function [cc, eVecs1, eVecs2] = cancor(X, Y)
%CANCOR Conducts a canonical correlation analysis between two data sets.
%
% USE:
% [ccor, as, bs] = cancor(X, Y)
%
% ccor are the  canonical correlations between the linear 
% relationship between u = a'y and v = b'x, where a and b are the coefficients,
% which are eigen vectors (as and bs) of association matrices.
% 

% Tomo Eguchi
% 1 March 2002

% the following data are from Rencher (1995), Example 11.3. p. 399. 
%data = load('d:\tomosFolders\classes\multiVariateSpring2002\RencherData\Chem.dat');
%data = standardize(data);
%Y = data(:, 2:4);
%X = [data(:, 5:end), data(:, 5).*data(:,6), data(:, 5).*data(:,7), data(:,6).*data(:,7), ...
%   data(:, 5).^2, data(:, 6).^2, data(:, 7).^2];

% Find out which is bigger.
[nrX, ncX] = size(X);
[nrY, ncY] = size(Y);

% check size of input matrices
if nrX ~= nrY,
   error('The number of rows in X and Y should be equal.');
end

% arrange X and Y according to their sizes.
if (ncY > ncX),
   XY = [Y, X];
   m1 = ncY;
   m2 = ncX;
else
   XY = [X, Y];
   m1 = ncX;
   m2 = ncY;
end

% standardize data
XY = standardize(XY);

C = corrcoef(XY);                       % compute correlation coefficients of XY
C11 = C(1:m1,1:m1);                     % Partition them into four parts
C21 = C((m1+1):end, 1:m1);
C12 = C(1:m1, (m1+1):end);
C22 = C((m1+1):end, (m1+1):end);

M1 = inv(C22)*C21 * inv(C11) * C12;      % compute the association matrix
[eVecs1, eVals1] = eigorder(M1);                % eigen decomposition
cc = sqrt(eVals1);

M2 = inv(C11)*C12 * inv(C22) * C21;      % compute the association matrix
[eVecs2, eVals2] = eigorder(M2);                % eigen decomposition