symmetricSigmaPoints(n, W_mean, isScaled, alpha, beta)

function [W_s, W_c, sigmaOffsets] = symmetricSigmaPoints(n, W_mean, isScaled, alpha, beta)
% input:
%  n = dimension of state
%  W_mean = real number between 0 and 1 = weight assigned to term
%           f(xbar), where xbar is the mean.
% outputs:
%  W_s = weights for state vector
%  W_c = weights for covariance matrix
%  points = cubature points
    
% symmetric sigma points
    if n == 0  % degenerate case where we want exact value for f(x) (i.e. covariance == 0)
        W(1) = 1;
        sigmaOffsets = zeros(0, 1);
    else
        W(1) = W_mean;
        W(2:2*n+1) = (1-W_mean)/(2*n);
        sigmaOffsets = zeros(n, 2*n+1);
        sigmaOffsets(:, 2:n+1) = sqrt(n/(1 - W_mean)) * eye(n);
        sigmaOffsets(:, n+2:2*n+1) = -sqrt(n/(1 - W_mean)) * eye(n);
    end
    
    if isScaled == false
        W_s = W;
        %W_c = diag(W);
        W_c = W;
    else
        W_s(1) = W(1) / alpha^2 + (1 - 1/alpha^2);
        W_s(2:2*n+1) = 1/alpha^2 * W(2:2*n+1);
        W_c = W_s;
        W_c(1) = W_s(1) + (1 - alpha^2 + beta);
        %W_c = diag(W_c);
        sigmaOffsets = alpha * sigmaOffsets;
    
    end
end