I cannot plot the Bisection Method Code

I must write a program with bisection methot which has initial guesses as xl=0 xu=3. The iterations must end when | Ea | < 10^(-3) . xr represent the current root. I must plot | Ea | versus i and also f(xr) versus i.

Also my output must be print the i , xl , xu, f(xl), f(xu), xr, f(xr), | Ea | in each iteration.

I try to do plotting but when I run my code there is:

Error using plot

Vectors must be the same length.

NOTE: I want to plot with using set because I think it is easier to understand for me.

THANKS..

clc
clear all
close all
f=@(x) x^3 - x - 3;

serr=[]  %empty set for plotting
sf=[]

xl=0;  %initial guesses
xu=3;  %initial guesses
xr1=100;
error=100; %initial error, here we assumed %100 error at the beginning
tolerance=1e-03; %stopping criteria
fl=f(xl);
fu=f(xu);
fr = f(xr1);
m=1; %counter for while loop
display('BISECTION METHOD')
display('---------------------')
fprintf('%10s %10s %10s %10s %10s %10s %10s %10s\n','m','xl','xu','f(xl)','f(xu)','f(xl)','f(xu)','|Ea|')

for i=1:1:1
 fprintf('%2.0f %12.5f %12.5f %12.5f %12.5f %12.5f %12.5f %12.5f\n', m, xl, xu,f(xl),f(xu), xr1,f(xr1), error)
 
 while error>tolerance
     xr2 = (xu+xl)/2;
     fr=f(xr2);
     
     if sign(fr)==sign(fl)
         xl = xr2;
         fl = fr;
     else
         xu = xr2;
         fu = fr;
     
     xr1=xr2;
     xr2 = (xl+xu)/2;
     
     end
     error = abs(xr2-xr1)/xr2*100;
     serr=[serr error];
     sf=[sf f(xr2)];
     m = m+1;
     fprintf('%2.0f %12.5f %12.5f %12.5f %12.5f %12.5f %12.5f %12.5f\n', m, xl, xu,f(xl),f(xu), xr2,f(xr2), error)
 end
end

     
subplot(1,2,1)
plot(1:m,serr,'-o')
xlabel(' i')
ylabel ('error')

subplot(1,2,2)
plot(1:m,sf,'-o')
xlabel(' i')
ylabel ('f(xr)')

Answer 1

[Geoff Hayes]

hgrlk - the problem is that your m is equal to the size of your serr and sf plus one. So when you call

plot(1:m,serr,'-o')

the array 1:m is one element larger than serr and so the error message makes sense. You can do one of three things - initialize m to zero so that

 serr=[serr error];
 sf=[sf f(xr2)];
 m = m+1;

are all kept in sync (here, m will now correspond to the length of serr and sf). Or you can plot your data like

 plot(1:length(serr),serr,'-o')

or simply

 plot(serr,'-o')

[hgrlk]

Oh, I get it. Thanks for the helping. I couldn't think m equal to size of set plus one.

Thanks again it works now..