SUBROUTINE RSB(NM,N,MB,A,W,MATZ,Z,FV1,FV2,IERR)
C***BEGIN PROLOGUE  RSB
C***DATE WRITTEN   760101   (YYMMDD)
C***REVISION DATE  830518   (YYMMDD)
C***CATEGORY NO.  D4A6
C***KEYWORDS  EIGENVALUES,EIGENVECTORS,EISPACK
C***AUTHOR  SMITH, B. T., ET AL.
C***PURPOSE  Computes eigenvalues and, optionally, eigenvectors of
C            symmetric band matrix
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     of a REAL SYMMETRIC BAND matrix.
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 matrix  A.
C
C        MB  is the half band width of the matrix, defined as the
C        number of adjacent diagonals, including the principal
C        diagonal, required to specify the non-zero portion of the
C        lower triangle of the matrix.
C
C        A  contains the lower triangle of the real symmetric
C        band matrix.  Its lowest subdiagonal is stored in the
C        last  N+1-MB  positions of the first column, its next
C        subdiagonal in the last  N+2-MB  positions of the
C        second column, further subdiagonals similarly, and
C        finally its principal diagonal in the  N  positions
C        of the last column.  Contents of storages not part
C        of the matrix are arbitrary.
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        W  contains the eigenvalues in ascending order.
C
C        Z  contains the eigenvectors if MATZ is not zero.
C
C        IERR  is an integer output variable set equal to an
C        error completion code described in section 2B of the
C        documentation.  The normal completion code is zero.
C
C        FV1  and  FV2  are temporary storage arrays.
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  BANDR,TQL2,TQLRAT
C***END PROLOGUE  RSB