_ORTBAK(3F)							   _ORTBAK(3F)

NAME    [Toc]    [Back]

     ORTBAK, SORTBAK  -	 EISPACK routine.  This	subroutine forms the
     eigenvectors of a REAL GENERAL matrix by back transforming	those of the
     corresponding upper Hessenberg matrix determined by  ORTHES.

SYNOPSYS    [Toc]    [Back]

	  subroutine  ortbak(nm, low, igh, a, ort, m, z)
	  integer	   nm, low, igh, m
	  double precision a(nm,igh), ort(igh),	z(nm,m)

	  subroutine sortbak(nm, low, igh, a, ort, m, z)
	  integer	   nm, low, igh, m
	  real		   a(nm,igh), ort(igh),	z(nm,m)

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.

     LOW and IGH are integers determined by the	balancing subroutine  BALANC.
     If	 BALANC	 has not been used, set	LOW=1 and IGH equal to the order of
     the matrix.

     A contains	information about the orthogonal trans-	formations used	in the
     reduction by  ORTHES in its strict	lower triangle.

     ORT contains further information about the	trans- formations used in the
     reduction by  ORTHES.  Only elements LOW through IGH are used.

     M is the number of	columns	of Z to	be back	transformed.

     Z contains	the real and imaginary parts of	the eigen- vectors to be back
     transformed in its	first M	columns.  On OUTPUT

     Z contains	the real and imaginary parts of	the transformed	eigenvectors
     in	its first M columns.

     ORT has been altered. NOTE	that ORTBAK preserves vector Euclidean norms.
     Questions and comments should be directed to B. S.	Garbow,	APPLIED
     MATHEMATICS DIVISION, ARGONNE NATIONAL LABORATORY


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