rombquad(f,a,b,m)

function anss = rombquad(f,a,b,m)
%ROMBQUAD(f,a,b,m) evaluates the integral of f from a to b.
% f is an inline function or function handle.
% a is the lower limit of integration.
% b is the upper limit of integration.
% m - is the exponent in the relative error.  For example m = 10 implies an
% estimated relative error of 1e-10.
%
% Example:  
%
%           f = @(x) x.^2; % Vectoized function handle.
%           rombquad(f,0,2); % The integral from 0 to 2.
%
% See also quad, quadl, quadv and gaussquad (on the FEX)
%
% Author:  Matt Fig
% Contact:  [e-mail]
 
if nargin<3
   error ('Not enough arguments. See help.')
elseif nargin<4 || floor(m)~=m || m <1
    m = 10;
end

if isinf(a) || isinf(b)
   error('Infinite limits not allowed.') 
end

h = 2.^((1:m)-1)*(b-a)/2^(m-1);             % These are the intervals used.
k1 = 2.^((m-2):-1:-1)*2+1;                  % Index into the intervals.
f1 = feval(f,a:h(1):b);                     % Function evaluations.
R = zeros(1,m);                             % Pre-allocation.
% Define the starting vector:
for ii = 1:m
	R(ii) = 0.5*h(ii)*(f1(1)+2*...
            sum(f1(k1(end-ii+1):k1(end-ii+1)-1:end-1)) + f1(end)); 
end
% Interpolations:
for jj = 2:m
    jpower = (4^(jj-1)-1);
    for kk = 1:(m-jj+1)
        R(kk) = R(kk)+(R(kk)-R(kk+1))/jpower;
    end 
end
anss = R(1);