SLATEC Routines --- QZHES ---

*DECK QZHES
      SUBROUTINE QZHES (NM, N, A, B, MATZ, Z)
C***BEGIN PROLOGUE  QZHES
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 orthogonal
C            transformations. Usually followed by QZIT, QZVAL, QZVEC.
C***LIBRARY   SLATEC (EISPACK)
C***CATEGORY  D4C1B3
C***TYPE      SINGLE PRECISION (QZHES-S)
C***KEYWORDS  EIGENVALUES, EIGENVECTORS, EISPACK
C***AUTHOR  Smith, B. T., et al.
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 the two-dimensional
C          array parameters, A, B, and Z, as declared in the calling
C          program dimension statement.  NM is an INTEGER variable.
C
C        N is the order of the matrices A and B.  N is an INTEGER
C          variable.  N must be less than or equal to NM.
C
C        A contains a real general matrix.  A is a two-dimensional
C          REAL array, dimensioned A(NM,N).
C
C        B contains a real general matrix.  B is a two-dimensional
C          REAL array, dimensioned B(NM,N).
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.  MATZ is a LOGICAL
C          variable.
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          Z is a two-dimensional REAL array, dimensioned Z(NM,N).
C
C     Questions and comments should be directed to B. S. Garbow,
C     APPLIED MATHEMATICS DIVISION, ARGONNE NATIONAL LABORATORY
C     ------------------------------------------------------------------
C
C***REFERENCES  B. T. Smith, J. M. Boyle, J. J. Dongarra, B. S. Garbow,
C                 Y. Ikebe, V. C. Klema and C. B. Moler, Matrix Eigen-
C                 system Routines - EISPACK Guide, Springer-Verlag,
C                 1976.
C***ROUTINES CALLED  (NONE)
C***REVISION HISTORY  (YYMMDD)
C   760101  DATE WRITTEN
C   890831  Modified array declarations.  (WRB)
C   890831  REVISION DATE from Version 3.2
C   891214  Prologue converted to Version 4.0 format.  (BAB)
C   920501  Reformatted the REFERENCES section.  (WRB)
C***END PROLOGUE  QZHES