Solving non-linear equation in vector form

Hi all, hope you are doing well.

Soi have a simple equation where the known value is a vector. So i need to get a vector as the solution.

The equation is very simple and can be easily caluclated by hand but i require it to be solved using Matlab.

Here is the code i have tried:

u2 = rand(1,1000);
syms t1
eq = t1.^2/64 == u2;
solve(eq, t1)

Any help would be appreciated, thanks.

Answer 1

[Matt J]

If you have the Optimization Toolbox,

u2=[1,4,9];

opts=optimoptions('fsolve','SpecifyObjectiveGradient',true,'OptimalityTolerance',1e-12);

t1=fsolve(@(t1)objfunc(t1,u2),u2,opts)

Equation solved, inaccuracy possible.

The vector of function values is near zero, as measured by the value
of the function tolerance. However, the last step was ineffective.

t1 = 1×3

8.0000 16.0000 24.0000

function  [err, J]=objfunc(t1,u2)

  err=t1.^2/64-u2;
  J=speye(numel(u2))/32; %Jacobian

end

[Tayyab Khalil]

Yes that works fine, but is there not a easier way to solve this relatively simple problem?

Answer 2

[Matt J]

syms u t
fun=matlabFunction( solve(t^2/64==u,t) );

u2=[1,4,9];

t1=fun(u2)

t1 = 2×3

-8 -16 -24 8 16 24

[Tayyab Khalil]

Yeah that's excellent. Thanks a lot!

Answer 3

[Matt J]

u2 = rand(1,1000);

t1=8*sqrt(u2);

[Tayyab Khalil]

Yes this is the simple manual solution but i require it in Matlab.

[Matt J]

All the commands in my solution are Matlab commands...

[Tayyab Khalil]

I meant that only putting the equation in its original form in Matlab and making matlab solve it for t1 rather than separting t1 ourself.