Are there any other ways(function) of finding jacobian matrix numerically beside the function numjac

Are there any other ways(known function) of finding jacobian matrix numerically beside the function numjac?

basically I am going to input something like x=[x1 x2 x3 .....xn]' into a function such as x'*x and find its jacobian

Answer 1

[Vladimir Sovkov]

The function you describe is no more than the squared norm of the vector x, i.e. it is a scalar function of a vector argument.

Its Jacobi matrix is just the doubled vector: 2*x.

[Kevin Lin]

yes true, I understand that , what I am asking is if there is any other call function that can give me a jacobian matrix like numjac do, in order to compare them.

[Walter Roberson]

You can use jacobian() from the Symbolic Toolbox, substitute in the current coordinates, and double() the result.

[Kevin Lin]

if the size of my x is change every time by iteration , it seems hard to define the symtex for jacobian()

[Walter Roberson]

Not sure what the difficulty is for the syntax?

for K  = 1 : 7
    X = sym('x', [1 K]);
    x = sort(rand(1,K) * 10);
    F = prod(X - randn(1,K));   %some function of the variables
    J{K} = double(subs(jacobian(F, X), X, x));
end

[Vladimir Sovkov]

I am unaware about other call functions. In my opinion, it is rather easy to find the Jacobi matrix "manualy" via a straightforward computing of the necessary derivatives by using either the finite-differenece algorithm or the Fourier-transform algorithm.

[Kevin Lin]

yes true, big thanks for the answer