subroutine rgg(nm,n,a,b,alfr,alfi,beta,matz,z,ierr)
c
integer n,nm,ierr,matz
real a(nm,n),b(nm,n),alfr(n),alfi(n),beta(n),z(nm,n)
logical tf
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 as declared in the calling program
c dimension statement.
c
c n is the order of the matrices a and b.
c
c a contains a real general matrix.
c
c b contains a real general matrix.
c
c matz is an integer variable set equal to zero if
c only eigenvalues are desired. otherwise it is set to
c any non-zero integer for both eigenvalues and eigenvectors.
c
c on output
c
c alfr and alfi contain the real and imaginary parts,
c respectively, of the numerators of the eigenvalues.
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
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
c ierr is an integer output variable set equal to an error
c completion code described in the documentation for qzit.
c the normal completion code is zero.
c
c questions and comments should be directed to burton s. garbow,
c mathematics and computer science div, argonne national laboratory
c
c this version dated august 1983.
c
c ------------------------------------------------------------------
c
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