SRC/slaneg.f(3)

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💅 SRC/slaneg.f 💅

Manual name: Library Functions Manual. Okay bestie, this page is literally the slaneg function's whole moment, and it's giving “I count pivots and eigenvalues.” 💖

✨ NAME ✨

SRC/slaneg.f

🌸 SYNOPSIS 🌸

Functions/Subroutines

  • integer function slaneg (n, d, lld, sigma, pivmin, r) — SLANEG computes the Sturm count.

🦋 Function/Subroutine Documentation 🦋

integer function slaneg (integer n, real, dimension( * ) d, real, dimension( * ) lld, real sigma, real pivmin, integer r)

SLANEG computes the Sturm count. ✨

🎀 Purpose 🎀

Okay so here's the tea: SLANEG computes the Sturm count, which is the number of negative pivots you encounter 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, SIAM Journal on Scientific Computing, v28, n5, 2006. DOI 10.1137/050641624 (Tech report version in LAWN 172 with the same title.)

🍓 Parameters 🍓

  • N — N is INTEGER. The order of the matrix. 💅
  • D — D is REAL array, dimension (N). The N diagonal elements of the diagonal matrix D.
  • LLD — LLD is REAL array, dimension (N-1). The (N-1) elements L(i)*L(i)*D(i).
  • SIGMA — SIGMA is REAL. Shift amount in T - sigma I = L D L^T.
  • PIVMIN — PIVMIN is REAL. The minimum pivot in the Sturm sequence. May be used when zero pivots are encountered on non-IEEE-754 architectures.
  • R — R is INTEGER. The twist index for the twisted factorization that is used for the negcount.

👑 Author 👑

  • Univ. of Tennessee
  • Univ. of California Berkeley
  • Univ. of Colorado Denver
  • NAG Ltd.

🌈 Contributors 🌈

  • Osni Marques, LBNL/NERSC, USA
  • Christof Voemel, University of California, Berkeley, USA
  • Jason Riedy, University of California, Berkeley, USA

Definition at line 117 of file slaneg.f.

📜 Author 📜

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Signed off with sparkle: LAPACK, Version 3.12.0 — page SRC/slaneg.f(3). Date: not shown in the original footer, so no invented date, bestie. 🫶

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