DEFINITION MODULE Jacobis;

   (* EXPORT QUALIFIED EigSrt, Jacobi; *)

   FROM NRVect IMPORT Vector;
   FROM NRMatr IMPORT Matrix;

   PROCEDURE EigSrt(D: Vector; 
                    V: Matrix); 
   (*
     Given the eigenvalues D[n] and eigenvectors V[n, n] as output
     from Jacobi (section 11.1) or TQLI (section 11.3), this routine sorts the
     eigenvalues into descending order, and rearranges the columns of V
     correspondingly. The method is straight insertion.
   *)

   PROCEDURE Jacobi(    A:    Matrix; 
                        D:    Vector; 
                        V:    Matrix; 
                    VAR nrot: INTEGER); 
   (*
     Computes all eigenvalues and eigenvectors of a real symmetric matrix 
     A[n, n]. On output, elements of A above the diagonal are destroyed. 
     D[n] returns the eigenvalues of A.  V[n, n] is a matrix whose columns 
     contain, on output, the normalized eigenvectors of A.  nrot returns 
     the number of Jacobi rotations that were required.
   *)

END Jacobis.