QZVEC(3F)

NAME
     QZVEC, ZQZVEC   -  EISPACK routine.  This subroutine is the optional
     fourth step of the QZ algorithm for solving generalized matrix eigenvalue
     problems,


SYNOPSYS
          subroutine  qzvec(nm, n, a, b, alfr, alfi, beta, z)
          integer          nm, n
          double precision a(nm,n),b(nm,n),alfr(n),alfi(n),beta(n),z(nm,n)

          subroutine sqzvec(nm, n, a, b, alfr, alfi, beta, z)
          integer          nm, n
          real             a(nm,n),b(nm,n),alfr(n),alfi(n),beta(n),z(nm,n)



DESCRIPTION
     This subroutine accepts a pair of REAL matrices, one of them in quasi-
     triangular form (in which each 2-by-2 block corresponds to a pair of
     complex eigenvalues) and the other in upper triangular form.  It computes
     the eigenvectors of the triangular problem and transforms the results
     back to the original coordinate system.  It is usually preceded by
     QZHES,  QZIT, and  QZVAL.

     On Input

     NM must be set to the row dimension of two-dimensional array parameters
     as declared in the calling program dimension statement.

     N is the order of the matrices.

     A contains a real upper quasi-triangular matrix.

     B contains a real upper triangular matrix.  In addition, location B(N,1)
     contains the tolerance quantity (EPSB) computed and saved in  QZIT.

     ALFR , ALFI, and BETA  are vectors with components whose ratios
     ((ALFR+I*ALFI)/BETA) are the generalized eigenvalues.  They are usually
     obtained from  QZVAL.

     Z contains the transformation matrix produced in the reductions by
     QZHES,  QZIT, and  QZVAL, if performed.  If the eigenvectors of the
     triangular problem are desired, Z must contain the identity matrix.  On
     Output

     A is unaltered.  Its subdiagonal elements provide information
        about the storage of the complex eigenvectors.

     B has been destroyed.

     ALFR , ALFI, and BETA are unaltered.
     Z contains the real and imaginary parts of the eigenvectors. If ALFI(I)
     .EQ. 0.0, the I-th eigenvalue is real and
        the I-th column of Z contains its eigenvector.  If ALFI(I) .NE. 0.0,
     the I-th eigenvalue is complex.
        If ALFI(I) .GT. 0.0, the eigenvalue is the first of
        a complex pair and the I-th and (I+1)-th columns
        of Z contain its eigenvector.
        If ALFI(I) .LT. 0.0, the eigenvalue is the second of
        a complex pair and the (I-1)-th and I-th columns
        of Z contain the conjugate of its eigenvector.  Each eigenvector is
     normalized so that the modulus of its largest component is 1.0 .
     Questions and comments should be directed to B. S. Garbow, APPLIED
     MATHEMATICS DIVISION, ARGONNE NATIONAL LABORATORY