Finding jacobian of a matrix

How to find jacobian of a matrix. I am trying to find out the jacobian of the following but still unable..

[J W] = jacobian(x,z) where z=ones(m,1) x is any matrix.

There are two variables J and W.How to find out the value of J and W manually

Answer 1

[Carlos]

The jacobian command calculates symbollically the jacobian of a given matrix.

The following example can be found in the Mathworks symbolic toolbox user's guide

    syms r l f 
    x = r*cos(l)*cos(f); y = r*cos(l)*sin(f); z = r*sin(l);
    J = jacobian([x; y; z], [r l f])

This code yields the following result

J =
[ cos(l)*cos(f), -r*sin(l)*cos(f), -r*cos(l)*sin(f)]

As you can infer from the explanation, the second argument of the command jacobian is a vector containing the symbolic variables of your matrix (not a numeric vector). Once you calculate the symbolic expression of the Jacobian of the given matrix, you can find the numeric value of the Jacobian matrix using the subs command.In this case if r l and f have a value of 1, we can do:

J=subs(J,{r,l,f},{ones(3,1)},0);