Débbut exercice 3

Author: Enzoupi

GCST.m

@@ -1,12 +1,13 @@
-function [x,Jx,GJx,nit] = GCST(J,GJ,x0,pas,epsil,nitmax,findic)
+function [x,Jx,GJx,nit] = GCST(J,GJ,x0,pas,epsil,nitmax)
 error = 10000;
 nit = 0;
+disp('In GCST')
 while (error > epsil) && (nit < nitmax)
-   error = abs(norm(GJ(x0,findic)));
-   x = x0 - pas .* GJ(x0,findic);
+   error = abs(norm(GJ(x0)));
+   x = x0 - pas .* GJ(x0);
    nit = nit +1;
    x0=x;
-   Jx = J(x,findic);
-   GJx = GJ(x,findic);
+   Jx = J(x);
+   GJx = GJ(x);
 end
 

GJ.m

@@ -3,6 +3,5 @@
 %   Detailed explanation goes here
 U=direct(F);
 G=adjoint(U);
-
 end
 

J.m

@@ -1,9 +1,9 @@
 function [Y] = J(F)
 %UNTITLED5 Summary of this function goes here
 %   Detailed explanation goes here
+global Uobs
 n=length(F)+1;
 h=1/n;
-J=h/2*sum(direct(F)-Uobs); % A faire
-
+Y=h/2*sum( (direct(F)-Uobs).^2 );
 end
 

TP2.m

@@ -6,7 +6,7 @@
 %% Tests de convergence du problème direct
 
 %Test dans un cas simple
-n = 150
+n = 150;
 h = 1/n;
 x=linspace(h,1-h,n-1);
 F = pi^2*sin(pi.*x)';
@@ -69,6 +69,14 @@
 ylabel('log10 de l erreur')
 title(['Convergence du probleme adjoint : ' num2str(coeff(1))])
 
-%% Exercice 3
-
+%% Exercice 3 Gradient et Gradient conjugué à pas constant
+n = 150;
+h = 1/n;
+x=linspace(h,1-h,n-1);
+Uobs = sin(pi.*x)';
+F = zeros(length(x),1);
+pas = 0.5;
+epsil = 1e-2;
+nitmax = 1000;
+[xmin,Jxmin,GJxmin,nit] = GCST(@J,@GJ,F,pas,epsil,nitmax);