SLANEG(3)

💖 SLANEG(3) — Sturm Count Bestie 💖

okay so this is SLANEG(3), from the Library Functions Manual, and she is here to compute the Sturm count. the source file is /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/slaneg.f. we are folding the manual-name situation in up here instead of copy-pasting the whole header line, because we are classy like that 💅

🌸 NAME 🌸

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

that is literally the NAME line, bestie. no cap, it is a path 💀

✨ 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 SLANEG 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. the way this implementation does it? it works directly on the factors without forming the tridiagonal matrix T. and the Sturm count is also the number of eigenvalues of T less than sigma. slay. 🦋

This routine is called from SLARRB. noted. 💅

quick caveat, bestie: 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 — 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

and the definition? Definition at line 117 of file slaneg.f. 💀

💫 Author 💫

Generated automatically by Doxygen for LAPACK from the source code.

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and that's the tea, bestie 🫶 this page is from LAPACK, Version 3.12.0, and the footer path is /home/abui...RC/slaneg.f(3). mwah 💋