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CBABK2(NM,N,LOW,IGH,SCALE,M,ZR,ZI)

       SUBROUTINE CBABK2(NM,N,LOW,IGH,SCALE,M,ZR,ZI)
 C
       INTEGER I,J,K,M,N,II,NM,IGH,LOW
       DOUBLE PRECISION SCALE(N),ZR(NM,M),ZI(NM,M)
       DOUBLE PRECISION S
 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 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  CBAL.
 C
 C        SCALE CONTAINS INFORMATION DETERMINING THE PERMUTATIONS
 C          AND SCALING FACTORS USED BY  CBAL.
 C
 C        M IS THE NUMBER OF EIGENVECTORS TO BE BACK TRANSFORMED.
 C
 C        ZR AND ZI CONTAIN THE REAL AND IMAGINARY PARTS,
 C          RESPECTIVELY, OF THE EIGENVECTORS TO BE
 C          BACK TRANSFORMED IN THEIR FIRST M COLUMNS.
 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 BURTON S. GARBOW,
 C     MATHEMATICS AND COMPUTER SCIENCE DIV, ARGONNE NATIONAL LABORATORY
 C
 C     THIS VERSION DATED AUGUST 1983.
 C
 C     ------------------------------------------------------------------
 C