Show every step of lsqnonlin won't work

Hello there,

I want so visualize every step of lsqnonlin() in an example of 10 random generated points for a circle in the same figure.

I start to generate 10 random points and show the curve fitting by lsqnonlin. Now, in the same figure, I want to visualize every iteration step as a circle.

This is my Code:

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

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 on
xlabel ('x-Achse');
ylabel ('y-Achse');
title ('Punktwolke für n=10');
legend ('n=10','Ausgleichskreis','Location','northeast');

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 

Can anyone show me how to do it right?

Thanks

Answer 1

[Stephan]

I think you look for something like this:

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

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 on
xlabel ('x-Achse');
ylabel ('y-Achse');
title ('Punktwolke für n=10');
legend ('n=10','Ausgleichskreis','Location','northeast');

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

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

However, the problem is that you have extra arguments that you have to give to the outputFcn. Im not sure if this result is exactly what you want, but im sure ith shows how to correct the error and see whats going on step by step