Multigrid1D_Vcycle_GenMat.m

function [A_list, R_list, max_level] = Multigrid1D_Vcycle_GenMat(A, direct_n, isTwo)
	n = size(A, 1);
	
	A_list = {};
	R_list = {};
	
	level = 1;
	A_list(level) = {A};
	
    % Levels are created by halving the original mesh until it reaches the
    % limit for the direct solver
    if isTwo
        coarse_n = floor((n - 1) / 2);
        % Construct full-weighted restriction operator 
		R = sparse(coarse_n, n);
		for i = 1 : coarse_n
	        col = 2 * i - 1;
			R(i, col)     = 0.25;
			R(i, col + 1) = 0.5;
			R(i, col + 2) = 0.25;
		end
		
		R_list(level) = {R};
		
		P = 2 * R';
		A = R * A * P;
		
		level = level + 1;
		A_list(level) = {A};
		n = coarse_n;
    else
	    while (n > direct_n)
		    coarse_n = floor((n - 1) / 2);
		
		    % Construct full-weighted restriction operator 
		    R = sparse(coarse_n, n);
		    for i = 1 : coarse_n
			    col = 2 * i - 1;
			    R(i, col)     = 0.25;
			    R(i, col + 1) = 0.5;
			    R(i, col + 2) = 0.25;
		    end
		
		    R_list(level) = {R};
		
		    P = 2 * R';
		    A = R * A * P;
		
		    level = level + 1;
		    A_list(level) = {A};
		    n = coarse_n;
        end
    end
	
	max_level = level;
end