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LAPACK-3 - computes the Sturm count, the number of negative pivots encountered while factoring tridiagonal T - sigma I = L D L^T
INTEGER FUNCTION SLANEG( N, D, LLD, SIGMA, PIVMIN, R ) IMPLICIT NONE INTEGER N, R REAL PIVMIN, SIGMA REAL D( * ), LLD( * )
SLANEG 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. This routine is called from SLARRB. 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.)
N (input) INTEGER The order of the matrix. D (input) REAL array, dimension (N) The N diagonal elements of the diagonal matrix D. LLD (input) REAL array, dimension (N-1) The (N-1) elements L(i)*L(i)*D(i). SIGMA (input) REAL Shift amount in T - sigma I = L D L^T. PIVMIN (input) REAL The minimum pivot in the Sturm sequence. May be used when zero pivots are encountered on non-IEEE-754 architectures. R (input) INTEGER The twist index for the twisted factorization that is used for the negcount.
Based on contributions by Osni Marques, LBNL/NERSC, USA Christof Voemel, University of California, Berkeley, USA Jason Riedy, University of California, Berkeley, USA LAPACK auxiliary routine (version 3.2.2) April 2011 SLANEG(3lapack)