Printing an error message if jacobi's method, does not converges.

Hi, so I want to print an error message if my jacobi's method does not converge. I've made it so it Converges but dont know how to code the part where it prints if it doesnt.

% Accepts Inputs from the User's Matrix A and Vector B
a = input('Matrix A: ');
b = input('Vector B: ');

% Initial Guess
P = [0;0;0];


% Number of iterations
I = 10; % Max Iterations
L = length(b);
Z = zeros(L,1);
itc = 0; %Counts Number of Iterations

% Convergence Tolerance
t = 0.0001;

% Code
while n0 <= I & itc <10
    for i = 1:L
        Z(i) = (b(i)/a(i,i)) - (a(i,[1:i-1,i+1:L])*P([1:i-1,i+1:L]))/a(i,i); %Jacobi's Method
    end
    itc = 1+ itc;
    fprintf (' %d Iteration \n',itc);
    Z
    % So ABS of X - Guess Vector?
    if abs (Z-P) < t % if norm(r) < some tolerance , it is converged
        break  
    end     
    P = Z;
end

Answer 1

[Star Strider]

One approach would be to set a limit on ‘itc’. If it fails to converge before ‘itc’ reaches some value (perhaps ‘iteration_limit’) then the error would display. Use an if bolck to test in each iteration, and display if ‘itc’ exceeds that limit.

EDIT — (28 May 2021 at 4:00)

% Code
iteration_limit = 11;
while n0 <= I & itc <10
    for i = 1:L
        Z(i) = (b(i)/a(i,i)) - (a(i,[1:i-1,i+1:L])*P([1:i-1,i+1:L]))/a(i,i); %Jacobi's Method
    end
    itc = 1+ itc;
    fprintf (' %d Iteration \n',itc);
    Z
    % So ABS of X - Guess Vector?
    if abs (Z-P) < t % if norm(r) < some tolerance , it is converged
        break  
    end     
    P = Z;
    if itc > iteration_limit
        error('Jacobi method did not converge by %d iterations.',iteration_limit)
        break
    end
end

.

[Mustafa Ali]

Sorry could you perhaps show me an example of what you mean. I'm kinda new to this haha.

[Mustafa Ali]

Hmm, I changed it to 11 and still no error

% Accepts Inputs from the User's Matrix A and Vector B
a = input('Matrix A: ');
b = input('Vector B: ');

% Initial Guess
P = [0;0;0];


% Number of iterations
I = 11; % Max Iterations
L = length(b);
Z = zeros(L,1);
itc = 0; %Counts Number of Iterations

% Convergence Tolerance
t = 0.0001;

% Code
iteration_limit = 11;
while n0 <= I & itc <10
    for i = 1:L
        Z(i) = (b(i)/a(i,i)) - (a(i,[1:i-1,i+1:L])*P([1:i-1,i+1:L]))/a(i,i); %Jacobi's Method
    end
    itc = 1+ itc;
    fprintf (' %d Iteration \n',itc);
    Z
    % So ABS of X - Guess Vector?
    if abs (Z-P) < t % if norm(r) < some tolerance , it is converged
        break  
    end     
    P = Z;
    if itc > iteration_limit
        error('Jacobi method did not converge by %d iterations.',iteration_limit)
        break
    end
end

[Star Strider]

I am not certain what the inputs should be, so I am not certain how to test your code.

First, check to see what ‘itc’ is. It may never be greater than 11.

Testing that if block itself:

iteration_limit = 11;
itc = 12;
    if itc > iteration_limit
        error('Jacobi method did not converge by %d iterations.',iteration_limit)
%         break
    end

Jacobi method did not converge by 11 iterations.

So that part of the code works! (I commented-out the break call because it throws an error if it is not inside a loop, so not applicable in this specific test.)

.

[Mustafa Ali]

Hey, thanks for helping out. For Matix A I used [2 1 3;8 8 13;10 9 19] and for Vector B i used [ 7;37;47]. I did get a result. But just to confirm. Did I input your code corretly?

% Accepts Inputs from the User's Matrix A and Vector B
a = input('Matrix A: ');
b = input('Vector B: ');

% Initial Guess
P = [0;0;0];


% Number of iterations
I = 10; % Max Iterations
L = length(b);
Z = zeros(L,1);
itc = 0; %Counts Number of Iterations

% Convergence Tolerance
t = 0.0001;

% Code
while itc < I;
    for i = 1:L
        Z(i) = (b(i)/a(i,i)) - (a(i,[1:i-1,i+1:L])*P([1:i-1,i+1:L]))/a(i,i); %Jacobi's Method
    end
    itc = 1+ itc;
    fprintf (' %d Iteration \n',itc);
    Z
    % So ABS of X - Guess Vector?
   
    if converged % if norm(r) < some tolerance , it is converged
        break
    end
    P = Z;
end
iteration_limit = 11;
itc = 12;
    if itc > iteration_limit
        error('Jacobi method did not converge by %d iterations.',iteration_limit)
%          break
    end

[Star Strider]

‘Did I input your code corretly?’

Not the way I intended that it be used.

I changed the code to do what I intended, and since the routine converges in about 11 iterations with the test matrices, I changed ‘iteration_limit’ to 9 to test the convergence failure if block.

It works correctly.

a = [2 1 3;8 8 13;10 9 19]

a = 3×3

2 1 3 8 8 13 10 9 19

b = [ 7;37;47]

b = 3×1

7 37 47

% Initial Guess
P = [0;0;0];
% Number of iterations
I = 10; % Max Iterations
L = length(b);
Z = zeros(L,1);
itc = 0; %Counts Number of Iterations
% Convergence Tolerance
t = 0.0001;
% Code
iteration_limit = 9;                            % <— CHANGE THIS TO 11 (OR WHATEVER VALUE YOU WANT FOR THE LIMIT)
while itc < I;
    for i = 1:L
        Z(i) = (b(i)/a(i,i)) - (a(i,[1:i-1,i+1:L])*P([1:i-1,i+1:L]))/a(i,i); %Jacobi's Method
    end
    itc = 1+ itc;
    fprintf (' %d Iteration \n',itc);
    Z
    % So ABS of X - Guess Vector?
   
    if abs (Z-P) < t % if norm(r) < some tolerance , it is converged
        break
    end
    P = Z;
    if itc >= iteration_limit
        error('Jacobi method did not converge by %d iterations.',iteration_limit)
        break
    end
end

 1 Iteration 

Z = 3×1

3.5000 4.6250 2.4737

 2 Iteration 

Z = 3×1

-2.5230 -2.8947 -1.5592

 3 Iteration 

Z = 3×1

7.2862 9.6817 5.1728

 4 Iteration 

Z = 3×1

-9.1000 -11.0670 -5.9472

 5 Iteration 

Z = 3×1

17.9543 23.3893 12.5054

 6 Iteration 

Z = 3×1

-26.9528 -33.6507 -18.0551

 7 Iteration 

Z = 3×1

47.4080 60.9174 32.5991

 8 Iteration 

Z = 3×1

-75.8574 -95.7566 -51.3335

 9 Iteration 

Z = 3×1

128.3785 163.8993 87.7570

Jacobi method did not converge by 9 iterations.

Success!

.

Answer 2

[Sulaymon Eshkabilov]

Hi,

Here is an easy solution:

... 
if abs (Z-P) < t % if norm(r) < some tolerance , it is converged
        break  
    else
        error('No convergence achieved!')
    end     
    P = Z;
    end
    ...

[Mustafa Ali]

If I do that, it still doesnt show the error message, I have to do something with the iteration number. I want it so that it goes to iteration 11 and says "ERROR" something like that.

[Sulaymon Eshkabilov]

The above proposed code works for convergence t = 0.0001. Test your example with tighter convergence, i.e. t = 0.00000001 or sth like that and you will see the ERROR message.

If you wish to set up with the interation number then

...
t = 0.00001;  % Convergence

while abs (Z-P) < t % convergence check 
    for i = 1:L
        Z(i) = (b(i)/a(i,i)) - (a(i,[1:i-1,i+1:L])*P([1:i-1,i+1:L]))/a(i,i); %Jacobi's Method
    end
    itc = 1+ itc;
    fprintf (' %d Iteration \n',itc);
    Z
    if itc > 10 % if norm(r) < some tolerance , it is converged
        error('No convergence achieved!')
    end
    P = Z;
end

[Mustafa Ali]

Hey, so it works but, is there a way where It can displays number if iterations until it can't converge anymore and prints an error message. The code you've given works very good but it stops at iteration 11 which is converged. I want it so that it displays until it actually cannot converge.

These are what im using for Matix A and vector B

Matix A: [19 3 1;3 10 2;1 2 10]

Vector B: [ 19;29;35]

PS: I commented saying I wanted it to go up to the 11th iteration and stop. But i realised it would just be incorrect for my task.