function [ fct ] = get_monotonous_function( a, b, step )
% get_monotonous_function return a strictly monotonous function
% a - a 1x2 matrix (lower point of the line)
% b - a 1x2 matrix (upper point of the line)
% step - sampling step
x = a(1):step:b(1)-step;
nperiods = 10;
ps = (b(2)-b(1))/2;
noise_strength = ps;
% create a periodic, noisy, positive function and integrate
y = ps*sin(1/((b(1)-a(1))/(nperiods*pi))*x)+(ps+noise_strength);
y = y+noise_strength*rand(1,length(x));
y = cumsum(y);
fct = y/(y(end)/(b(2)-0.0001));
if ~all(diff(fct)>0), disp('Error: function not monotonic'); end;
return;
% plot(x,y);
% hold on;
% plot(x,fct,'r');
% hold off;
%
% fct = [a(2)];
% x = a(1):step:b(1)-step;
% l = interp1([a(1) b(1)], [a(2) b(2)], a(1):step:b(1), 'linear');
% yrange = b(2)-a(2);
% xrange = b(1)-a(1);
%
% num_crossings = round(size(x,2)/5);
% p = 0; % plotting? (debugging)
%
% if p==1
% close all;
% figure;
% plot([a(1) b(1)], [a(2) b(2)]);
% axis([a(1)-100 b(1)+100 a(2)-100 b(2)+100]);
% hold on;
% end;
%
%
% % crossings is a num_crossings x 2 matrix, containing the points on
% % the input line where it is crossed
% tmp = (rand(num_crossings,1).*xrange)+a(1);
% crossings = zeros(num_crossings,2);
% for c = 1:size(tmp,1)
% [v i] = min(abs(x-tmp(c)));
% crossings(c,:) = [x(i) l(i)];
% end;
% [tmp m] = unique(crossings(:,1));
% crossings = sort(crossings(m,:),1);
% crossings = [crossings; b(1) b(2)];
%
% %fct((crossings(:,1)))=crossings(:,2);
% lborder = a(2); % moving lower border
% crange = diff(crossings(:,2)); % y-range between two crossing-points
% % find a random traversal through the crossing points
% for i=2:size(x,2)
% if ~isempty(find(crossings(:,1)==x(i)))
% lborder = crossings(find(crossings(:,1)==x(i)),2);
% fct(i)=lborder;
% continue;
% end;
%
% j = find(x(i)<crossings(:,1),1);
% cy = crossings(j,2);
% avail = cy-lborder; % available range
% assert(avail>0, 'no way, dude');
% if j<=1, pcy = 0; else, pcy=crossings(j-1,2); end;
% remainder = avail/(cy-pcy);
% while 1
% if remainder*8>1, k = remainder*8; else, k=1; end;
% r = (rand(1).^k)*avail; % map it to x^n to encourage low prob
% % r = (0.5.^(k))*avail;
% if r<=0, continue; end;
% if (cy-lborder-r)>0, break; end;
% end;
% lborder = lborder+r;
% fct(i)=lborder;
% end;
%
% if p==1
% plot(x, fct, 'r.');
% plot(fct, x, 'k');
% plot(crossings(:,1), crossings(:,2), 'ro');
% axis square;
% hold off;
% end;
%
% if(~all(diff(fct)>0)), disp('function not strictly monotonous'); end;
%
%
% return;
