%=====================================================
%
% MOS21 - 2013
% 
% Minimisation de l'Ed de 2 ressorts par dichotomie.
%
%=====================================================

%=== nettoyage de matlab
clc;
clear all;
close all;

%=== parametres
L=2;
L1=1.5;
L2=1.2;
k1=10;
k2=15;

x_exact=(k1*L1+k2*L-k2*L2)/(k1+k2);

n=100;%nb points tracés Ed(x)
epsilon_cvg=1E-8;

%=== courbes Ed(x) Edp(x)
table_x=zeros(n,1);
table_Ed=zeros(n,1);
table_Edp=zeros(n,1);
for i=1:n
    xi=(i-1)*L/(n-1);
    table_x(i,1)=xi;
    table_Ed(i,1)=Ed(xi,k1,k2,L1,L2,L);
    table_Edp(i,1)=Edp(xi,k1,k2,L1,L2,L);
end

figure(1)
hold on
plot(table_x,table_Ed,'-b','markersize',10,'linewidth',2);
plot(x_exact,Ed(x_exact,k1,k2,L1,L2,L),'rx','markersize',10,'linewidth',2);
grid;
xlabel('x');
ylabel('E(x)');
legend('energie de deformation p/r x','minimum analytique');
hold off

figure(2)
hold on
plot(table_x,table_Edp,'-g','markersize',10,'linewidth',2);
plot(x_exact,Edp(x_exact,k1,k2,L1,L2,L),'rx','markersize',10,'linewidth',2);
grid;
xlabel('x');
ylabel('dE(x)/dx');
legend('derivee de l energie de deformation p/r x','zero analytique');
hold off


%=== algo dichotomie
xG=0;
xC=L/2;
xD=L;

compteur=1;
test_fin=0;

while(test_fin==0)

    fG=Edp(xG,k1,k2,L1,L2,L);
    fC=Edp(xC,k1,k2,L1,L2,L);
    fD=Edp(xD,k1,k2,L1,L2,L);

    h3=figure(3);
    hold on
    plot(table_x,table_Edp,'-g','markersize',10,'linewidth',2);
    plot(x_exact,Edp(x_exact,k1,k2,L1,L2,L),'rx','markersize',10,'linewidth',2);
    plot([xG,xD],[fG,fD],'ko','markersize',10,'linewidth',2);
    grid;
    xlabel('x');
    ylabel('E(x)');
    legend('energie de deformation p/r x','minimum analytique','bornes dichotomie');
    hold off
    
    input('pour continuer presser ENTER');
    close(h3);
    
    if(fG*fC<0)
        xG=xG;
        xD=xC;
        xC=(xG+xD)/2;
    else
        xG=xC;
        xD=xD;
        xC=(xG+xD)/2;
    end
    
    if(abs(xG-xD)<epsilon_cvg)
        test_fin=1;
    end
    
    fprintf('* fin itération %d\n-> xG=%f\n-> xD=%f\n',compteur,xG,xD);
    
    compteur=compteur+1;
end

figure(3)
hold on
plot(table_x,table_Edp,'-g','markersize',10,'linewidth',2);
plot(x_exact,Edp(x_exact,k1,k2,L1,L2,L),'rx','markersize',10,'linewidth',2);
plot(xC,Edp(xC,k1,k2,L1,L2,L),'ro','markersize',10,'linewidth',2);
grid;
xlabel('x');
ylabel('dE(x)/dx');
legend('derivee de l energie de deformation p/r x','zero analytique','zero par dichotomie');
hold off

figure(4)
hold on
plot(table_x,table_Ed,'-b','markersize',10,'linewidth',2);
plot(x_exact,Ed(x_exact,k1,k2,L1,L2,L),'rx','markersize',10,'linewidth',2);
plot(xC,Ed(xC,k1,k2,L1,L2,L),'ro','markersize',10,'linewidth',2);
grid;
xlabel('x');
ylabel('E(x)');
legend('energie de deformation p/r x','minimum analytique','minimum par dichotomie');
hold off