bandv.f

      SUBROUTINE BANDV (NM, N, MBW, A, E21, M, W, Z, IERR, NV, RV, RV6)
C***BEGIN PROLOGUE  BANDV
C***PURPOSE  Form the eigenvectors of a real symmetric band matrix
C            associated with a set of ordered approximate eigenvalues
C            by inverse iteration.
C***LIBRARY   SLATEC (EISPACK)
C***CATEGORY  D4C3
C***TYPE      SINGLE PRECISION (BANDV-S)
C***KEYWORDS  EIGENVECTORS, EISPACK
C***AUTHOR  Smith, B. T., et al.
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 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        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.  MBW is an INTEGER variable.  MB must not
C          be greater than N.
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.  Contents of storage locations
C          not part of the matrix are arbitrary.  A is a two-dimensional
C          REAL array, dimensioned A(NM,MBW).
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.  E21 is a REAL
C          variable.
C
C        M is the number of specified eigenvalues or the number of
C          systems of linear equations.  M is an INTEGER variable.
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(J)*I)*X(J)=B(J), where I is the identity
C          matrix, W(J) should be set accordingly, for J=1,2,...,M.
C          W is a one-dimensional REAL array, dimensioned W(M).
C
C        Z contains the constant matrix columns (B(J),J=1,2,...,M), if
C          the subroutine is used to solve systems of linear equations.
C          Z is a two-dimensional REAL array, dimensioned Z(NM,M).
C
C        NV must be set to the dimension of the array parameter RV
C          as declared in the calling program dimension statement.
C          NV is an INTEGER variable.
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(J),J=1,2,...,M).
C
C        IERR is an INTEGER flag set to
C          Zero       for normal return,
C          -J         if the eigenvector corresponding to the J-th
C                     eigenvalue fails to converge, or if the J-th
C                     system of linear equations is nearly singular.
C
C        RV and RV6 are temporary storage arrays.  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          RV and RV6 are one-dimensional REAL arrays.  Note that RV
C          is dimensioned RV(NV), where NV must be at least N*(2*MB-1).
C          RV6 is dimensioned RV6(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  BANDV