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SUBROUTINE COMHES(NM,N,LOW,IGH,AR,AI,INT)
C
INTEGER I,J,M,N,LA,NM,IGH,KP1,LOW,MM1,MP1
DOUBLE PRECISION AR(NM,N),AI(NM,N)
DOUBLE PRECISION XR,XI,YR,YI
INTEGER INT(IGH)
C
C THIS SUBROUTINE IS A TRANSLATION OF THE ALGOL PROCEDURE COMHES,
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 COMPLEX 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 CBAL. IF CBAL HAS NOT BEEN USED,
C SET LOW=1, IGH=N.
C
C AR AND AI CONTAIN THE REAL AND IMAGINARY PARTS,
C RESPECTIVELY, OF THE COMPLEX INPUT MATRIX.
C
C ON OUTPUT
C
C AR AND AI CONTAIN THE REAL AND IMAGINARY PARTS,
C RESPECTIVELY, OF THE HESSENBERG MATRIX. THE
C MULTIPLIERS WHICH WERE USED IN THE REDUCTION
C ARE STORED IN THE REMAINING TRIANGLES UNDER THE
C 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 CALLS CDIV FOR COMPLEX DIVISION.
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