tridib.f
SUBROUTINE TRIDIB (N, EPS1, D, E, E2, LB, UB, M11, M, W, IND,
+ IERR, RV4, RV5)
C***BEGIN PROLOGUE TRIDIB
C***PURPOSE Compute the eigenvalues of a symmetric tridiagonal matrix
C in a given interval using Sturm sequencing.
C***LIBRARY SLATEC (EISPACK)
C***CATEGORY D4A5, D4C2A
C***TYPE SINGLE PRECISION (TRIDIB-S)
C***KEYWORDS EIGENVALUES OF A REAL SYMMETRIC MATRIX, EISPACK
C***AUTHOR Smith, B. T., et al.
C***DESCRIPTION
C
C This subroutine is a translation of the ALGOL procedure BISECT,
C NUM. MATH. 9, 386-393(1967) by Barth, Martin, and Wilkinson.
C HANDBOOK FOR AUTO. COMP., VOL.II-LINEAR ALGEBRA, 249-256(1971).
C
C This subroutine finds those eigenvalues of a TRIDIAGONAL
C SYMMETRIC matrix between specified boundary indices,
C using bisection.
C
C On Input
C
C N is the order of the matrix. N is an INTEGER variable.
C
C EPS1 is an absolute error tolerance for the computed eigen-
C values. If the input EPS1 is non-positive, it is reset for
C each submatrix to a default value, namely, minus the product
C of the relative machine precision and the 1-norm of the
C submatrix. EPS1 is a REAL 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.
C E2(1) is arbitrary. E2 is a one-dimensional REAL array,
C dimensioned E2(N).
C
C M11 specifies the lower boundary index for the set of desired
C eigenvalues. M11 is an INTEGER variable.
C
C M specifies the number of eigenvalues desired. The upper
C boundary index M22 is then obtained as M22=M11+M-1.
C M is an INTEGER variable.
C
C On Output
C
C EPS1 is unaltered unless it has been reset to its
C (last) default value.
C
C D and E are unaltered.
C
C Elements of E2, corresponding to elements of E regarded
C as negligible, have been replaced by zero causing the
C matrix to split into a direct sum of submatrices.
C E2(1) is also set to zero.
C
C LB and UB define an interval containing exactly the desired
C eigenvalues. LB and UB are REAL variables.
C
C W contains, in its first M positions, the eigenvalues
C between indices M11 and M22 in ascending order.
C W is a one-dimensional REAL array, dimensioned W(M).
C
C IND contains in its first M positions the submatrix indices
C associated with the corresponding eigenvalues in W --
C 1 for eigenvalues belonging to the first submatrix from
C the top, 2 for those belonging to the second submatrix, etc.
C IND is an one-dimensional INTEGER array, dimensioned IND(M).
C
C IERR is an INTEGER flag set to
C Zero for normal return,
C 3*N+1 if multiple eigenvalues at index M11 make
C unique selection of LB impossible,
C 3*N+2 if multiple eigenvalues at index M22 make
C unique selection of UB impossible.
C
C RV4 and RV5 are one-dimensional REAL arrays used for temporary
C storage of the lower and upper bounds for the eigenvalues in
C the bisection process. RV4 and RV5 are dimensioned RV4(N)
C and RV5(N).
C
C Note that subroutine TQL1, IMTQL1, or TQLRAT is generally faster
C than TRIDIB, if more than N/4 eigenvalues are to be found.
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 R1MACH
C***REVISION HISTORY (YYMMDD)
C 760101 DATE WRITTEN
C 890531 Changed all specific intrinsics to generic. (WRB)
C 890531 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 TRIDIB