SUBROUTINE BANDR(NM,N,MB,A,D,E,E2,MATZ,Z)
C***BEGIN PROLOGUE  BANDR
C***DATE WRITTEN   760101   (YYMMDD)
C***REVISION DATE  830518   (YYMMDD)
C***CATEGORY NO.  D4C1B1
C***KEYWORDS  EIGENVALUES,EIGENVECTORS,EISPACK
C***AUTHOR  SMITH, B. T., ET AL.
C***PURPOSE  Reduces real symmetric band matrix to symmetric
C            tridiagonal matrix and, optionally, accumulates
C            orthogonal similarity transformations.
C***DESCRIPTION
C
C     This subroutine is a translation of the ALGOL procedure BANDRD,
C     NUM. MATH. 12, 231-241(1968) by Schwarz.
C     HANDBOOK FOR AUTO. COMP., VOL.II-lINEAR ALGEBRA, 273-283(1971).
C
C     This subroutine reduces a REAL SYMMETRIC BAND matrix
C     to a symmetric tridiagonal matrix using and optionally
C     accumulating orthogonal similarity transformations.
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        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 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 the last column.
C          Contents of storages not part of the matrix are arbitrary.
C
C        MATZ should be set to .TRUE. if the transformation matrix is
C          to be accumulated, and to .FALSE. otherwise.
C
C     On OUTPUT
C
C        A has been destroyed, except for its last two columns which
C          contain a copy of the tridiagonal matrix.
C
C        D contains the diagonal elements of the tridiagonal matrix.
C
C        E contains the subdiagonal elements of the tridiagonal
C          matrix in its last N-1 positions.  E(1) is set to zero.
C
C        E2 contains the squares of the corresponding elements of E.
C          E2 may coincide with E if the squares are not needed.
C
C        Z contains the orthogonal transformation matrix produced in
C          the reduction if MATZ has been set to .TRUE.  Otherwise, Z
C          is not referenced.
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  BANDR