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QZHES(NM,N,A,B,MATZ,Z)

       SUBROUTINE QZHES(NM,N,A,B,MATZ,Z)
 C
       INTEGER I,J,K,L,N,LB,L1,NM,NK1,NM1,NM2
       DOUBLE PRECISION A(NM,N),B(NM,N),Z(NM,N)
       DOUBLE PRECISION R,S,T,U1,U2,V1,V2,RHO
       LOGICAL MATZ
 C
 C     THIS SUBROUTINE IS THE FIRST STEP OF THE QZ ALGORITHM
 C     FOR SOLVING GENERALIZED MATRIX EIGENVALUE PROBLEMS,
 C     SIAM J. NUMER. ANAL. 10, 241-256(1973) BY MOLER AND STEWART.
 C
 C     THIS SUBROUTINE ACCEPTS A PAIR OF REAL GENERAL MATRICES AND
 C     REDUCES ONE OF THEM TO UPPER HESSENBERG FORM AND THE OTHER
 C     TO UPPER TRIANGULAR FORM USING ORTHOGONAL TRANSFORMATIONS.
 C     IT IS USUALLY FOLLOWED BY  QZIT,  QZVAL  AND, POSSIBLY,  QZVEC.
 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 MATRICES.
 C
 C        A CONTAINS A REAL GENERAL MATRIX.
 C
 C        B CONTAINS A REAL GENERAL MATRIX.
 C
 C        MATZ SHOULD BE SET TO .TRUE. IF THE RIGHT HAND TRANSFORMATIONS
 C          ARE TO BE ACCUMULATED FOR LATER USE IN COMPUTING
 C          EIGENVECTORS, AND TO .FALSE. OTHERWISE.
 C
 C     ON OUTPUT
 C
 C        A HAS BEEN REDUCED TO UPPER HESSENBERG FORM.  THE ELEMENTS
 C          BELOW THE FIRST SUBDIAGONAL HAVE BEEN SET TO ZERO.
 C
 C        B HAS BEEN REDUCED TO UPPER TRIANGULAR FORM.  THE ELEMENTS
 C          BELOW THE MAIN DIAGONAL HAVE BEEN SET TO ZERO.
 C
 C        Z CONTAINS THE PRODUCT OF THE RIGHT HAND TRANSFORMATIONS IF
 C          MATZ HAS BEEN SET TO .TRUE.  OTHERWISE, Z IS NOT REFERENCED.
 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