SUBROUTINE IMTQLV (N, D, E, E2, W, IND, IERR, RV1)
C***BEGIN PROLOGUE IMTQLV
C***PURPOSE Compute the eigenvalues of a symmetric tridiagonal matrix
C using the implicit QL method. Eigenvectors may be computed
C***LIBRARY SLATEC (EISPACK)
C***CATEGORY D4A5, D4C2A
C***TYPE SINGLE PRECISION (IMTQLV-S)
C***KEYWORDS EIGENVALUES, EIGENVECTORS, EISPACK
C***AUTHOR Smith, B. T., et al.
C This subroutine is a variant of IMTQL1 which is a translation of
C ALGOL procedure IMTQL1, NUM. MATH. 12, 377-383(1968) by Martin and
C Wilkinson, as modified in NUM. MATH. 15, 450(1970) by Dubrulle.
C HANDBOOK FOR AUTO. COMP., VOL.II-LINEAR ALGEBRA, 241-248(1971).
C This subroutine finds the eigenvalues of a SYMMETRIC TRIDIAGONAL
C matrix by the implicit QL method and associates with them
C their corresponding submatrix indices.
C On INPUT
C N is the order of the matrix. N is an INTEGER variable.
C D contains the diagonal elements of the symmetric tridiagonal
C matrix. D is a one-dimensional REAL array, dimensioned D(N).
C E contains the subdiagonal elements of the symmetric
C tridiagonal matrix in its last N-1 positions. E(1) is
C arbitrary. E is a one-dimensional REAL array, dimensioned
C E2 contains the squares of the corresponding elements of E in
C its last N-1 positions. E2(1) is arbitrary. E2 is a one-
C dimensional REAL array, dimensioned E2(N).
C On OUTPUT
C D and E are unaltered.
C Elements of E2, corresponding to elements of E regarded as
C negligible, have been replaced by zero causing the matrix to
C split into a direct sum of submatrices. E2(1) is also set
C to zero.
C W contains the eigenvalues in ascending order. If an error
C exit is made, the eigenvalues are correct and ordered for
C indices 1, 2, ..., IERR-1, but may not be the smallest
C eigenvalues. W is a one-dimensional REAL array, dimensioned
C IND contains the submatrix indices associated with the
C corresponding eigenvalues in W -- 1 for eigenvalues belonging
C to the first submatrix from the top, 2 for those belonging to
C the second submatrix, etc. IND is a one-dimensional REAL
C array, dimensioned IND(N).
C IERR is an INTEGER flag set to
C Zero for normal return,
C J if the J-th eigenvalue has not been
C determined after 30 iterations.
C The eigenvalues should be correct for indices
C 1, 2, ..., IERR-1. These eigenvalues are
C ordered, but are not necessarily the smallest.
C RV1 is a one-dimensional REAL array used for temporary storage,
C dimensioned RV1(N).
C Calls PYTHAG(A,B) for sqrt(A**2 + B**2).
C Questions and comments should be directed to B. S. Garbow,
C APPLIED MATHEMATICS DIVISION, ARGONNE NATIONAL LABORATORY
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***ROUTINES CALLED PYTHAG
C***REVISION HISTORY (YYMMDD)
C 760101 DATE WRITTEN
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 IMTQLV