tql2.f
SUBROUTINE TQL2 (NM, N, D, E, Z, IERR)
C***BEGIN PROLOGUE TQL2
C***PURPOSE Compute the eigenvalues and eigenvectors of symmetric
C tridiagonal matrix.
C***LIBRARY SLATEC (EISPACK)
C***CATEGORY D4A5, D4C2A
C***TYPE SINGLE PRECISION (TQL2-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 TQL2,
C NUM. MATH. 11, 293-306(1968) by Bowdler, Martin, Reinsch, and
C Wilkinson.
C HANDBOOK FOR AUTO. COMP., VOL.II-LINEAR ALGEBRA, 227-240(1971).
C
C This subroutine finds the eigenvalues and eigenvectors
C of a SYMMETRIC TRIDIAGONAL matrix by the QL method.
C The eigenvectors of a FULL SYMMETRIC matrix can also
C be found if TRED2 has been used to reduce this
C full matrix to tridiagonal form.
C
C On Input
C
C NM must be set to the row dimension of the two-dimensional
C array parameter, Z, as declared in the calling program
C dimension statement. NM is an INTEGER variable.
C
C N is the order of the matrix. N is an INTEGER variable.
C N must be less than or equal to NM.
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 Z contains the transformation matrix produced in the
C reduction by TRED2, if performed. If the eigenvectors
C of the tridiagonal matrix are desired, Z must contain
C the identity matrix. Z is a two-dimensional REAL array,
C dimensioned Z(NM,N).
C
C On Output
C
C D contains the eigenvalues in ascending order. If an
C error exit is made, the eigenvalues are correct but
C unordered for indices 1, 2, ..., IERR-1.
C
C E has been destroyed.
C
C Z contains orthonormal eigenvectors of the symmetric
C tridiagonal (or full) matrix. If an error exit is made,
C Z contains the eigenvectors associated with the stored
C eigenvalues.
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
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 TQL2