How to plot a function dependent on no. of iterations, provided it plots till nth iteration where n is the number where the function is converged?

Hello All,

I am trying to plot a function vs no. of iterations. In the for loop, i have given the convergence condition, but I am unable to plot for f(x) vs no. iterations (till convergence). Please help.

Its of the form:

for m=1:n
    pu(m)=(-1)^m)/((2*m)+1))*(exp(-((2*m)+1)))
    e = e+pu;
    if (abs(pu)/e)<(10^(-6))    %convergence check
        break
    end
    
end
hold all
plot(1:n,pu,'linestyle','none','marker','*')

Answer 1

[VBBV]

n= 10;
e = 0;
for m=1:n
  pu(m)=(-1)^m/((2*m)+1)*(exp(-((2*m)+1)))
  e = e+pu(m);
  if (abs(pu(m))/e)>(10^(-6))    %convergence check
      break
  end  
end

pu = -0.0166

pu = 1×2

-0.0166 0.0013

pu = 1×3

-0.0166 0.0013 -0.0001

pu = 1×4

-0.0166 0.0013 -0.0001 0.0000

pu = 1×5

-0.0166 0.0013 -0.0001 0.0000 -0.0000

pu = 1×6

-0.0166 0.0013 -0.0001 0.0000 -0.0000 0.0000

pu = 1×7

-0.0166 0.0013 -0.0001 0.0000 -0.0000 0.0000 -0.0000

pu = 1×8

-0.0166 0.0013 -0.0001 0.0000 -0.0000 0.0000 -0.0000 0.0000

pu = 1×9

-0.0166 0.0013 -0.0001 0.0000 -0.0000 0.0000 -0.0000 0.0000 -0.0000

pu = 1×10

-0.0166 0.0013 -0.0001 0.0000 -0.0000 0.0000 -0.0000 0.0000 -0.0000 0.0000

hold all
plot(1:n,pu,'linestyle','-','marker','.')

Check the convergence condition

[VBBV]

Note that your error term is inverse with respect to your tol criteria in convergence condition

[ISHA ARORA]

Sir, please have a look at this full code. I want my plot for 'pu' v/s no. of iterations (till convergence). But instead I am getting till 100th iteration. But my convergence check tells that at 11th iteration, series is converged. So I want that value of 'pu' should be plotted only until 11th iteration.

n=100;
b=6.9;
r=5;
y=(r-1)+0.5;
e=0;z=2;
U = 4500;
q=2*pi*(U/60)*r;
pu=zeros(1,n);
u=zeros(1,n);
for m=1:n
    pu(m)=(4*q/pi)*((((-1)^m)/((2*m)+1))*(exp(-((2*m)+1)*(pi/(2*b))*z))*(cos(((2*m)+1)*(pi/(2*b))*y)));
    e = e+pu;
    if (abs(pu)/e)<(10^(-6))    %convergence check
        break
    end
    
end
hold all
plot(1:n,pu,'linestyle','none','marker','*')

[VBBV]

n=100;
b=6.9;
r=5;
y=(r-1)+0.5;
e=0;z=2;
U = 4500;
q=2*pi*(U/60)*r;
pu=zeros(1,n);
u=zeros(1,n);
for m=1:n
    pu(m)=(4*q/pi)*((((-1)^m)/((2*m)+1))*(exp(-((2*m)+1)*(pi/(2*b))*z))*(cos(((2*m)+1)*(pi/(2*b))*y)));
    e = e+pu(m);  % note change here
    if (abs(pu(m))/e)>(10^(-6))    %convergence check
        u(m)=pu(m);
        hold all
        plot(1:m,u(1:m),'linestyle','-','color','b','linewidth',2); % note change here 
        grid on
    elseif (abs(pu(m))/e)<(10^(-6))
        break
    end
end

There are few changes how you plot it.

[ISHA ARORA]

Thank you so much for your kind help, Sir.

[ISHA ARORA]

While plotting the graph for different U values, legend is not taking the different markers specified, but taking a single red colour * marker for all values, can you please help me with this, Sir?

mrkr = {'*','o','^','.','+','x','square','diamond','pentagram','<'};
clr={'red' 'green' 'blue' 'cyan'	'magenta'	'yellow'	'black' '#D95319' '#0072BD' '#7E2F8E'};
figure
for cidx=1:npoints
    q=2*pi*(U(cidx)/60)*r;
for m=1:n
    pu(m)=(4*q/pi)*((((-1)^m)/((2*m)+1))*(exp(-((2*m)+1)*(pi/(2*b))*z))*(cos(((2*m)+1)*(pi/(2*b))*y)));
    e = e+pu(m);
    if (abs(pu(m))/e)>(10^(-6))    %convergence check
        u(m)=pu(m);
        hold all
        plot(1:m,u(1:m),'linestyle','none','marker',mrkr{cidx},'Color',clr{cidx})
        xlabel('Number of Iterations') 
        ylabel('Velocity at different iterations') 
        title('Velocity v/s No. of Iterations for U varying from 4500RPM to 9000RPM')
        legendInfo{cidx} = ['U = ' num2str(U(cidx))];
        grid on
    elseif (abs(pu(m))/e)<(10^(-6)) 
        break
    end
end
legend(mrkr{cidx},legendInfo)
end

[VBBV]

legend(mrkr{cidx},legendInfo)

Put this line inside the inner for loop. After legendInfo. Everytime the inner for loop exits, it's over written with initial values for mrkr and clr index.

[VBBV]

u=zeros(n,npoints); % change also This line in beginning 
u(m,cidx)=pu(m);
hold all 
plot(1:m,u(1:m,cidx),'linestyle','none','marker',mrkr{cidx},'Color',clr{cidx})

You also need to change these two lines inside the for loop. As you can see the u value is dependent on pu which is again varying with each outer iteration of for loop.