Nonlinear equations with Jacobian

Hi I am trying to solve a system of nonlinear equations with Jacobean provided. I solved the system with the Jacobean approximated with finite difference methods. However, I could not do it with the jacobean provided. the structure I followed is

function [y, JAC] =finalmodyld20002d_withjac(x) y = zeros (8, 1);

y(1)=(abs(((2/3)*x(1)+(1/3)*x(2))).^a)+... ((abs((2/3)*x(3)-(2/3)*x(4))).^a)+... ((abs((4/3)*x(5)-(x(6)/3))).^a)-... 2*(equivsigma/sigma0).^a; y(2)=... y(3)=... y(4)=... y(5)=... y(6)=... y(7)=... y(8)=...

if (nargout == 8)
  JAC = zeros (8, 8);

% end function JAC(1,1)=(16*abs((2*x(1))/3 + x(2)/3)^7*sign((2*x(1))/3 + x(2)/3))/3; JAC(1,2)=(8*abs((2*x(1))/3 + x(2)/3)^7*sign((2*x(1))/3 + x(2)/3))/3; JAC(1,3)=(16*abs((2*x(3))/3 - (2*x(4))/3)^7*sign((2*x(3))/3 - (2*x(4))/3))/3; JAC(1,4)=-(16*abs((2*x(3))/3 - (2*x(4))/3)^7*sign((2*x(3))/3 - (2*x(4))/3))/3; JAC(1,5)=-(32*abs(x(6)/3 - (4*x(5))/3)^7*sign(x(6)/3 - (4*x(5))/3))/3; JAC(1,6)=(8*abs(x(6)/3 - (4*x(5))/3)^7*sign(x(6)/3 - (4*x(5))/3))/3; JAC(1,7)=0; JAC(1,8)=0;

%%% JAC(2,1)= ... JAC(2,2)= JAC(2,3)= JAC(2,4)= JAC(2,5)= JAC(2,6)= JAC(2,7)=0; JAC(2,8)=0;

continue for other elements in the 8x8 jaconean

%%%

end  
end

after I constructed the function with its Jacobean, I run x0=[0.23;1.3;1.6;1.3;2.4;1;1.3;3]; options = optimoptions('fsolve','Display','iter','Algorithm','trust-region dogleg','FinDiffType','central','Jacobian','on'); [x,iter,fval]= fsolve(@finalmodyld20002d_withjac, x0,options)

But the following error shows:

Error using feval Output argument "JAC" (and maybe others) not assigned during call to "C:\Users\Hamzah Alharthi\Documents\MATLAB\finalmodyld20002d_withjac.m>finalmodyld20002d_withjac".

Error in fsolve (line 228) [fuser,JAC] = feval(funfcn{3},x,varargin{:});

Caused by: Failure in initial user-supplied objective function evaluation. FSOLVE cannot continue.

could you please help solving this issue?

Hamzah

Answer 1

[Torsten]

Take a look at the example under

http://de.mathworks.com/help/optim/ug/nonlinear-equations-with-analytic-jacobian.html

You will have to replace

if (nargout == 8)

by

if nargout > 1,

I guess.

Best wishes

Torsten.