qzhes.f
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