% CAAM 453 Homework 6 helper function for problem 3.
%
%    fw = Watch(f)
%
% Input
%      f: function handle (function to be integrated)
%
% Output
%     fw: new function handle that behaves like f, but also creates
%          a plot illustrating the x values passed to f.

function fw = Watch(f)
    xv = [];
    dv = [];
    il0 = [];
    batch = [];
    batchSize = 0;
    fw = @(x) WatchWrapper(f,x);
    
    function y = WatchWrapper(f,x)
        y = f(x);
        
        if numel(x) == 1,
            switch numel(batch)
                case 0
                    batchSize = 15;
                case 1
                    if batch == x, batchSize = 30; end
            end
            batch = [batch x];
            if numel(batch) < batchSize, return; end
            x = batch; batch = [];
        end
        
        x = x(:).';
        il = -log2(max(x) - min(x));
        if isempty(il0), il0 = il; end
        xv = [xv x];
        dv = [dv repmat(il-il0, size(x))];
        
        scatter(xv, dv, 'fill');
        ylabel('Recursion Depth');
        title(sprintf('Total Function Calls = %d', length(xv)));
    end
end