hermite.m % Using a better approach to recursion

hermite.m

classdef hermite
	% Hermite class for hermite functions
	properties
		x
		polynomes
		hermites
	end
	
	methods
		function self = hermite(x, n)
			self.x = x;
			self.polynomes = {};
			self.hermites = {};
			
			for i = 0:n
				self.calc_polynomes(i);
			end
		end
		
		function calc_polynomes(self, n) %, (SetAccess = private)
			% calculates the Hermite polynomial, as given by the notes on page 24.
			% Relies on n-1 already having been calculated!
			if n == 0
				h_poly = [1];
			elseif n == 1
				h_poly = [2 0];
			else
				% Split in two, so that h(n-2) can be evaluated first!
				part2 = -2 * (n-1) * self.h(n-2);
				part1 = 2 .* [self.h(n-1) 0]; % 2 * H_n-1 * x
				h_poly = polyadd(part1, part2); % Recursive definition
			end
			self.set(polynomes{n+1}, h_poly);
		end
		
		function h_poly = h(self, n)
			% Returns the n-th hermite polynomial
			h_poly = self.polynomes{n+1};
		end
		
		function h = get(self, n)
			% Returns the nth Hermite function
			try self.hermites(n+1)
			catch
				% Use given formula for hermite function. Notes p. 24.
				val = 1/sqrt(factorial(n)*2^n*sqrt(pi)) * exp(-self.x.^2/2) .* polyval(self.h(n), self.x);
				self.hermites{n+1} = val;
			end
			h = self.hermites{n+1};
		end
	end

end