How do I calculate the numerical Jacobian for a set of six non linear equations ?

Hi All

how do I calculate the Jacobian matrix for the following equations based on the example I put afterwards ?

please don't share tutorial links

F(1) = (x(1) - h1 )^2 + (x(2)- v1 )^2 + (x(3)-w1)^2 - A(1)^2;
F(2) = (x(1) - h2 )^2 + (x(2)- v2 )^2 + (x(3)-w2)^2 - A(2)^2;
F(3)=  (x(1)-x(2))^2 + (x(2)-x(3))^2 + (x(3)-w3)^2 - A(3)^2;

x is the varaible to solve

% Example: (nonlinear least squares)
%  xdata = (0:.1:1)';
%  ydata = 1+2*exp(0.75*xdata);
%  fun = @(c) ((c(1)+c(2)*exp(c(3)*xdata)) - ydata).^2;
%
%  [jac,err] = jacobianest(fun,[1 1 1])

My problem : in the example only the coeficients have been differentiated. in my equations , x should be differentiated

[Matt J]

The title of your post says 6 non-linear equations, but your post has only 3.

[Star Strider]

Context: Do I need to reset Fsolve Parameters if I use Fsolve twice in my code ?

[farzad]

Star : why have you linked this question to another of mine ?

Matt : does not matter , your answer was great enoough. I got it

[Matt J]

No, it doesn't matter. Just a remark.

Answer 1

[Matt J]

Jac=nan(3,3); %pre-allocate

 Jac(1,:) =  2*[ x(1)-h1  , x(2)-v1  ,  x(3)-w1 ];

 Jac(2,:) =  2*[ x(1)-h2  , x(2)-v2  ,  x(3)-w2 ];

 Jac(3,:) =  2*[ x(1)-x(2)  , 2*x(2)-x(1)-x(3) , 2*x(3)-x(2)-w3];