How to display the results of each iterative step until convergence is reached?

Hi

I am very, very new to matlab. Below is my code. The solution is getting converged in 4th iteration. I wish to display the four values of u1, lam1. Please help.

Thank you.

clc
clear all
close all
%%Stability Problem
%Input
syms u lam phi 
H(u,lam)= u^3-8*u^2+18*u-2*lam;
K(u,lam)= diff(H,u);
DK(u) = diff(K,u);
l(phi)= phi-1;
r0 = 2;
tolX = 10^-4;
%Initial Step
u0= 1.17573;
lam0=5.86484;
phi0=1;
%Iterative step (K=0)
for k= 1:10;
    H0 = vpa(H(u0,lam0));
    K0 = vpa(K(u0,lam0));
    del_u_r = vpa(-K0^-1*H0);
    del_u_lam = vpa(K0^-1*r0);
    h_phi = K0*phi0+DK(u0)*phi0*del_u_r;
    del_phi_phi = (-K0^-1)*h_phi;
    h_lam =DK(u0)*phi0*del_u_lam;
    del_phi_lam = (-K0^-1)*h_lam;
    l_com_phi=(phi0)/norm(phi0); 
    del_lam =( -l_com_phi*del_phi_phi+l(phi0))/(l_com_phi*del_phi_lam);
    del_phi = del_phi_phi+del_lam*del_phi_lam;
    del_u = del_u_r+del_u_lam*del_lam;
    %update
    u1 = u0+del_u;
    lam1=lam0+del_lam;
    phi1=phi0+del_phi;
    u0=u1;
    lam0=lam1;
    phi0=phi1;
    if (norm(del_u)/norm(u1))< tolX
        break
    end

end

msg = ['The solution converged in ', num2str(k),'th iterations.'];
disp(msg)
fprintf('U = %.5f\n',u1); 
fprintf('lambda = %.5f\n',lam1);
fprintf('phi = %.0f\n',phi1);

[Jesus Sanchez]

Format your code properly please, its very difficult to read. Also, what do you want exactly? You are already showing the values at the end of the loop with fprint

[Hrishikesh Das]

Thank you for your comment. As you can see the solution converges in 4th iteration, I wish to display the results u1 and lam1 in every iterative step at the end. Hope I am able make you understand my question. Your help is highly appreciated.

Answer 1

[Image Analyst]

Before the last end of your for loop, insert this code:

	valueToCheck = norm(del_u)/norm(u1);
	fprintf('In iteration %d, norm(del_u)/norm(u1) = %f.\n', k, valueToCheck);
	if valueToCheck < tolX
		fprintf('    This is more than tolX, so we will continue with the loop now.\n', tolX);
	else
		fprintf('    This is less than tolX, so we will exit the loop now.\n', tolX);
		break
	end	

[Hrishikesh Das]

Thank you for you answer, however when I insert your code into mine I get the following output. Please have a look. I appreciate your help.

[Hrishikesh Das]

The value of tolX is 10^-4.

[Jesus Sanchez]

You have to sustitute your if condition for the one that Image analyst gave you. I include here the solution with his modification. Also, note that the solution provided by Image Analyst has a little mistake, as instead of a "<" it should be a ">".

Edit: I also modified it to show the values that you ask in your question.

clc
clear all
close all
%%Stability Problem
%Input
syms u lam phi 
H(u,lam)= u^3-8*u^2+18*u-2*lam;
K(u,lam)= diff(H,u);
DK(u) = diff(K,u);
l(phi)= phi-1;
r0 = 2;
tolX = 10^-4;
%Initial Step
u0= 1.17573;
lam0=5.86484;
phi0=1;
%Iterative step (K=0)
for k= 1:10;
    H0 = vpa(H(u0,lam0));
    K0 = vpa(K(u0,lam0));
    del_u_r = vpa(-K0^-1*H0);
    del_u_lam = vpa(K0^-1*r0);
    h_phi = K0*phi0+DK(u0)*phi0*del_u_r;
    del_phi_phi = (-K0^-1)*h_phi;
    h_lam =DK(u0)*phi0*del_u_lam;
    del_phi_lam = (-K0^-1)*h_lam;
    l_com_phi=(phi0)/norm(phi0); 
    del_lam =( -l_com_phi*del_phi_phi+l(phi0))/(l_com_phi*del_phi_lam);
    del_phi = del_phi_phi+del_lam*del_phi_lam;
    del_u = del_u_r+del_u_lam*del_lam;
    %update
    u1 = u0+del_u;
    lam1=lam0+del_lam;
    phi1=phi0+del_phi;
    u0=u1;
    lam0=lam1;
    phi0=phi1;
    
valueToCheck = norm(del_u)/norm(u1);
	fprintf('In iteration %d, \nlam1 = %f. \nu1 = %f. \nnorm(del_u)/norm(u1) = %f.\n',k,lam1,u1, valueToCheck);
	if valueToCheck > tolX
		fprintf('    This is more than tolX, so we will continue with the loop now.\n', tolX);
	else
		fprintf('    This is less than tolX, so we will exit the loop now.\n', tolX);
		break
	end
end

[Image Analyst]

Thanks for the fix Jesus. I couldn't actually run the code because I don't have the Symbolic Toolbox and the error crept in when I decided to copy and paste so it would say what happened in each case.

[Jesus Sanchez]

You are welcome! :)

[Hrishikesh Das]

I thank you all for extending your generous support. Thank you to help me learn and code better.