,:)-u(2,:).*v_c(1,:);
        for i=1:2
            for j=1:2
                OOT_All(i,j,:)=f(i,:).*f(j,:);
                OOT_Mean(i,j) = mean(OOT_All(i,j,:));
            end
        end
        OOT = 2.*OOT_Mean-eye(2);
        [directions,orient_parameters]=eig(OOT);
        [Orientation_order_parameter,I] = max(max(orient_parameters));
        COOP_Cor(case_num)=Orientation_order_parameter
        fs(1,:)=sign(f(2,:)).*f(1,:);
        fs(2,:)=sign(f(2,:)).*f(2,:);
        COOPhist=mod(atan2(fs(2,:),fs(1,:)),pi().*ones(size(u(1,:))));
        [n,xout] = hist(COOPhist,angle_vec_dist);
        Fig_Num = Fig_Num +1;
        figure(Fig_Num)
        bar(xout,n./sum(n),'hist');
        h = findobj(gca,'Type','patch');
        set(h,'FaceColor','g','EdgeColor','m')
        title(['Co-Orientation (Correlated) P_sigma=',num2str(P_sigma(case_num)),', Q_sigma=',num2str(Q_sigma(case_num)),'COOP=',num2str(COOP_Cor(case_num))],'FontName','Arial','FontSize',8,'FontWeight','bold');
        xlabel('Co-Orientation Angle (rad)','FontName','Arial','FontSize',8,'FontWeight','bold');
        ylabel('Normalized Occurence','FontName','Arial','FontSize',8,'FontWeight','bold');
        xlim([0 pi]);
        %y_max = max(n./sum(n));
        ylim([0 F_Ylim(case_num)]);
        set(gca,'XTick',0:pi/4:pi)
        set(gca,'XTickLabel',{'0','pi/4','pi/2','3pi/4','pi'},'FontSize',8)
        saveas(figure(Fig_Num), ['COOP_case_num',num2str(case_num),'.fig']);
        saveas(figure(Fig_Num), ['COOP_case_num',num2str(case_num),'.pdf']);
    end
end
Theoretical_Uncor_COOP = Orientation_order_parameter_2_u.*Orientation_order_parameter_1;
Theoretical_Corr_COOP = Orientation_order_parameter_2_c./Orientation_order_parameter_1;
save('Output_Cor_Uncor_COOP.mat','Theoretical_Uncor_COOP','COOP_Uncor','Theoretical_Corr_COOP','COOP_Cor','Orientation_order_parameter_1','Orientation_order_parameter_2_u','Orientation_order_parameter_2_c');