MATLAB: Gradient of Substituted Symbolic Variables

gradientsubstitutionsymbolic variable

Hello, I'm having a problem with finding the gradient of a substituted symbolic variable:

My code is:

syms x y z
f = x^2 + x + y^2 - y;
subs(f, y, z)
g = gradient(f, [x, z])

When I run it, the gradient turns out to be [2*x+1, 0]. It doesn't seem to calculate the z variable derivative. Does anyone know why?

Tks

Best Answer

It is because your function f is not updated. Here is what you need to do.

syms x y z
 f = x^2 + x + y^2 - y;
 f = subs(f,y,z);
 g = gradient(f, [x,z])

The result is

 g =
 2*x + 1
 2*z - 1

Related Solutions

MATLAB: How to calculate gradients of a symbolic function

%construct the input
syms x y z
f(x,y,z) = 2*y*z*sin(x) + 3*x*sin(z)*cos(y);
%and assume you are passing f into a different function so x y z are not still around
g = yadayada(f);
function g = yadayada(f)
  %so we have an input symbolic function but for some reason
  %we are not in the context where the variables came from. 
  %it turns out to be as simple as
  g = gradient(f);
  %or for greater certainty you could
  g = gradient(f, symvar(f));  %which is what the simple call does
  %or perhaps you have a reason to do
  syms x y z
  g = gradient(f(x, y, z), [x y z])
  %for example it might be a symbolic function in three other
  %variables that you want to re-label as x, y, z.
end

MATLAB: Finding the null gradient

See if this does what you want:

syms x y
f = [x^2 + x, y^2 - y];
g1 = gradient(f(1), [x, y]);
g2 = gradient(f(2), [x, y]);
x0 = solve(g1 == 0)
y0 = solve(g2 == 0)

Best Answer

Related Solutions

MATLAB: How to calculate gradients of a symbolic function

MATLAB: Finding the null gradient

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