DEFINITION MODULE TQLIM;

   (* EXPORT QUALIFIED TQLI; *)

   FROM NRVect IMPORT Vector;
   FROM NRMatr IMPORT Matrix;

   PROCEDURE TQLI(DD, E: Vector; Z: Matrix); 
   (*
     QL algorithm with implicit shifts, to determine the eigenvalues
     and eigenvectors of a real, symmetric, tridiagonal matrix, or of a
     real, symmetric matrix previously reduced by TRED2 section 11.2.
     On input, D[n] contains the diagonal elements of the tridiagonal
     matrix.  On output, it returns the eigenvalues. The vector E[n] inputs
     the subdiagonal elements of the tridiagonal matrix, with E[0] arbitrary. 
     On output E is destroyed. When finding only the eigenvalues, several 
     lines may be omitted, as noted in the comments. If the eigenvectors
     of a tridiagonal matrix are desired, the matrix Z[n, n] is input as the 
     identity matrix. If the eigenvectors of a matrix that has been reduced by
     TRED2 are required, then Z is input as the matrix output by TRED2. In
     either case, the kth column of Z returns the normalized eigenvector
     corresponding to D[k].
   *)

END TQLIM.