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COMBAK(NM,LOW,IGH,AR,AI,INT,M,ZR,ZI)

       SUBROUTINE COMBAK(NM,LOW,IGH,AR,AI,INT,M,ZR,ZI)
 C
       INTEGER I,J,M,LA,MM,MP,NM,IGH,KP1,LOW,MP1
       DOUBLE PRECISION AR(NM,IGH),AI(NM,IGH),ZR(NM,M),ZI(NM,M)
       DOUBLE PRECISION XR,XI
       INTEGER INT(IGH)
 C
 C     THIS SUBROUTINE IS A TRANSLATION OF THE ALGOL PROCEDURE COMBAK,
 C     NUM. MATH. 12, 349-368(1968) BY MARTIN AND WILKINSON.
 C     HANDBOOK FOR AUTO. COMP., VOL.II-LINEAR ALGEBRA, 339-358(1971).
 C
 C     THIS SUBROUTINE FORMS THE EIGENVECTORS OF A COMPLEX GENERAL
 C     MATRIX BY BACK TRANSFORMING THOSE OF THE CORRESPONDING
 C     UPPER HESSENBERG MATRIX DETERMINED BY  COMHES.
 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        LOW AND IGH ARE INTEGERS DETERMINED BY THE BALANCING
 C          SUBROUTINE  CBAL.  IF  CBAL  HAS NOT BEEN USED,
 C          SET LOW=1 AND IGH EQUAL TO THE ORDER OF THE MATRIX.
 C
 C        AR AND AI CONTAIN THE MULTIPLIERS WHICH WERE USED IN THE
 C          REDUCTION BY  COMHES  IN THEIR LOWER TRIANGLES
 C          BELOW THE SUBDIAGONAL.
 C
 C        INT CONTAINS INFORMATION ON THE ROWS AND COLUMNS
 C          INTERCHANGED IN THE REDUCTION BY  COMHES.
 C          ONLY ELEMENTS LOW THROUGH IGH ARE USED.
 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