*DECK RGG
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
C
INTEGER N,NM,IERR,MATZ
REAL A(NM,*),B(NM,*),ALFR(*),ALFI(*),BETA(*),Z(NM,*)
LOGICAL TF
C
C***FIRST EXECUTABLE STATEMENT RGG
IF (N .LE. NM) GO TO 10
IERR = 10 * N
GO TO 50
C
10 IF (MATZ .NE. 0) GO TO 20
C .......... FIND EIGENVALUES ONLY ..........
TF = .FALSE.
CALL QZHES(NM,N,A,B,TF,Z)
CALL QZIT(NM,N,A,B,0.0E0,TF,Z,IERR)
CALL QZVAL(NM,N,A,B,ALFR,ALFI,BETA,TF,Z)
GO TO 50
C .......... FIND BOTH EIGENVALUES AND EIGENVECTORS ..........
20 TF = .TRUE.
CALL QZHES(NM,N,A,B,TF,Z)
CALL QZIT(NM,N,A,B,0.0E0,TF,Z,IERR)
CALL QZVAL(NM,N,A,B,ALFR,ALFI,BETA,TF,Z)
IF (IERR .NE. 0) GO TO 50
CALL QZVEC(NM,N,A,B,ALFR,ALFI,BETA,Z)
50 RETURN
END