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 later. 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***DESCRIPTION C 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 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 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 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 C On OUTPUT C C D and E are unaltered. C C Elements of E2, corresponding to elements of E regarded as C negligible, have been replaced by zero causing the matrix to C split into a direct sum of submatrices.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 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 W(N). C 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 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 RV1 is a one-dimensional REAL array used for temporary storage, C dimensioned RV1(N). 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 IMTQLV