How to show every iteration step of lsqnonlin()?

Hello again,

I am solving a nonlinear compensation problem on a cirlce. So first i am creating 10 points randomly.

phi1=1:((2*pi/10.71)):2*pi;
r = -0.5 + (0.5 + 0.5) * rand(1,10);  
xrand = sin(phi1) + 0.25 * r;              
yrand = cos(phi1) + 0.25 * r;               

figure (1)                              
sz = 80;                                
scatter(xrand,yrand,sz,'ob','linewidth',1);    
axis ([-1.5 1.5 -1.5 1.5]);
grid on;
hold on

After that, I am using lsqnonlin to solve the equation for a circle and plot the result with the 10 points.

f=@(x)((xrand-x(1)).^2+(yrand-x(2)).^2-x(3).^2)';
x0=[0,0,1];                       
KreisFit1 = lsqnonlin(f,x0);        
                                     
figure (1)                             
phi = linspace(0,2*pi,100);             
xFit1 = KreisFit1(3)*cos(phi) + KreisFit1(1); 
yFit1 = KreisFit1(3)*sin(phi) + KreisFit1(2); 
plot(xFit1,yFit1,'b-','linewidth',3)
hold off

I also want to show every step of the iteration done by lsqnonlin in the same figure.

How can i visualize each Step of the iteration?

Thanks for every help :)

Answer 1

[Steven Lord]

You probably want to specify a PlotFcn as part of the options that get passed into lsqnonlin. See this documentation page for more information.

[Nico Lange]

Okay, i've tried it like this:

f=@(x)((xrand-x(1)).^2+(yrand-x(2)).^2-x(3).^2)';

x0=[0,0,1];                          
KreisFit = lsqnonlin(f,x0);       
                                     
figure (1)                              
phi = linspace(0,2*pi,100);          
xFit = KreisFit(3)*cos(phi) + KreisFit(1); 
yFit = KreisFit(3)*sin(phi) + KreisFit(2); 
plot(xFit,yFit,'b-','linewidth',3)
hold off

options = optimoptions(@lsqnonlin,'Display','iter-detailed','MaxfunEvals',35);
[x1abw,resnorm,residual,exitflag,output] = lsqnonlin(f,x0,[],[],options);

xplot = x(1);
yplot = x(2);
rplot = x(3);
str1 = ['Parameter x = ' num2str(x(1))];
str2 = ['Parameter y = ' num2str(x(2))];
str3 = ['Parameter r = ' num2str(x(3))];
disp(str1)
disp(str2)
disp(str3)

But I get an Error at xplot = x(1), because x is an unrecognized function or variable?

[Steven Lord]

options = optimoptions(@lsqnonlin,'Display','iter-detailed','MaxfunEvals',35);

You did not specify that you wanted lsqnonlin to use a PlotFcn. Consider something along the lines of the attached.

[Nico Lange]

Sorry, the example didn't really helped. But i understood what you mean with PlotFcn. I've tried it like this

options = optimoptions(@lsqnonlin,'Display','iter','OutputFcn',@outfun);
[x,resnorm,residual,exitflag,output] = lsqnonlin(f,x0,[],[],options);

function stop = outfun(xrand,yrand,state)
        stop=false;
        switch state
            case 'iter'
                figure (1);
                hold on;
                grid on;
                plot(xrand,yrand,'ko')
                plot(xrand,((xrand-x(1)).^2+(yrand-x(2)).^2-x(3).^2), 'r');
                hold off
            case 'interrupt'
            case 'init'
            case 'done'  
            otherwise
        end
    end 

But it tells me that there is an invalid data argument at plot(xrand, yrand,'ko').