Evaluate in a single value a function matrix

Hi i have a to program Newton Raphson in many variables so for example: If i have a function

just like

It is known the Jacobian of f will return in this case a matrix of 2x2. I need to evaluate in a value for example u1=1 and u2=2. But f(1,1) obviously doenst work, i need to evaluate numerically this function and its jacobian and extend this for many variables above 2. By the way the jacobian is:

As you can see for example matrix A(1,1) returns element not a value so how can i evaluate a matrix and a vector in a known number without using x=rand(2,1), x(1),x(2) cause for many variables this will be more dificult to do it.

Thank you

Answer 1

[Walter Roberson]

Use the Symbolic Toolbox to build the equations. Then use matlabFunction with the 'vars' option passing in a cell array that contains a single entry that is the vector of variable names. matlabFunction will then generate an anonymous function with all of the variables extracted from a single vector of inputs.

syms u1 u2
f = [exp(u1)-cos(u2); exp(u2)-u1^2];
fh = matlabFunction(f, 'vars', {[u1, u2]})

fh = function_handle with value:
    @(in1)[-cos(in1(:,2))+exp(in1(:,1));exp(in1(:,2))-in1(:,1).^2]

[JORGE ORDOÑEZ CARRASCO]

It worked thank you.

[JORGE ORDOÑEZ CARRASCO]

Is your suggestion but i evaluate r=matlabFunction(fundJdu) as r (x) where x=rand(2,1) but didnt work. It worked in a expresion that was scalar thats why it worked. what im doing wrong

[Walter Roberson]

That is not my suggestion. I specifically said that you need to use the vars option with {} and I gave an example to emphasize what hasto be done .

[JORGE ORDOÑEZ CARRASCO]

Thank you i realized it wasnt your suggestion i just did it again and it work.Thank you so much