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ORTRAN(NM,N,LOW,IGH,A,ORT,Z)

       SUBROUTINE ORTRAN(NM,N,LOW,IGH,A,ORT,Z)
 C
       INTEGER I,J,N,KL,MM,MP,NM,IGH,LOW,MP1
       DOUBLE PRECISION A(NM,IGH),ORT(IGH),Z(NM,N)
       DOUBLE PRECISION G
 C
 C     THIS SUBROUTINE IS A TRANSLATION OF THE ALGOL PROCEDURE ORTRANS,
 C     NUM. MATH. 16, 181-204(1970) BY PETERS AND WILKINSON.
 C     HANDBOOK FOR AUTO. COMP., VOL.II-LINEAR ALGEBRA, 372-395(1971).
 C
 C     THIS SUBROUTINE ACCUMULATES THE ORTHOGONAL SIMILARITY
 C     TRANSFORMATIONS USED IN THE REDUCTION OF A REAL GENERAL
 C     MATRIX TO UPPER HESSENBERG FORM BY  ORTHES.
 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 THE BALANCING
 C          SUBROUTINE  BALANC.  IF  BALANC  HAS NOT BEEN USED,
 C          SET LOW=1, IGH=N.
 C
 C        A CONTAINS INFORMATION ABOUT THE ORTHOGONAL TRANS-
 C          FORMATIONS USED IN THE REDUCTION BY  ORTHES
 C          IN ITS STRICT LOWER TRIANGLE.
 C
 C        ORT CONTAINS FURTHER INFORMATION ABOUT THE TRANS-
 C          FORMATIONS USED IN THE REDUCTION BY  ORTHES.
 C          ONLY ELEMENTS LOW THROUGH IGH ARE USED.
 C
 C     ON OUTPUT
 C
 C        Z CONTAINS THE TRANSFORMATION MATRIX PRODUCED IN THE
 C          REDUCTION BY  ORTHES.
 C
 C        ORT HAS BEEN ALTERED.
 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
 C