Hi I am trying to solve a system of equations using fsolve or something similar with 4 variables. Please help

Equations are

r(1)= sqrt((x-15600)^2+(y-7540)^2+(z-20140)^2)-(300000(0.07074-d))

r(2)=sqrt((x-18760)^2+(y-2750)^2+(z-18610)^2)-(300000(0.07220-d))

r(3)=sqrt((x-17610)^2+(y-14630)^2+(z-13480)^2)-(300000(0.07690-d))

r(4)=sqrt((x-19170)^2+(y-610)^2+(z-18340)^2)-(300000(0.07242-d))

I am trying to use fsolve

F=nle(x) ; I am actually substitution x,y,z,d as x(1)….x(4)

Then writing the equation for F and then i do x0= a range which i dont understand at all what to pick.

And then fsolve(@nle,x0)

I am getting a lot of errors and nowhere near to my answer.

Answer 1

[Mischa Kim]

Rishav, try

 function r = test(r0)
 % options  = optimoptions('fsolve','Display','iter');  % new as of R2013a
 % options  = optimset('Display','iter','TolFun',1e-8); % before R2013a
 % [r,fval] = fsolve(@myfun,r0,options)                
 [r,fval] = fsolve(@myfun,r0)
 end
 function F = myfun(r)
 x = r(1);
 y = r(2);
 z = r(3);
 d = r(4);
 F = [sqrt((x-15600)^2+(y-7540)^2 +(z-20140)^2)-(300000*(0.07074-d));... 
      sqrt((x-18760)^2+(y-2750)^2 +(z-18610)^2)-(300000*(0.07220-d));...
      sqrt((x-17610)^2+(y-14630)^2+(z-13480)^2)-(300000*(0.07690-d));...
      sqrt((x-19170)^2+(y-610)^2  +(z-18340)^2)-(300000*(0.07242-d))];
 end

and use in the MATLAB command window

 r0 = [15000 10000 20000 0];
 r  = test(r0)

[Rishav]

Thanks for your help, but i am getting this error

Undefined function or method 'optimoptions' for input arguments of type 'char'.

[Rishav]

Also I have tried putting the myfun and test function in diff .m files and together as well, FYI

[Rishav]

I only need values for x,y and z. I think in my assignment there is a hint that says to subtract equation 1 from the last 3. I think that makes them equal to zero. Not sure again why x=r(1)…… Sorry, i am still a rookie.

[Mischa Kim]

OK. The above code should work, the options part is now commented out. Once you have this code running, you can use optimset, instead of optimoptions (new as of R2013a).

The starting values used above, r0 = [15000 10000 20000 0], seem to work.