title 'Example 1.5'; 
title2 'Example :  Eigenvvalues and Vectors of S';
title3 'Run on PROC IML';
options ps = 60 ;
data cardbd; 
infile 'T1-2.DAT' missover;
input x1-x3; 
d1=x1-4; d2=x2-50; d3=x3-10; one=1;
label x1='density '
      x2='machdir'
      x3='crosdir';
proc iml;
reset nolog nocenter fw=10 spaces=5;
start;
use cardbd; read all var {x1 x2 x3} into XT;
X=XT` ; XBAR=X(|,:|); n=ncol(X); p=nrow(X); one=J(n,1,1);
SSCP=X*(I(n)-(1/n)*one*one` )*XT; S=(1/(n-1))*SSCP; mu0={4,50,10};
call eigen(lambda,evectors,S);
lambda=lambda`;
SI=inv(S);
print 'Summary Statistics:  ' XBAR S, ;
print 'Inverse of S:  ' SI, ;
print 'Eigenvalues of S: ' lambda,;
print 'Eigenvectors of S:' evectors,;
finish;
run;
quit;