_TQL2(3F)							     _TQL2(3F)

NAME    [Toc]    [Back]

     TQL2, STQL2   -  EISPACK routine.	This subroutine	finds the eigenvalues
     and eigenvectors of a SYMMETRIC TRIDIAGONAL matrix	by the QL method.  The
     eigenvectors of a FULL SYMMETRIC matrix can also be found if  TRED2  has
     been used to reduce this full matrix to tridiagonal form.

SYNOPSYS    [Toc]    [Back]

	  subroutine  tql2(nm, n, d, e,	z, ierr)
	  integer	   nm, n, ierr
	  double precision d(n), e(n), z(nm,n)

	  subroutine stql2(nm, n, d, e,	z, ierr)
	  integer	   nm, n, ierr
	  real		   d(n), e(n), z(nm,n)

DESCRIPTION    [Toc]    [Back]

     On	Input

     NM	must be	set to the row dimension of two-dimensional array parameters
     as	declared in the	calling	program	dimension statement.

     N is the order of the matrix.

     D contains	the diagonal elements of the input matrix.

     E contains	the subdiagonal	elements of the	input matrix in	its last N-1
     positions.	 E(1) is arbitrary.

     Z contains	the transformation matrix produced in the reduction by	TRED2,
     if	performed.  If the eigenvectors	of the tridiagonal matrix are desired,
     Z must contain the	identity matrix.  On Output

     D contains	the eigenvalues	in ascending order.  If	an error exit is made,
     the eigenvalues are correct but unordered for indices 1,2,...,IERR-1.

     E has been	destroyed.

     Z contains	orthonormal eigenvectors of the	symmetric tridiagonal (or
     full) matrix.  If an error	exit is	made, Z	contains the eigenvectors
     associated	with the stored	eigenvalues.

     IERR is set to Zero       for normal return, J	     if	the J-th
     eigenvalue	has not	been
	determined after 30 iterations.	 Calls PYTHAG(A,B) for sqrt(A**2 +
     B**2).  Questions and comments should be directed to B. S.	Garbow,
     APPLIED MATHEMATICS DIVISION, ARGONNE NATIONAL LABORATORY


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