OPTIONS NOCENTER;
TITLE1 'Generating Orthogonal Polynomial Matrix';
PROC IML;
 
/* 4 equal interval timepoints  (including the constant) */
xraw     = { 1   1   1   1,
             0   1   2   3,
             0   1   4   9,
             0   1   8  27};

xorth      = INV(T(ROOT(xraw*T(xraw))))*xraw;

PRINT '4 equal interval timepoints - including the constant';
PRINT 'Matrix of Time Polynomials',                 xraw   [FORMAT=10.4];
PRINT 'Orthonormalized Matrix of Time Polynomials', xorth  [FORMAT=10.4];
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Generating Orthogonal Polynomial Matrix                  

4 equal interval timepoints - including the constant


Matrix of Time Polynomials
                    XRAW

    1.0000     1.0000     1.0000     1.0000
    0.0000     1.0000     2.0000     3.0000
    0.0000     1.0000     4.0000     9.0000
    0.0000     1.0000     8.0000    27.0000


Orthonormalized Matrix of Time Polynomials
                   XORTH

    0.5000     0.5000     0.5000     0.5000
   -0.6708    -0.2236     0.2236     0.6708
    0.5000    -0.5000    -0.5000     0.5000
   -0.2236     0.6708    -0.6708     0.2236