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ELMHES(NM,N,LOW,IGH,A,INT)

       SUBROUTINE ELMHES(NM,N,LOW,IGH,A,INT)
 C
       INTEGER I,J,M,N,LA,NM,IGH,KP1,LOW,MM1,MP1
       DOUBLE PRECISION A(NM,N)
       DOUBLE PRECISION X,Y
       INTEGER INT(IGH)
 C
 C     THIS SUBROUTINE IS A TRANSLATION OF THE ALGOL PROCEDURE ELMHES,
 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     GIVEN A REAL GENERAL MATRIX, THIS SUBROUTINE
 C     REDUCES A SUBMATRIX SITUATED IN ROWS AND COLUMNS
 C     LOW THROUGH IGH TO UPPER HESSENBERG FORM BY
 C     STABILIZED ELEMENTARY SIMILARITY TRANSFORMATIONS.
 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 THE INPUT MATRIX.
 C
 C     ON OUTPUT
 C
 C        A CONTAINS THE HESSENBERG MATRIX.  THE MULTIPLIERS
 C          WHICH WERE USED IN THE REDUCTION ARE STORED IN THE
 C          REMAINING TRIANGLE UNDER THE HESSENBERG MATRIX.
 C
 C        INT CONTAINS INFORMATION ON THE ROWS AND COLUMNS
 C          INTERCHANGED IN THE REDUCTION.
 C          ONLY ELEMENTS LOW THROUGH IGH ARE USED.
 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