DLANEG(3)

💖 DLANEG(3) 💖

okay so bestie, this page is from the LAPACK Library Functions Manual, and the whole vibe is “we’re computing a Sturm count and we’re gonna be precise about it.” 🦋

🌸 NAME 🌸

The NAME here is literally this source file path:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dlaneg.f

So yes, this is the DLANEG page, and DLANEG computes the Sturm count. 💅

✨ SYNOPSIS ✨

🫶 Functions/Subroutines 🫶

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

🎀 Function/Subroutine Documentation 🎀

The full signature is giving very “I live in a numerical linear algebra library” energy:

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

And once again, for the people in the back: DLANEG computes the Sturm count. 👑

💅 Purpose 💅

okay so here’s the lore: DLANEG computes the Sturm count, which is 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 — it does not form the tridiagonal matrix T. The Sturm count is also the number of eigenvalues of T less than sigma. ✨

This routine is called from DLARRB. 🫶

The current routine does not use the PIVMIN parameter; instead it requires IEEE-754 propagation of Infinities and NaNs. This routine 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. 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 — INTEGER. The order of the matrix. 👑
• D — DOUBLE PRECISION array, dimension (N). The N diagonal elements of the diagonal matrix D. 🍓
• LLD — DOUBLE PRECISION array, dimension (N-1). The (N-1) elements L(i)*L(i)*D(i). 💅
• SIGMA — DOUBLE PRECISION. Shift amount in T - sigma I = L D L^T. ✨
• PIVMIN — DOUBLE PRECISION. The minimum pivot in the Sturm sequence. May be used when zero pivots are encountered on non-IEEE-754 architectures. 🫶
• R — 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 dlaneg.f.

🪄 Author 🪄

Generated automatically by Doxygen for LAPACK from the source code. Not handwritten, but still iconic. 💀✨

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Final sign-off from the footer, bestie: LAPACK Version 3.12.0, from /home/abui...RC/dlaneg.f(3) — and the footer doesn’t give us a separate date, so that’s the source/version/date-ish moment. 💖🦋