_HQR2(3F)							     _HQR2(3F)

NAME    [Toc]    [Back]

     HQR2, SHQR2  -  EISPACK routine.  This subroutine finds the eigenvalues
     and eigenvectors of a REAL	UPPER Hessenberg matrix	by the QR method.  The
     eigenvectors of a REAL GENERAL matrix can also be found if	 ELMHES	 and
     ELTRAN  or	 ORTHES	 and  ORTRAN  have been	used to	reduce this general
     matrix to Hessenberg form and to accumulate the similarity
     transformations.

SYNOPSYS    [Toc]    [Back]

	  subroutine  hqr2(nm, n, low, igh, h, wr, wi, z, ierr)
	  integer	    nm,	n, low,	igh, ierr
	  double precision h(nm,n), wr(n), wi(n), z(nm,n)

	  subroutine shqr2(nm, n, low, igh, h, wr, wi, z, ierr)
	  integer	    nm,	n, low,	igh, ierr
	  real		   h(nm,n), wr(n), wi(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.

     LOW and IGH are integers determined by the	balancing subroutine  BALANC.
     If	 BALANC	 has not been used, set	LOW=1, IGH=N.

     H contains	the upper Hessenberg matrix.

     Z contains	the transformation matrix produced by  ELTRAN after the
     reduction by  ELMHES, or by  ORTRAN  after	the reduction by  ORTHES, if
     performed.	 If the	eigenvectors of	the Hessenberg matrix are desired, Z
     must contain the identity matrix.	On OUTPUT

     H has been	destroyed.

     WR	and WI contain the real	and imaginary parts, respectively, of the
     eigenvalues.  The eigenvalues are unordered except	that complex conjugate
     pairs of values appear consecutively with the eigenvalue having the
     positive imaginary	part first.  If	an error exit is made, the eigenvalues
     should be correct for indices IERR+1,...,N.

     Z contains	the real and imaginary parts of	the eigenvectors. If the I-th
     eigenvalue	is real, the I-th column of Z contains its eigenvector.	 If
     the I-th eigenvalue is complex with positive imaginary part, the I-th and
     (I+1)-th columns of Z contain the real and	imaginary parts	of its
     eigenvector.  The eigenvectors are	unnormalized.  If an error exit	is



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_HQR2(3F)							     _HQR2(3F)



     made, none	of the eigenvectors has	been found.

     IERR is set to Zero       for normal return, J	     if	the J-th
     eigenvalue	has not	been
	determined after a total of 30*N iterations.  Calls CDIV for complex
     division.	Questions and comments should be directed to B.	S. Garbow,
     APPLIED MATHEMATICS DIVISION, ARGONNE NATIONAL LABORATORY


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