MATLAB: Solving non-linear parametric system of equations

fsolve parameter non linear system equations

Hi everyone
I've been struggling to solve a non-linear system of parametric equations for a certain range of of values with the command fsolve.
Here is my discribed system function :
function F=thsol(th)
th3=1
        F = @(th) [1.*cos(th1)+0.6.*cos(th2)+0.2.*cos(th3)
1.*sin(th1)+0.6.*sin(th2)+0.2.*sin(th3)-1];
this works :
sol = fsolve (thsol(th),[1,1])
but when i define th3 as a variable as followed :
function F=thsol(th,th3)
        F = @(th,th3) [1.*cos(th1)+0.6.*cos(th2)+0.2.*cos(th3)
1.*sin(th1)+0.6.*sin(th2)+0.2.*sin(th3)-1];
and write down :
th3=1
sol = fsolve (@(th) thsol(th,th3),[1,1])
i get this :
"Warning: Trust-region-dogleg algorithm of FSOLVE cannot handle non-square systems; using
Levenberg-Marquardt algorithm instead. 
> In fsolve at 314
??? Undefined function or method 'isfinite' for input arguments of type 'function_handle'.
Error in ==> levenbergMarquardt at 14
if any(~isfinite(costFun))
Error in ==> fsolve at 373
    [x,FVAL,JACOB,EXITFLAG,OUTPUT,msgData] = ..."
I really don't get what's going wrong since i'm trying to solve the exact same system with the exact same values, only calling th3 as variable parameter. Anyone could tell me where i went wrong? thank you all

Best Answer

It seems that the function thsol returns a function handle instead of a vector for the output F.
Your first call:
sol = fsolve (thsol(th),[1,1])
does pass the function handle, which is the output of thsol(th)
sol = fsolve (@(th) thsol(th,th3),[1,1])
Here thsol still returns a function handle which is wrapped around another function handle which is not the expected input for fsolve.
Try the following
    F =  @(th,th3) [1.*cos(th1)+0.6.*cos(th2)+0.2.*cos(th3) 1.*sin(th1)+0.6.*sin(th2)+0.2.*sin(th3)-1];
th3=1;
sol = fsolve(@(th)F(th,th3),[1,1])
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