# rgg.f

          SUBROUTINE RGG (NM, N, A, B, ALFR, ALFI, BETA, MATZ, Z, IERR)
    C***BEGIN PROLOGUE  RGG
    C***PURPOSE  Compute the eigenvalues and eigenvectors for a real
    C            generalized eigenproblem.
    C***LIBRARY   SLATEC (EISPACK)
    C***CATEGORY  D4B2
    C***TYPE      SINGLE PRECISION (RGG-S)
    C***KEYWORDS  EIGENVALUES, EIGENVECTORS, EISPACK
    C***AUTHOR  Smith, B. T., et al.
    C***DESCRIPTION
    C
    C     This subroutine calls the recommended sequence of
    C     subroutines from the eigensystem subroutine package (EISPACK)
    C     to find the eigenvalues and eigenvectors (if desired)
    C     for the REAL GENERAL GENERALIZED eigenproblem  Ax = (LAMBDA)Bx.
    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 is an INTEGER variable set equal to zero if only
    C          eigenvalues are desired.  Otherwise, it is set to any
    C          non-zero integer for both eigenvalues and eigenvectors.
    C
    C     On Output
    C
    C        A and B have been destroyed.
    C
    C        ALFR and ALFI contain the real and imaginary parts,
    C          respectively, of the numerators of the eigenvalues.
    C          ALFR and ALFI are one-dimensional REAL arrays,
    C          dimensioned ALFR(N) and ALFI(N).
    C
    C        BETA contains the denominators of the eigenvalues,
    C          which are thus given by the ratios  (ALFR+I*ALFI)/BETA.
    C          Complex conjugate pairs of eigenvalues appear consecutively
    C          with the eigenvalue having the positive imaginary part first.
    C          BETA is a one-dimensional REAL array, dimensioned BETA(N).
    C
    C        Z contains the real and imaginary parts of the eigenvectors
    C          if MATZ is not zero.  If the J-th eigenvalue is real, the
    C          J-th column of  Z  contains its eigenvector.  If the J-th
    C          eigenvalue is complex with positive imaginary part, the
    C          J-th and (J+1)-th columns of  Z  contain the real and
    C          imaginary parts of its eigenvector.  The conjugate of this
    C          vector is the eigenvector for the conjugate eigenvalue.
    C          Z is a two-dimensional REAL array, dimensioned Z(NM,N).
    C
    C        IERR is an INTEGER flag set to
    C          Zero       for normal return,
    C          10*N       if N is greater than NM,
    C          J          if the J-th eigenvalue has not been
    C                     determined after a total of 30*N iterations.
    C                     The eigenvalues should be correct for indices
    C                     IERR+1, IERR+2, ..., N, but no eigenvectors are
    C                     computed.
    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  QZHES, QZIT, QZVAL, QZVEC
    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  RGG