SUBROUTINE BANDV(NM,N,MBW,A,E21,M,W,Z,IERR,NV,RV,RV6)
C***BEGIN PROLOGUE  BANDV
C***DATE WRITTEN   760101   (YYMMDD)
C***REVISION DATE  830518   (YYMMDD)
C***CATEGORY NO.  D4C3
C***KEYWORDS  EIGENVALUES,EIGENVECTORS,EISPACK
C***AUTHOR  SMITH, B. T., ET AL.
C***PURPOSE  Forms eigenvectors of real symmetric band matrix
C            associated with a set of ordered approximate eigenvalue
C            by inverse iteration.
C***DESCRIPTION
C
C     This subroutine finds those eigenvectors of a REAL SYMMETRIC
C     BAND matrix corresponding to specified eigenvalues, using inverse
C     iteration.  The subroutine may also be used to solve systems
C     of linear equations with a symmetric or non-symmetric band
C     coefficient matrix.
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        MBW is the number of columns of the array A used to store the
C          band matrix.  If the matrix is symmetric, MBW is its (half)
C          band width, denoted MB and defined as the number of adjacent
C          diagonals, including the principal diagonal, required to
C          specify the non-zero portion of the lower triangle of the
C          matrix.  If the subroutine is being used to solve systems
C          of linear equations and the coefficient matrix is not
C          symmetric, it must however have the same number of adjacent
C          diagonals above the main diagonal as below, and in this
C          case, MBW=2*MB-1.
C
C        A contains the lower triangle of the symmetric band input
C          matrix stored as an N by MB array.  Its lowest subdiagonal
C          is stored in the last N+1-MB positions of the first column,
C          its next subdiagonal in the last N+2-MB positions of the
C          second column, further subdiagonals similarly, and finally
C          its principal diagonal in the N positions of column MB.
C          If the subroutine is being used to solve systems of linear
C          equations and the coefficient matrix is not symmetric, A is
C          N by 2*MB-1 instead with lower triangle as above and with
C          its first superdiagonal stored in the first N-1 positions of
C          column MB+1, its second superdiagonal in the first N-2
C          positions of column MB+2, further superdiagonals similarly,
C          and finally its highest superdiagonal in the first N+1-MB
C          positions of the last column.
C          Contents of storages not part of the matrix are arbitrary.
C
C        E21 specifies the ordering of the eigenvalues and contains
C            0.0E0 if the eigenvalues are in ascending order, or
C            2.0E0 if the eigenvalues are in descending order.
C          If the subroutine is being used to solve systems of linear
C          equations, E21 should be set to 1.0E0 if the coefficient
C          matrix is symmetric and to -1.0E0 if not.
C
C        M is the number of specified eigenvalues or the number of
C          systems of linear equations.
C
C        W contains the M eigenvalues in ascending or descending order.
C          If the subroutine is being used to solve systems of linear
C          equations (A-W(R)*I)*X(R)=B(R), where I is the identity
C          matrix, W(R) should be set accordingly, for R=1,2,...,M.
C
C        Z contains the constant matrix columns (B(R),R=1,2,...,M), if
C          the subroutine is used to solve systems of linear equations.
C
C        NV must be set to the dimension of the array parameter RV
C          as declared in the calling program dimension statement.
C
C     On OUTPUT
C
C        A and W are unaltered.
C
C        Z contains the associated set of orthogonal eigenvectors.
C          Any vector which fails to converge is set to zero.  If the
C          subroutine is used to solve systems of linear equations,
C          Z contains the solution matrix columns (X(R),R=1,2,...,M).
C
C        IERR is set to
C          Zero       for normal return,
C          -R         if the eigenvector corresponding to the R-th
C                     eigenvalue fails to converge, or if the R-th
C                     system of linear equations is nearly singular.
C
C        RV and RV6 are temporary storage arrays.  Note that RV is
C          of dimension at least N*(2*MB-1).  If the subroutine
C          is being used to solve systems of linear equations, the
C          determinant (up to sign) of A-W(M)*I is available, upon
C          return, as the product of the first N elements of RV.
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  BANDV