LAPACK
3.6.1
LAPACK: Linear Algebra PACKage
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integer function slaneg | ( | integer | N, |
real, dimension( * ) | D, | ||
real, dimension( * ) | LLD, | ||
real | SIGMA, | ||
real | PIVMIN, | ||
integer | R | ||
) |
SLANEG computes the Sturm count.
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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.)
[in] | N | N is INTEGER The order of the matrix. |
[in] | D | D is REAL array, dimension (N) The N diagonal elements of the diagonal matrix D. |
[in] | LLD | LLD is REAL array, dimension (N-1) The (N-1) elements L(i)*L(i)*D(i). |
[in] | SIGMA | SIGMA is REAL Shift amount in T - sigma I = L D L^T. |
[in] | PIVMIN | PIVMIN is REAL The minimum pivot in the Sturm sequence. May be used when zero pivots are encountered on non-IEEE-754 architectures. |
[in] | R | R is INTEGER The twist index for the twisted factorization that is used for the negcount. |
Definition at line 120 of file slaneg.f.