SUBROUTINE BALBAK(NM,N,LOW,IGH,SCALE,M,Z)
C***BEGIN PROLOGUE  BALBAK
C***DATE WRITTEN   760101   (YYMMDD)
C***REVISION DATE  830518   (YYMMDD)
C***CATEGORY NO.  D4C4
C***KEYWORDS  EIGENVALUES,EIGENVECTORS,EISPACK
C***AUTHOR  SMITH, B. T., ET AL.
C***PURPOSE  Forms eigenvectors of real general matrix from
C            eigenvectors of matrix output from BALANC.
C***DESCRIPTION
C
C     This subroutine is a translation of the ALGOL procedure BALBAK,
C     NUM. MATH. 13, 293-304(1969) by Parlett and Reinsch.
C     HANDBOOK FOR AUTO. COMP., Vol.II-LINEAR ALGEBRA, 315-326(1971).
C
C     This subroutine forms the eigenvectors of a REAL GENERAL
C     matrix by back transforming those of the corresponding
C     balanced matrix determined by  BALANC.
C
C     On INPUT
C
C        NM must be set to the row dimension of two-dimensional
C          array parameters as declared in the calling program
C          dimension statement.
C
C        N is the order of the matrix.
C
C        LOW and IGH are integers determined by  BALANC.
C
C        SCALE contains information determining the permutations
C          and scaling factors used by  BALANC.
C
C        M is the number of columns of Z to be back transformed.
C
C        Z contains the real and imaginary parts of the eigen-
C          vectors to be back transformed in its first M columns.
C
C     On OUTPUT
C
C        Z contains the real and imaginary parts of the
C          transformed eigenvectors in its first M columns.
C
C     Questions and comments should be directed to B. S. Garbow,
C     Applied Mathematics Division, ARGONNE NATIONAL LABORATORY
C     ------------------------------------------------------------------
C***REFERENCES  B. T. SMITH, J. M. BOYLE, J. J. DONGARRA, B. S. GARBOW,
C                 Y. IKEBE, V. C. KLEMA, C. B. MOLER, *MATRIX EIGEN-
C                 SYSTEM ROUTINES - EISPACK GUIDE*, SPRINGER-VERLAG,
C                 1976.
C***ROUTINES CALLED  (NONE)
C***END PROLOGUE  BALBAK