Code covered by the BSD License

### Highlights fromNumerical Methods Using MATLAB, 2e

```function [SRmat,quad,err] = adapt(f,a,b,tol)
%---------------------------------------------------------------------------
% Sample call
% Inputs
%   f       name of the function
%   a       left  endpoint of [a,b]
%   b       right endpoint of [a,b]
%   toler   convergence tolerance
% Return
%   err     error estimate
%
% NUMERICAL METHODS: MATLAB Programs, (c) John H. Mathews 1995
% To accompany the text:
% NUMERICAL METHODS for Mathematics, Science and Engineering, 2nd Ed, 1992
% Prentice Hall, Englewood Cliffs, New Jersey, 07632, U.S.A.
% Prentice Hall, Inc.; USA, Canada, Mexico ISBN 0-13-624990-6
% Prentice Hall, International Editions:   ISBN 0-13-625047-5
% This free software is compliments of the author.
%
%---------------------------------------------------------------------------

SRmat = zeros(30,6);
iterating = 0;
done = 1;
SRvec = zeros(6);
SRvec = srule('f',a,b,tol);
SRmat(1,1:6) = SRvec;
m = 1;
state = iterating;
while (state == iterating)
n = m;
for j=n:-1:1,
p = j;
SR0vec = SRmat(p,:);
err = SR0vec(5);
tol = SR0vec(6);
if  (tol <= err),
state = done;
SR1vec = SR0vec;
SR2vec = SR0vec;
a = SR0vec(1);
b = SR0vec(2);
c = (a + b)/2;
err = SR0vec(5);
tol = SR0vec(6);
tol2 = tol/2;
SR1vec = srule('f',a,c,tol2);
SR2vec = srule('f',c,b,tol2);
err = abs(SR0vec(3)-SR1vec(3)-SR2vec(3))/10;
if  (err < tol),
SRmat(p,:) = SR0vec;
SRmat(p,4) = SR1vec(3) + SR2vec(3);
SRmat(p,5) = err;
else
SRmat(p+1:m+1,:) = SRmat(p:m,:);
m = m+1;
SRmat(p,:) = SR1vec;
SRmat(p+1,:) = SR2vec;
state = iterating;
end
end
end
end