function [S1 S2] = proj1(V1,V2,S,n)
%PROJ  Projection of a vector A onto vector B.
%   C = PROJ(A,B) returns the vector of the projection of A onto B.
%   A and B must be vectors of the same length.
%
% Created by A. Trujillo-Ortiz and R. Hernandez-Walls
%            Facultad de Ciencias Marinas
%            Universidad Autonoma de Baja California
%            Apdo. Postal 453
%            Ensenada, Baja California
%            Mexico.
%            atrujo@uabc.mx
%
% Copyright. June 12, 2009.
%
% To cite this file, this would be an appropriate format:
% Trujillo-Ortiz, A. and R. Hernandez-Walls. (2006). proj:Projection of a 
%   vector A onto vector B. A MATLAB file. [WWW document].
%   URL http://www.mathworks.com/matlabcentral/fileexchange/24435
%
% Reference:
% Gerber, H. (1990), Elementary Linear Algebra. Brooks/Cole Pub. Co. Pacific
%     Grove, CA. 
%
S1 = zeros(n,1);S2 = S1;

for j=1:n
S1(j) = S(:,j)'*V1/norm(S(:,j));
S2(j) = S(:,j)'*V2/norm(S(:,j));
end