How to a complex plot of three different variables ?

Hi all,

I have this function,

 k=[0.5 0.8]; 
 F(x,y,z,k)=0.1*x*y+(k^2)*sqrt((1/x*y)^2+(2/z)^2)+3*z*y);

I am trying to plot this function in terms of three parameters for 2 values of k, k=0.5, 0.8; my ultimate goal is to find the optimal values for x,y and z for minimum F,

any help and hint in this?

Answer 1

[Walter Roberson]

Vectorize the code on the right side. Put it into an anonymous function of three four variables. Now create an anonymous function

Fv1 = @(x) F(x(1),x(2),x(3), k(1))

now you can

X0 = rand(1,3);
[x1,f1] = fminsearch(Fv1, X0)

and construct similar for k(2). Compare f1 and f2 to determine which k value leads to a better optimized value. Use x1 or x2 for the x, y, z values.

[AbuYusuf]

Thanks Walton for your input,

when I use the fminsearch, I always got an error; this is what I use,

 k=0.8; x0=0;
fv=@(x)(0.1*x(3)*x(2)+4*x(1)*x(2)+(k^2)*sqrt((1/(x(2)*x(3)))^2+(0.65/x(1))^2));
[x,fval] = fminsearch(fv,x0);

I changed the initial condition x0 to 1e-6 but still I am getting the same error, I am not sure which x0 shoud I pick, but diffentaly they are bigger than zero for all and different ranges, ex. x(1) in micro range, x(2) in pico range and x(3) in Mega range.

I am expecting results like; x(1)=1e-6, x(2)=1e-12; x(3)=1e6; Is there a clue how can i choose the right x0?

Answer 2

[Image Analyst]

What is the value of z? If it's variable, then how do you expect to "plot" a function of 3 continuous variables? That would be like you're trying to model the temperature distribution in a solid at every single (x,y,z) point in the solid. You can't "plot" that. You'd have to do volume visualization of the solid volume, like isosurfaces or cutaway views. Or else you could do it for a few discrete values of z and use plot3().