# Evaluate a changing function in loop

sweden

Hi! I am writing a code that generates a function f in a loop. This function f changes in every loop, for example from f = x + 2x to f = 3x^2 + 1 (randomly), and I want to evaluate f at different points in every loop. I have tried using subs, eval, matlabFunction etc but it is still running slowly. How would you tackle a problem like this in the most efficient way?

This is as fast as I have been able to do it. ****matlabFunction and subs go slower than this.
The code below is my solution and it is one loop. In my larger code the function f and point x0 change in every loop so you can imagine why I want this to go as fast as possible. I would greatly appreciate it if someone could go through this, and give me any pointers. If my coding is crap feel free to tell me

x = sym('x',[2,1]);
f = [x(1)-x(1)cos(x(2)), x(2)-3x(2)^2*cos(x(1))];
J = jacobian(f,x);
x0 = [2,1];
N=length(x0); % Number of equations

%% Transform into string
fstr = map2mat(char(f));
Jstr = map2mat(char(J));

% replace every occurence of 'xi' with 'x(i)'

x = x0;

phi0 = eval(fstr)
J = eval(Jstr)

% Transforms every occurence of xi in str into x(i)
% N is the maximum value of i
% replace every occurence of xi with x(i)
% note that we do this backwards to avoid x10 being
% replaced with x(1)0

for i=N1
is = num2str(i);
xis = ['x' is];
xpis = ['x(' is ')'];
str = strrep(str,xis,xpis);
end

function r = map2mat(r)

% MAP2MAT Maple to MATLAB string conversion.
% Lifted from the symbolic toolbox source code
% MAP2MAT(r) converts the Maple string r containing
% matrix, vector, or array to a valid MATLAB string.
%
% Examples: map2mat(matrix([[a,b], [c,d]]) returns
% [a,b;c,d]
% map2mat(array([[a,b], [c,d]]) returns
% [a,b;c,d]
% map2mat(vector([[a,b,c,d]]) returns
% [a,b,c,d]
% Deblank.

r(findstr(r,' ')) = [];

% Special case of the empty matrix or vector
if strcmp(r,'vector([])') | strcmp(r,'matrix([])') | ...
strcmp(r,'array([])')
r = [];
else
% Remove matrix, vector, or array from the string.
r = strrep(r,'matrix([[','['); r = strrep(r,'array([[','[');
r = strrep(r,'vector([','['); r = strrep(r,'],[',';');
r = strrep(r,']])',']'); r = strrep(r,'])',']');
end