How to plot these function plesa help

Hello.

I tried almost everything, but with no succsess. Maybe anyone knows and can share matlab code to plot these function: f(x) = (4 - 2.1*x1^2 + x1^4/3)*x1^2 + x1*x2 + (-4 + 4*x2^2)*x2^2

the function is taken from here: http://www.mathworks.com/help/gads/examples/minimization-using-simulated-annealing-algorithm.html

Thank you

Answer 1

[Mischa Kim]

Joe, you could use

 [x1,x2] = meshgrid(0:0.5:10,0:0.5:10);
 f = (4 - 2.1*x1.^2 + x1.^4/3).*x1.^2 + x1.*x2 + (-4 + 4*x2.^2).*x2.^2;
 surf(x1,x2,f)

[Joe Gani]

thank you I fugured these solution too but why the function is not like these made with WOLFRAM ALPHA: http://www.wolframalpha.com/input/?i=plot+y+%3D+%284+-+2.1*x%5E2+%2B+x%5E%284%2F3%29%29*x%5E2+%2B+x*z+%2B+%28-4+%2B+4*z%5E2%29*z%5E2

[Mischa Kim]

It is a slightly different function (see 4/3) and a different range. Try

 [x1,x2] = meshgrid(0.9:0.1:1.4,-1:0.1:1);
 f = (4 - 2.1*x1.^2 + x1.^(4/3)).*x1.^2 + x1.*x2 + (-4 + 4*x2.^2).*x2.^2;
 surf(x1,x2,f)

[Joe Gani]

Thank you I understand but these answer made new question. Why I get an error if i change bounds in meshgrid I want to draw in range -64 to 64 on x1 and x2 axes.

Thank you for your help.

[Walter Roberson]

The function has x1^(4/3) . When x1 is negative, the result is complex.

Note that x1^(4/3) is not the same thing as (x1^4)^(1/3) and is potentially different again from (x1^(1/3))^4; just as x1^(1/2) is not the same as (x1^2)^(1/4) . Taking a number to a fractional power requires choosing one root, not hunting through the integer multiples of the exponent to find one that will make the root real-valued.

Perhaps you want,

f = (4 - 2.1*x1.^2 + (x1.^4).^(1/3)).*x1.^2 + x1.*x2 + (-4 + 4*x2.^2).*x2.^2;

but be aware that might not match the formula on the paper.

[Joe Gani]

if helps the function in matlab code is:

   y = (4-2.1.*x1.^2+x1.^4./3).*x1.^2+x1.*x2+(-4+4.*x2.^2).*x2.^2;