function x = fpi(g, x_1, tol, tol_0)
	x = [x_1, g(x_1)];
	k = 1;
	plot(x(k,1), x(k,2), '.');
	if (tol > 0.0001 * tol_0)
		drawtol = tol;
	else
		drawtol = 0.0001 * tol_0;
	end
	x_plot = x_1-tol_0:drawtol:x_1+tol_0;
	grid;
	plot([x_1-tol_0 x_1+tol_0], [x_1-tol_0 x_1+tol_0], x_plot, g(x_plot));
	hold on;
	while k == 1 || tol < abs(x(k,1)-x(k-1,1))
		j = k;
		while j > 1
			j = j - 1;
			if tol > abs(x(k,1)-x(j,1))
				return;
			end
		end
		if abs(x(k)-x(1)) > tol_0
			r = NaN;
			return;
		end
		k = k + 1;
		x(k,1) = x(k-1,2);
		x(k,2) = g(x(k,1));
%		x(k,:)
		plot(x(k,1), x(k,2), '.');
		x_plot = [x(k-1,1), x(k,1)];
		y_plot = [x(k-1,2), x(k-1,2)];
		plot(x_plot, y_plot);
		y_plot = [x(k,1), x(k,2)];
		x_plot = [x(k,1), x(k,1)];
		plot(x_plot, y_plot);
	end
	r = x(k,1);