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CORTB(NM,LOW,IGH,AR,AI,ORTR,ORTI,M,ZR,ZI)

       SUBROUTINE CORTB(NM,LOW,IGH,AR,AI,ORTR,ORTI,M,ZR,ZI)
 C
       INTEGER I,J,M,LA,MM,MP,NM,IGH,KP1,LOW,MP1
       REAL AR(NM,IGH),AI(NM,IGH),ORTR(IGH),ORTI(IGH),
      X       ZR(NM,M),ZI(NM,M)
       REAL H,GI,GR
 C
 C     THIS SUBROUTINE IS A TRANSLATION OF A COMPLEX ANALOGUE OF
 C     THE ALGOL PROCEDURE ORTBAK, NUM. MATH. 12, 349-368(1968)
 C     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  CORTH.
 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 INFORMATION ABOUT THE UNITARY
 C          TRANSFORMATIONS USED IN THE REDUCTION BY  CORTH
 C          IN THEIR STRICT LOWER TRIANGLES.
 C
 C        ORTR AND ORTI CONTAIN FURTHER INFORMATION ABOUT THE
 C          TRANSFORMATIONS USED IN THE REDUCTION BY  CORTH.
 C          ONLY ELEMENTS LOW THROUGH IGH ARE USED.
 C
 C        M IS THE NUMBER OF COLUMNS OF ZR AND ZI 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        ORTR AND ORTI HAVE BEEN ALTERED.
 C
 C     NOTE THAT CORTB PRESERVES VECTOR EUCLIDEAN NORMS.
 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