SRC/dlaneg.f(3)

💖 NAME 💖

Okay bestie, welcome to the Library Functions Manual page for SRC/dlaneg.f — that's literally the whole name section. It's giving "just the file name," and honestly? Iconic minimalism. 🎀

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

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

🎀 Function/Subroutine Documentation 🎀

Here's the full signature, exactly as it appears, because we do not mess with source code in this group chat:

   integer function dlaneg (integer n, double precision, dimension( * ) d,
       double precision, dimension( * ) lld, double precision sigma, double
       precision pivmin, integer r)

DLANEG computes the Sturm count.

Purpose

So what does it actually do? DLANEG computes the Sturm count: the number of negative pivots you encounter while factoring the tridiagonal matrix 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. It's literally counting eigenvalues via pivots, iykyk. 💅

This routine is called from DLARRB. Noted, bestie. 📌

Now, the tea: the current routine does not use the PIVMIN parameter, but rather requires IEEE-754 propagation of Infinities and NaNs. It also has no input range restrictions, but it does require default exception handling such that x/0 produces Inf when x is non-zero, and Inf/Inf produces NaN. That's the vibe check: special floating-point behavior is load-bearing here. 🫶

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 DOUBLE PRECISION array, dimension (N). The N diagonal elements of the diagonal matrix D.
• LLD — LLD is DOUBLE PRECISION array, dimension (N-1). The (N-1) elements L(i)*L(i)*D(i).
• SIGMA — SIGMA is DOUBLE PRECISION. Shift amount in T - sigma I = L D L^T.
• PIVMIN — PIVMIN is DOUBLE PRECISION. The minimum pivot in the Sturm sequence. May be used when zero pivots are encountered on non-IEEE-754 architectures. (Remember: this routine doesn't use PIVMIN but rather requires IEEE-754 behavior — so this is a "may be used" situation, not a "this is doing the work here" situation. 🙈)
• R — R is INTEGER. The twist index for the twisted factorization that is used for the negcount. Twisted factorization? Ate. 🔥

✨ 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 dlaneg.f.

💅 Author 💅

Generated automatically by Doxygen for LAPACK from the source code.

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Cute sign-off time, bestie: that footer is LAPACK, Version 3.12.0, page SRC/dlaneg.f(3) — and if you were looking for a date, the original footer doesn't give one, so I'm not inventing it. Periodt. 💜