Appendix E: Application of the square root matrix

Given an array P(N,NPAR) and a vector O(N) representing the left and right hand side of N observation equations with NPAR parameters, then the multiplication of the N by N matrix LI with P and O produces a set of decorrelated observation equations (PO,OO):

    L=1
    DO J=1,N
C
C   initialization of PO, OO
C
      DO I = 1, NPAR
        PO(J,I) = 0.0D0
        END DO
      OO(J) = 0.0D0
C
C   de-correlation processing
C
      DO K = 1, J
        DO I = 1,NPAR
          PO(J,I) = PO(J,I) + LI(L) * P(K,I)
          END DO
        OO(J) = OO(J) + LI(L) * O(K)
        L = L+1
        END DO
      END DO
    END DO

The new set of observation equations can now be used in e.g. a Householder transformations based least squares solution (see Bierman 1977).