SUBROUTINE BAKVEC(NM,N,T,E,M,Z,IERR)
C***BEGIN PROLOGUE  BAKVEC
C***DATE WRITTEN   760101   (YYMMDD)
C***REVISION DATE  830518   (YYMMDD)
C***CATEGORY NO.  D4C4
C***KEYWORDS  EIGENVALUES,EIGENVECTORS,EISPACK
C***AUTHOR  SMITH, B. T., ET AL.
C***PURPOSE  Forms eigenvectors of certain real non-symmetric
C            tridiagonal matrix from symmetric tridiagonal matrix
C            output from FIGI.
C***DESCRIPTION
C
C     This subroutine forms the eigenvectors of a NONSYMMETRIC
C     TRIDIAGONAL matrix by back transforming those of the
C     corresponding symmetric matrix determined by  FIGI.
C
C     On INPUT
C
C        NM must be set to the row dimension of two-dimensional
C          array parameters as declared in the calling program
C          dimension statement.
C
C        N is the order of the matrix.
C
C        T contains the nonsymmetric matrix.  Its subdiagonal is
C          stored in the last N-1 positions of the first column,
C          its diagonal in the N positions of the second column,
C          and its superdiagonal in the first N-1 positions of
C          the third column.  T(1,1) and T(N,3) are arbitrary.
C
C        E contains the subdiagonal elements of the symmetric
C          matrix in its last N-1 positions.  E(1) is arbitrary.
C
C        M is the number of eigenvectors to be back transformed.
C
C        Z contains the eigenvectors to be back transformed
C          in its first M columns.
C
C     On OUTPUT
C
C        T is unaltered.
C
C        E is  Destroyed.
C
C        Z contains the transformed eigenvectors
C          in its first M columns.
C
C        IERR is set to
C          Zero       for normal return,
C          2*N+I      if E(I) is zero with T(I,1) or T(I-1,3) non-zero.
C                     In this case, the symmetric matrix is not similar
C                     to the original matrix, and the eigenvectors
C                     cannot be found by this program.
C
C     Questions and comments should be directed to B. S. Garbow,
C     APPLIED MATHEMATICS DIVISION, ARGONNE NATIONAL LABORATORY
C     ------------------------------------------------------------------
C***REFERENCES  B. T. SMITH, J. M. BOYLE, J. J. DONGARRA, B. S. GARBOW,
C                 Y. IKEBE, V. C. KLEMA, C. B. MOLER, *MATRIX EIGEN-
C                 SYSTEM ROUTINES - EISPACK GUIDE*, SPRINGER-VERLAG,
C                 1976.
C***ROUTINES CALLED  (NONE)
C***END PROLOGUE  BAKVEC