Calculate the Gradient of a given function using the forward and central quotients.

I am very bad at this, it would be hard for me to calculate it even for only one variable, but now that I have to calculate the Gradient i am completely lost.

Please help me out, any sort of help is very much appreciated.

My failed code:

function f1x = vordiff(f,x,h,y,z)
%Vorwärtsdifferenzenquotienten
  function f = f(x,y,z)
    f = (4*x+3*y+2*z)*e^(-3*x^2)-4*y^2-8*x*y-2*z^2
  end

f1x = (f(x+h)-f(x))/h;
f1z = (f(z+h)-f(z))/h;
f1y = (f(y+h)-f(y))/h;

end

Answer 1

[KSSV]

function f1x = vordiff(f,x,h,y,z)
%Vorwärtsdifferenzenquotienten
syms x y z ;
f = (4*x+3*y+2*z)*e^(-3*x^2)-4*y^2-8*x*y-2*z^2
fx = diff(f,x) ; 
fy = diff(f,y) ;
fz = diff(f,z) ; 

end

[kai kai]

Yeah but I think we are not allowed to use the syms package.

[Bobby Fischer]

Try this: (for small h)

function [grad]=evaluation_grad(x,y,z,h)
f=(4*x+3*y+2*z)*exp(-3*x^2)-4*y^2-8*x*y-2*z^2; % f(x,y,z)

f1x=(4*(x+h)+3*y+2*z)*exp(-3*(x+h)^2)-4*y^2-8*(x+h)*y-2*z^2; % f(x+h,y,z)
f1y= (4*x+3*(y+h)+2*z)*exp(-3*x^2)-4*(y+h)^2-8*x*(y+h)-2*z^2; % f(x,y+h,z)
f1z= (4*x+3*y+2*(z+h))*exp(-3*x^2)-4*y^2-8*x*y-2*(z+h)^2; % f(x,y,z+h)

fx=(f1x-f)/h;
fy=(f1y-f)/h;
fz=(f1z-f)/h;

grad=[fx; fy; fz];
end

And this:

function[grad]=eval_vordiff(x0,y0,z0)
syms x y z ;
f = (4*x+3*y+2*z)*exp(-3*x^2)-4*y^2-8*x*y-2*z^2;
fx = diff(f,x) ; 
fy = diff(f,y) ;
fz = diff(f,z) ; 

x=x0;
y=y0;
z=z0;

fx0=subs(fx);
fy0=subs(fy);
fz0=subs(fz);

grad=[fx0; fy0; fz0];
grad=double(grad);
end 

Compare the results between the two.

[kai kai]

Thank you so so much you saved me. Very helpful. I don't know if you can put it as an answer so that I can vote it as best answer.

[kai kai]

And the results were exactly the same, I don't know if this is how it is supposed to be.