Why am I not able to plot the error vs iterations?

I am new to MATLAB. Can someone please tell what should I do to get a plot of the error (here, abs (z-Z)) vs the number of iterations? Another question is, earlier I used different variables and for x-axis plot of i (using plot(i,abs(z-Z)), I used ilim([0 20]), which showed "undefined function ilim for input argument double". Does this mean I can plot only when variables are named as x and y?

z=1;
for i=1:100
    f=(1-z)*exp(-2*z)-3*exp(-z)+2;
    fprime=exp(-2*z)*(2*z-3)+3*exp(-z);
    Z=z;
    z=Z-f/fprime;
    if abs (Z-z)<10^(-6)
        break
    end
x=i;
y=abs (Z-z);
plot(x,y)
xlim([0 20])
ylim([0 1])
end

[Serhiy Shtovba]

1. Type "hold on" before plot.
2. But your code is not perfect. It is not a good idea to use plot inside for. It will be better to collect error on each iteration in vector, for example, y(i)=abs (Z-z), and finnaly, after end_of_for make your graph: plot(1:100, y, 'ro--'

Answer 1

[Image Analyst]

You plotted inside the loop but did not put "hold on" so each time you plotted it blew away the prior data point. It's probably better to just keep track of the error and plot everything all at once once the loop exists:

z = 1;
for k = 1 : 100
	f = (1-z)*exp(-2*z)-3*exp(-z)+2;
	fprime = exp(-2*z)*(2*z-3)+3*exp(-z);
	Z = z;
	z = Z - f / fprime;
	theError(k) = abs(Z - z);
	if abs (Z-z)<10^(-6)
		break
	end
end
iterationNumber = 1 : length(theError);
plot(iterationNumber, theError, 'b.-', 'LineWidth', 2, 'MarkerSize', 30)
grid on;
xlim([1, max(iterationNumber)])
title('Error vs. Iteration Number', 'FontSize', 20);
xlabel('Iteration Number', 'FontSize', 20);
ylabel('abs(Error)', 'FontSize', 20);

Or else you'd have to say "hold on" inside the loop but then you'd only get markers and no lines connecting the markers.

z = 1;
for k = 1 : 100
	f = (1-z)*exp(-2*z)-3*exp(-z)+2;
	fprime = exp(-2*z)*(2*z-3)+3*exp(-z);
	Z = z;
	z = Z - f / fprime;
	theError = abs(Z - z);
	plot(k, theError, 'b.-', 'LineWidth', 2, 'MarkerSize', 30)
	hold on;
	if abs (Z-z)<10^(-6)
		break
	end
end
grid on;
title('Error vs. Iteration Number', 'FontSize', 20);
xlabel('Iteration Number', 'FontSize', 20);
ylabel('abs(Error)', 'FontSize', 20);

[Setsuna Yuuki.]

Awesome!

[Ipshita]

Thankyou very much for explaining so nicely and for fast response. I understood now :)

[Leo Torres]

Thanks for this clear answer. I was having a 'brain fart' plotting the relative error norm within a for loop and this helped greatly. Cheers! Saludos!

Answer 2

[Setsuna Yuuki.]

You can store the data of (Z-z) in a vector:

for ...
zz(i) = (Z-z)
 if abs(zz)<10^(-6)
        break
    end
end...
    

And leave the graph out of the loop

x=1:100;
y=zz;
plot(x,y);
xlim([0 20])
ylim([0 1])

[Ipshita]

Thanks for answering :)