SLATEC Routines --- BANDR ---

*DECK BANDR
      SUBROUTINE BANDR (NM, N, MB, A, D, E, E2, MATZ, Z)
C***BEGIN PROLOGUE  BANDR
C***PURPOSE  Reduce a real symmetric band matrix to symmetric
C            tridiagonal matrix and, optionally, accumulate
C            orthogonal similarity transformations.
C***LIBRARY   SLATEC (EISPACK)
C***CATEGORY  D4C1B1
C***TYPE      SINGLE PRECISION (BANDR-S)
C***KEYWORDS  EIGENVALUES, EIGENVECTORS, EISPACK
C***AUTHOR  Smith, B. T., et al.
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 the two-dimensional
C          array parameters, A and Z, as declared in the calling
C          program dimension statement.  NM is an INTEGER variable.
C
C        N is the order of the matrix A.  N is an INTEGER variable.
C          N must be less than or equal to NM.
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.  MB is less than or equal
C          to N.  MB is an INTEGER variable.
C
C        A contains the lower triangle of the real symmetric band
C          matrix.  Its lowest subdiagonal is stored in the last
C          N+1-MB  positions of the first column, its next subdiagonal
C          in the last  N+2-MB  positions of the second column, further
C          subdiagonals similarly, and finally its principal diagonal
C          in the  N  positions of the last column.  Contents of storage
C          locations not part of the matrix are arbitrary.  A is a
C          two-dimensional REAL array, dimensioned A(NM,MB).
C
C        MATZ should be set to .TRUE. if the transformation matrix is
C          to be accumulated, and to .FALSE. otherwise.  MATZ is a
C          LOGICAL variable.
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          D is a one-dimensional REAL array, dimensioned D(N).
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          E is a one-dimensional REAL array, dimensioned E(N).
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          E2 is a one-dimensional REAL array, dimensioned E2(N).
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.  Z is a two-dimensional REAL array,
C          dimensioned Z(NM,N).
C
C     Questions and comments should be directed to B. S. Garbow,
C     Applied Mathematics Division, ARGONNE NATIONAL LABORATORY
C     ------------------------------------------------------------------
C
C***REFERENCES  B. T. Smith, J. M. Boyle, J. J. Dongarra, B. S. Garbow,
C                 Y. Ikebe, V. C. Klema and C. B. Moler, Matrix Eigen-
C                 system Routines - EISPACK Guide, Springer-Verlag,
C                 1976.
C***ROUTINES CALLED  (NONE)
C***REVISION HISTORY  (YYMMDD)
C   760101  DATE WRITTEN
C   890531  Changed all specific intrinsics to generic.  (WRB)
C   890831  Modified array declarations.  (WRB)
C   890831  REVISION DATE from Version 3.2
C   891214  Prologue converted to Version 4.0 format.  (BAB)
C   920501  Reformatted the REFERENCES section.  (WRB)
C***END PROLOGUE  BANDR