incsearch.m

function xb = incsearch(func,xmin,xmax,ns)
% incsearch: incremental search root locator
%   xb = incsearch(func,xmin,xmax,ns):
%     finds brackets of x that contain sign changes
%     of a function on an interval
% input:
%   func = name of function
%   xmin, xmax = endpoints of interval
%   ns = number of subintervals (default = 50)
% output:
%   xb(k,1) is the lower bound of the kth sign change
%   xb(k,2) is the upper bound of the kth sign change
%   If no brackets found, xb = [].
if nargin < 3, error('at least 3 arguments required'), end
if nargin < 4, ns = 50; end %if ns blank set to 50
% Incremental search
x = linspace(xmin,xmax,ns);
f = func(x);
nb = 0; xb = []; %xb is null unless sign change detected
%for k = 1:length(x)-1
%  if sign(f(k)) ~= sign(f(k+1)) %check for sign change
%    nb = nb + 1;
%    xb(nb,1) = x(k);
%    xb(nb,2) = x(k+1);
%  end
%end
sign_change = diff(sign(f));
[~,i_change] = find(sign_change~=0);
nb=length(i_change);
xb=[x(i_change)',x(i_change+1)'];

if isempty(xb) %display that no brackets were found
  fprintf('no brackets found\n')
  fprintf('check interval or increase ns\n')
else
  fprintf('number of brackets: %i\n',nb) %display number of brackets
end