BANDR(3F)

NAME
     BANDR, SBANDR   -  EISPACK routine.  This subroutine reduces a REAL
     SYMMETRIC BAND matrix to a symmetric tridiagonal matrix using and
     optionally accumulating orthogonal similarity transformations.


SYNOPSYS
          subroutine  bandr(nm, n, mb, a, d, e, e2, matz, z)
          integer          nm, n, mb, z
          double precision a(nm,mb), d(n), e(n), e2(n), z(nm,n)
          logical          matz

          subroutine sbandr(nm, n, mb, a, d, e, e2, matz, z)
          integer          nm, n, mb, z
          real             a(nm,mb), d(n), e(n), e2(n), z(nm,n)
          logical          matz



DESCRIPTION
     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 matrix.

     MB is the (half) band width of the matrix, defined as the number of
     adjacent diagonals, including the principal diagonal, required to specify
     the non-zero portion of the lower triangle of the matrix.

     A contains the lower triangle of the symmetric band input matrix stored
     as an N by MB array.  Its lowest subdiagonal is stored in the last N+1-MB
     positions of the first column, its next subdiagonal in the last N+2-MB
     positions of the second column, further subdiagonals similarly, and
     finally its principal diagonal in the N positions of the last column.
     Contents of storages not part of the matrix are arbitrary.

     MATZ should be set to .TRUE. if the transformation matrix is to be
     accumulated, and to .FALSE. otherwise.  On OUTPUT

     A has been destroyed, except for its last two columns which contain a
     copy of the tridiagonal matrix.

     D contains the diagonal elements of the tridiagonal matrix.

     E contains the subdiagonal elements of the tridiagonal matrix in its last
     N-1 positions.  E(1) is set to zero.

     E2 contains the squares of the corresponding elements of E. E2 may
     coincide with E if the squares are not needed.
     Z contains the orthogonal transformation matrix produced in the reduction
     if MATZ has been set to .TRUE.  Otherwise, Z is not referenced.
     Questions and comments should be directed to B. S. Garbow, Applied
     Mathematics Division, ARGONNE NATIONAL LABORATORY