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

Question

Hrishikesh Das 2019-12-14

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/496596-how-to-display-the-results-of-each-iterative-step-until-convergence-is-reached

评论： Hrishikesh Das 2019-12-14

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);

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Jesus Sanchez 2019-12-14

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 2019-12-14

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.

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Answer 1

Image Analyst 2019-12-14

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/496596-how-to-display-the-results-of-each-iterative-step-until-convergence-is-reached#answer_406357

在 MATLAB Online 中打开

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	

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Jesus Sanchez 2019-12-14

编辑：Jesus Sanchez 2019-12-14

在 MATLAB Online 中打开

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

Jesus Sanchez 2019-12-14

You are welcome! :)

Hrishikesh Das 2019-12-14

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

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

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

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