.TH DLANEG 1 "November 2006" " LAPACK auxiliary routine (version 3.1) " " LAPACK auxiliary routine (version 3.1) " .SH NAME DLANEG - the Sturm count, the number of negative pivots encountered while factoring tridiagonal T - sigma I = L D L^T .SH SYNOPSIS .TP 17 FUNCTION DLANEG( N, D, LLD, SIGMA, PIVMIN, R ) .TP 17 .ti +4 IMPLICIT NONE .TP 17 .ti +4 INTEGER DLANEG .TP 17 .ti +4 INTEGER N, R .TP 17 .ti +4 DOUBLE PRECISION PIVMIN, SIGMA .TP 17 .ti +4 DOUBLE PRECISION D( * ), LLD( * ) .SH PURPOSE DLANEG computes the Sturm count, the number of negative pivots encountered while factoring tridiagonal T - sigma I = L D L^T. This implementation works directly on the factors without forming the tridiagonal matrix T. The Sturm count is also the number of eigenvalues of T less than sigma. .br This routine is called from DLARRB. .br The current routine does not use the PIVMIN parameter but rather requires IEEE-754 propagation of Infinities and NaNs. This routine also has no input range restrictions but does require default exception handling such that x/0 produces Inf when x is non-zero, and Inf/Inf produces NaN. For more information, see: Marques, Riedy, and Voemel, "Benefits of IEEE-754 Features in Modern Symmetric Tridiagonal Eigensolvers," SIAM Journal on Scientific Computing, v28, n5, 2006. DOI 10.1137/050641624 (Tech report version in LAWN 172 with the same title.) .br .SH ARGUMENTS .TP 8 N (input) INTEGER The order of the matrix. .TP 8 D (input) DOUBLE PRECISION array, dimension (N) The N diagonal elements of the diagonal matrix D. .TP 8 LLD (input) DOUBLE PRECISION array, dimension (N-1) The (N-1) elements L(i)*L(i)*D(i). .TP 8 SIGMA (input) DOUBLE PRECISION Shift amount in T - sigma I = L D L^T. .TP 8 PIVMIN (input) DOUBLE PRECISION The minimum pivot in the Sturm sequence. May be used when zero pivots are encountered on non-IEEE-754 architectures. .TP 8 R (input) INTEGER The twist index for the twisted factorization that is used for the negcount. .SH FURTHER DETAILS Based on contributions by .br Osni Marques, LBNL/NERSC, USA .br Christof Voemel, University of California, Berkeley, USA Jason Riedy, University of California, Berkeley, USA .br