# cbabk2.f

          SUBROUTINE CBABK2 (NM, N, LOW, IGH, SCALE, M, ZR, ZI)
    C***BEGIN PROLOGUE  CBABK2
    C***PURPOSE  Form the eigenvectors of a complex general matrix from the
    C            eigenvectors of matrix output from CBAL.
    C***LIBRARY   SLATEC (EISPACK)
    C***CATEGORY  D4C4
    C***TYPE      COMPLEX (BALBAK-S, CBABK2-C)
    C***KEYWORDS  EIGENVECTORS, EISPACK
    C***AUTHOR  Smith, B. T., et al.
    C***DESCRIPTION
    C
    C     This subroutine is a translation of the ALGOL procedure
    C     CBABK2, which is a complex version of 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 COMPLEX GENERAL
    C     matrix by back transforming those of the corresponding
    C     balanced matrix determined by  CBAL.
    C
    C     On INPUT
    C
    C        NM must be set to the row dimension of the two-dimensional
    C          array parameters, ZR and ZI, as declared in the calling
    C          program dimension statement.  NM is an INTEGER variable.
    C
    C        N is the order of the matrix Z=(ZR,ZI).  N is an INTEGER
    C          variable.  N must be less than or equal to NM.
    C
    C        LOW and IGH are INTEGER variables determined by  CBAL.
    C
    C        SCALE contains information determining the permutations and
    C          scaling factors used by  CBAL.  SCALE is a one-dimensional
    C          REAL array, dimensioned SCALE(N).
    C
    C        M is the number of eigenvectors to be back transformed.
    C          M is an INTEGER variable.
    C
    C        ZR and ZI contain the real and imaginary parts, respectively,
    C          of the eigenvectors to be back transformed in their first
    C          M columns.  ZR and ZI are two-dimensional REAL arrays,
    C          dimensioned ZR(NM,M) and ZI(NM,M).
    C
    C     On OUTPUT
    C
    C        ZR and ZI contain the real and imaginary parts,
    C          respectively, of the transformed eigenvectors
    C          in their first M columns.
    C
    C     Questions and comments should be directed to B. S. Garbow,
    C     APPLIED MATHEMATICS DIVISION, ARGONNE NATIONAL LABORATORY
    C     ------------------------------------------------------------------
    C
    C***REFERENCES  B. T. Smith, J. M. Boyle, J. J. Dongarra, B. S. Garbow,
    C                 Y. Ikebe, V. C. Klema and C. B. Moler, Matrix Eigen-
    C                 system Routines - EISPACK Guide, Springer-Verlag,
    C                 1976.
    C***ROUTINES CALLED  (NONE)
    C***REVISION HISTORY  (YYMMDD)
    C   760101  DATE WRITTEN
    C   890831  Modified array declarations.  (WRB)
    C   890831  REVISION DATE from Version 3.2
    C   891214  Prologue converted to Version 4.0 format.  (BAB)
    C   920501  Reformatted the REFERENCES section.  (WRB)
    C***END PROLOGUE  CBABK2