SLATEC Routines --- BANDV ---
*DECK BANDV
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