** Program to compute eigenvalues and eigenvectors
of (X'X) matrix (after normalization) **;

options ls=80 nocenter;

** Read in X matrix **;
data indat;
input obs x1 x2 x3 x4 x5;
cards;
 1     1.02608    1.02461    1.00589    1.00290    1.04109
 2     1.01259    1.01725   -0.97663   -0.97464   -0.99381
 3     1.00222    1.00396    1.03925    1.02450    1.01480
 4     1.00835    1.01537   -0.98868   -0.97407   -0.99746
 5    -0.96519   -0.98171    1.04362    1.01111    1.04390
 6    -0.95359   -0.96563   -0.97973   -0.96899   -0.97741
 7    -0.95045   -0.99967    1.04098    1.02708    1.00034
 8    -0.95349   -0.96943   -0.95564   -0.95102   -0.98772
;

** Enter SAS matrix processing utility **;
proc iml;

** Cutoff point for calling an eigenvalue close to 0 **;
evcut = 0.001;

** Transfer in X matrix **;
use indat var {x1 x2 x3 x4 x5};
read all;
n = nrow(x1);
x = j(n,1)||x1||x2||x3||x4||x5;

** Normalize **;
do ic = 1 to ncol(x);
x[,ic] = x[,ic] / sqrt(ssq(x[,ic]));
end;

** Compute **;
xtx = x`*x;
call eigen(evals,evecs,xtx);
v = evecs;
vt = evecs`;
xv = x*v;
xvtil = xv; 
do i = 1 to ncol(x);
  if (evals[i,] <= evcut)
    then xvtil[,i] = j(n,1,0);
 end;
xtil = xvtil*vt;

** Print out results **;
print xtx;
print evals vt;
print x;
print v;
print xv;
print xvtil;
print xtil;