imtql1.f
SUBROUTINE IMTQL1 (N, D, E, IERR)
C***BEGIN PROLOGUE IMTQL1
C***PURPOSE Compute the eigenvalues of a symmetric tridiagonal matrix
C using the implicit QL method.
C***LIBRARY SLATEC (EISPACK)
C***CATEGORY D4A5, D4C2A
C***TYPE SINGLE PRECISION (IMTQL1-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 IMTQL1,
C NUM. MATH. 12, 377-383(1968) by Martin and Wilkinson,
C as modified in NUM. MATH. 15, 450(1970) by Dubrulle.
C HANDBOOK FOR AUTO. COMP., VOL.II-LINEAR ALGEBRA, 241-248(1971).
C
C This subroutine finds the eigenvalues of a SYMMETRIC
C TRIDIAGONAL matrix by the implicit QL method.
C
C On INPUT
C
C N is the order of the matrix. N is an INTEGER variable.
C
C D contains the diagonal elements of the symmetric tridiagonal
C matrix. D is a one-dimensional REAL array, dimensioned D(N).
C
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 E(N).
C
C On OUTPUT
C
C D 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.
C
C E has been destroyed.
C
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
C Calls PYTHAG(A,B) for sqrt(A**2 + B**2).
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 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 IMTQL1