MATLAB: Calculate the gradient of a function

gradient

Hello. I want to calculate the gradient of the function :

g={@(x)-x;@(x)x-1;@(y)-y;@(y)y-1};

with the following command :

gradient(g, [x, y]);

but I get the following error :

Undefined function or variable 'x'.

How I should proceed? Thanks.

Best Answer

You are confusing the numeric gradient function http://www.mathworks.com/help/matlab/ref/gradient.html with the symbolic gradient function, http://www.mathworks.com/help/symbolic/gradient.html

On the other hand, neither gradient() accepts a vector or cell array of function handles. Numeric gradient() accepts a numeric vector or array, and spacing distances for each of the dimensions. Symbolic gradient() accepts a scalar symbolic expression or symbolic function together with the variables to take the gradient over.

When you have a vector of functions to work with, you almost certainly want a jacobian rather than a gradient. Symbolic jacobian http://www.mathworks.com/help/symbolic/jacobian.html accepts a symbolic expression, symbolic function, or symbolic vector (but not a cell array of function handles.)

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MATLAB: About gradient and diff

Symbolic gradient, http://www.mathworks.com/help/symbolic/gradient.html, is the gradient vector of a scalar function, but numeric gradient, http://www.mathworks.com/help/matlab/ref/gradient.html is just "Numerical gradient". It is numerical gradient for which the "2" would mean a point spacing of 2, and it is the symbolic gradient for which the "2" would mean double differentiation.

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

Best Answer

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MATLAB: About gradient and diff

MATLAB: How to calculate gradients of a symbolic function

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