function Y=andrews(X,nox)

%
% Andrews Diagrams: Plots high-dimensional data using the method proposed 
% by Andrews (1972).
% Y = ANDREWS(X,N) plots each row of the matrix X as a trigonometric function 
% defined in the interval (-pi,pi).
% N is the number of points taken into account in the interval(-pi,pi).
% The default value for N is 100.
% Y is the matrix containing the values f(t) of the trigonometric functions.
% Reference:
% D.F. Andrews (1972), "Plots of High-Dimensional data", Biometrics, pp. 125-136
% Author: 
% Marco Sandri - Verona - Italy - Email: sandri.marco@gmail.com
%

if nargin<2
   nox=100;
end   

[nrows,p]=size(X);
if nrows>nox-1
   disp('Warning! Number of points in (-pi,pi) too low.');
   disp('N has been setted equal to the number of rows of X plus one.');
   nox=nrows+1;
end
t=[-pi:2*pi/(nox-1):pi];

Y=zeros(nrows,nox);
if mod(p,2)
   for j=1:nrows
      Y(j,:)=X(j,1)/sqrt(2).*ones(1,nox);
      for  i=2:2:p-1
         Y(j,:)=Y(j,:)+X(j,i).*sin(t*i/2)+X(j,i+1).*cos(t*i/2);
      end
   end
else
   for j=1:nrows
      Y(j,:)=X(j,1)/sqrt(2).*ones(1,nox);
      for  i=2:2:p-2
         Y(j,:)=Y(j,:)+X(j,i).*sin(t*i/2)+X(j,i+1).*cos(t*i/2);
      end
      Y(j,:)=Y(j,:)+X(j,p).*sin(t*i/2);
   end
end

Ymin=min(min(Y));
Ymax=max(max(Y));
Yrange=Ymax-Ymin;
Ycrt=Yrange/10;
plot(t,Y);
axis([-pi pi Ymin-Ycrt Ymax+Ycrt]);
title('Andrews Diagrams');
xlabel('t'); ylabel('f(t)');
hold on;
for i=1:nrows
   pos=round(nox/(nrows+1)*i);
   text(t(pos),Y(i,pos),num2str(i));
end;
hold off;