/home/abui.../slartgs.f(3)

💅 slartgs.f(3) — Library Functions Manual 💅

okay so welcome to the slartgs.f page from the Library Functions Manual, bestie! This is the LAPACK subroutine that serves plane-rotation realness for the bidiagonal SVD problem, and it is lowkey iconic. 🦋

🎀 NAME 🎀

• /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/slartgs.f — that's the source file name, exactly as listed. yes, the whole path. no cap. 💅

✨ SYNOPSIS ✨

🌸 Functions/Subroutines 🌸

• subroutine SLARTGS (x, y, sigma, cs, sn) — SLARTGS generates a plane rotation designed to introduce a bulge in implicit QR iteration for the bidiagonal SVD problem.

💖 Function/Subroutine Documentation 💖

🦋 subroutine SLARTGS (real x, real y, real sigma, real cs, real sn) 🦋

SLARTGS generates a plane rotation designed to introduce a bulge in implicit QR iteration for the bidiagonal SVD problem.

🎀 Purpose 🎀

okay bestie, here's the actual purpose, fr fr: SLARTGS generates a plane rotation designed to introduce a bulge in Golub-Reinsch-style implicit QR iteration for the bidiagonal SVD problem. X and Y are the top-row entries, and SIGMA is the shift. The computed CS and SN define a plane rotation satisfying

   [  CS  SN  ]  .  [ X^2 - SIGMA ]  =  [ R ],
   [ -SN  CS  ]     [    X * Y    ]     [ 0 ]

with R nonnegative. If X^2 - SIGMA and X * Y are 0, then the rotation is by PI/2.

yes, that's PI/2 — the rotation is by PI/2 when both of those things are zero. the math said what it said. 💀✨

🌈 Parameters 🌈

• X — X is REAL. The (1,1) entry of an upper bidiagonal matrix.
• Y — Y is REAL. The (1,2) entry of an upper bidiagonal matrix.
• SIGMA — SIGMA is REAL. The shift.
• CS — CS is REAL. The cosine of the rotation.
• SN — SN is REAL. The sine of the rotation.

👑 Author 👑

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

Definition at line 89 of file slartgs.f.

🌟 Author 🌟

Generated automatically by Doxygen for LAPACK from the source code.

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mwah 💋 — this page is signed off by LAPACK Version 3.12.0, and the footer path is /home/abui.../slartgs.f(3). there's no date printed in that footer, bestie, just the version and the path. 🫶🎀