SUBROUTINE QZHES(NM,N,A,B,MATZ,Z)
C***BEGIN PROLOGUE  QZHES
C***DATE WRITTEN   760101   (YYMMDD)
C***REVISION DATE  830518   (YYMMDD)
C***CATEGORY NO.  D4C1B3
C***KEYWORDS  EIGENVALUES,EIGENVECTORS,EISPACK
C***AUTHOR  SMITH, B. T., ET AL.
C***PURPOSE  The first step of the QZ algorithm for solving generalized
C            matrix eigenproblems. Accepts a pair of real general
C            matrices and reduces one of them to upper Hessenberg
C            and the other to upper triangular form using orthogo
C            transformations. Usually followed by QZIT, QZVAL, QZ
C***DESCRIPTION
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 B. S. Garbow,
C     APPLIED MATHEMATICS DIVISION, ARGONNE NATIONAL LABORATORY
C     ------------------------------------------------------------------
C***REFERENCES  B. T. SMITH, J. M. BOYLE, J. J. DONGARRA, B. S. GARBOW,
C                 Y. IKEBE, V. C. KLEMA, C. B. MOLER, *MATRIX EIGEN-
C                 SYSTEM ROUTINES - EISPACK GUIDE*, SPRINGER-VERLAG,
C                 1976.
C***ROUTINES CALLED  (NONE)
C***END PROLOGUE  QZHES