% this script demonstrate why the slope a is critical manipulation
% seperating the self-localization hypothesis from the homing hypothesis 
% To find a reduction in heading variance but not in homing variance, we
% try to make the distances between two heading weights that produce the
% largest reductions in homing variance and heading variance as far as
% possible.

%?_?^2=W_(?_PI)^2× ?_(?_PI)^2 + W_(?_LM)^2 × ?_(?_LM)^2, find W_(?_LM)
%makes
%?_?^2 minimum.
%?_(?OPO’)^2=(a - W_(?_PI ) )^2× ?_(?_PI)^2 + W_(?_LM)^2 × ?_(?_LM)^2+
%?_ue^2. find W_(?_LM) makes
%?_(?OPO’)^2 minimum.
%get the distance between these two weights. the distance = (1-a)*
%W_(?_LM)that makes %?_?^2 minimum.

close all;
a = [0.5,0.66,0.33]; % use three slope a

H_STD_L=[20,20,20]; % assume variance in estimating heading from Landmark is 0.25 of that from PI
H_STD_PI=2*H_STD_L; % H_STD_L the heading SD in the Landmark Condition, H_STD_PI Path integration condition

H_Var_PI=H_STD_PI.^2;
H_Var_L=H_STD_L.^2;

%using our theory we can get beta_Var_PI, beta_Var_L, and also any beta_Var
%in conflict condition using different weight of PI, the weight=1 for beta_Var_PI, weight=0 for beta_Var_L

P_Var_PI=a.^2.*H_Var_PI; % position error variance is the same for all conditions.
P_Var_L=P_Var_PI;

beta_Var_PI=(a-1).^2.*H_Var_PI; % beta is the homing error
beta_Var_L = a.^2.*H_Var_PI+H_Var_L;


weight = [0:0.01:1]; % PI weight
landmarWeight=1-weight;



for j=1:size(a,2)
beta_Var_BO_SelfLocalization (j,:) = (a(j)- weight).^2*H_Var_PI(j)+(1-weight).^2*H_Var_L(j);%homing error in the BOth condition according to self localization hypothesis , see table 7B or equation 10
beta_Var_BO_beta_combination(j,:)=weight.^2.*beta_Var_PI(j) + (1-weight).^2.*beta_Var_L(j); %homing error in the Both condition according to the homing hypothesis

He_Var_BO_He_combination(j,:)=weight.^2.*H_Var_PI(j) + (1-weight).^2.*H_Var_L(j);%combination for heading

Pe_Var_BO_Pe_combination(j,:)=weight.*P_Var_PI(j) + (1-weight).*P_Var_L(j);%combination for position, should be the same value 

end


for j=1:size(a,2)
    
   
    figure ('position', [0, 0, 300, 250]) 
    
    Y=sqrt(beta_Var_BO_SelfLocalization(j,:));
    Y1=sqrt(beta_Var_BO_beta_combination(j,:));
    Y2=sqrt(He_Var_BO_He_combination(j,:));
    Y3=sqrt(Pe_Var_BO_Pe_combination(j,:));
    
    plot (landmarWeight, Y , 'g-',  landmarWeight, Y2 , 'r-', landmarWeight, Y3 , 'k-');
    [M,I]=min(Y);
    
    text(landmarWeight(I)-0.1,M+1, ['Homing error' ]);
    hold on
    
  
    
    
    plot(landmarWeight(I),0,'--ro','LineWidth',2,'MarkerEdgeColor','k','MarkerFaceColor','g','MarkerSize',5)
    %text(landmarWeight(I)-0.25,3, [ 'Weight for' char(10) 'smallest homing SD' ]);
    
    hold on
    
    [M,I]=min(Y2);
    
    text(landmarWeight(I),M, ['Heading error']);
    
    plot(landmarWeight(I),0,'--ro','LineWidth',2,'MarkerEdgeColor','k','MarkerFaceColor','r','MarkerSize',5)
    %text(landmarWeight(I)-0.1,3, ['Weight for ' char(10) 'smallest heading SD']);
   
    
    
    hold on
    plot(landmarWeight(I),Y(I),'--rs','LineWidth',2,'MarkerEdgeColor','k','MarkerFaceColor','r','MarkerSize',10)
   % text(landmarWeight(I),Y(I), ['both cue' char(10) '']);
    
    [M,I]=min(Y3);
    text(landmarWeight(I)/8,M, 'Position error');
    
    
   
    
    
    
    hold on
    

    title (['a=',num2str(a(j))])
    xlabel('Landmark weight in heading estimation')
    ylabel({'Predicted circular SD (°)'})
    axis ([0,1,0,40])
    
   
    set(findall(gcf,'-property','FontSize'),'FontSize',9)

end