multiple function_handle in one function

Hello there,

I have the following function handle (function of a cirlce):

f1=@(a)((x1-a(1)).^2+(y1-a(2)).^2-a(3).^2);

x=a(1);
y=a(2);
r=a(3);

x1 and y1 are generated randomly (10 points)

phi1 = linspace(0, 2*pi, 10);             
r1 = -0.5 + (0.5 + 0.5) * rand(1,10);     
x1 = sin(phi1) + 0.25 * r1;               
y1 = cos(phi1) + 0.25 * r1;

To continue, I need the derivate of f1 for x, y and r in one function df(x0), where x0 describes inital values.

So, if i set for example x0=[0,0,1] i need df(x0) as a Matrix with the soultions of df out of x=0, y=0, r=1. I tried to build the derivates by hand:

DFx1= @(a) 2.*((sqrt((x1-a(1)).^2 + (y1-a(2)).^2) - a(3)).*(a(1)-x1))./(sqrt((x1-a(1)).^2 + (y1-a(2)).^2));
DFy1= @(a) 2.*((sqrt((x1-a(1)).^2 + (y1-a(2)).^2) - a(3)).*(a(2)-y1))./(sqrt((x1-a(1)).^2 + (y1-a(2)).^2));
DFr1= @(a) 2.*(a(3)-sqrt((x1-a(1)).^2 + (y1-a(2)).^2));

but I don't know how to continue.

Any ideas? Thanks

Sry for bad english, not my first language.

Answer 1

[Ameer Hamza]

Instead of defining three function handles, you can defined one vector-valued functions

df = @(a) [2.*((sqrt((x1-a(1)).^2 + (y1-a(2)).^2) - a(3)).*(a(1)-x1))./(sqrt((x1-a(1)).^2 + (y1-a(2)).^2));
           2.*((sqrt((x1-a(1)).^2 + (y1-a(2)).^2) - a(3)).*(a(2)-y1))./(sqrt((x1-a(1)).^2 + (y1-a(2)).^2));
           2.*(a(3)-sqrt((x1-a(1)).^2 + (y1-a(2)).^2))];

[Nico Lange]

Thank you :)

[Ameer Hamza]

I am glad to be of help!!! :)