MATLAB: How do you change the romberg.m file so that it derives instead of integrates

romberg

I am trying to change the romberg.m file so that it derives a function, instead of integrate it. I was trying to change the 26th line (seen below) to grad instead of trap, but I am given a set of numbers and NOT a function, so that wouldn't work.
If anyone had an idea of how to either change the .m file so that it would derive, or if you knew how to make a set of data points into a function so that it can be used in the function that would be awesome.
I am pretty sure it is something as simple as changing trap to something else, but I can't figure it out.
Thank you in advance.
.m
function [q,ea,iter]=romberg(func,a,b,es,maxit,varargin)
% romberg: Romberg integration quadrature
%   q = romberg(func,a,b,es,maxit,varargin):
%                    Romberg integration.
% input:
%   func = name of function to be integrated
%   a, b = integration limits
%   es = desired relative error (default = 0.000001%)
%   maxit = maximum allowable iterations (default = 30)
%   p1,p2,... = additional parameters used by func
% output:
%   q = integral estimate
%   ea = approximate relative error (%)
%   iter = number of iterations
if nargin<3,error('at least 3 input arguments required'),end
if nargin<4|isempty(es), es=0.000001;end
if nargin<5|isempty(maxit), maxit=50;end
n = 1;
I(1,1) = trap(func,a,b,n,varargin{:});
iter = 0;
while iter<maxit
    iter = iter+1;
    n = 2^iter;
    I(iter+1,1) = trap(func,a,b,n,varargin{:});
    for k = 2:iter+1
      j = 2+iter-k;
      I(j,k) = (4^(k-1)*I(j+1,k-1)-I(j,k-1))/(4^(k-1)-1);
    end
    ea = abs((I(1,iter+1)-I(2,iter))/I(1,iter+1))*100;
    if ea<=es, break; end
  end
  q = I(1,iter+1);

Best Answer

I have a hard time imagining why you think it would be appropriate to change an integration tool to differentiate, especially an integration tool that expects to be passed a function handle and you want to switch to providing an array.
But to answer your specific question:
grad() is not a Mathworks routine. There are contributions in the File Exchange that provide a grad() routine, but you would need to examine them to see if they are suitable for your purpose.
The numeric gradient routine in MATLAB is named gradient(), which does operate given a numeric array.
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