SRC/slartgs.f(3)

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version 3.12.1 · 4 versions
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🌸 NAME 🌸

SRC/slartgs.f — bestie, this is the Library Functions Manual entry for SRC/slartgs.f(3), and we’re folding that manual-name detail in right here so you don’t have to squint at a dusty header line 💅

✨ 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)

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 so here’s the whole plot: 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.

🎀 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

Definition at line 89 of file slartgs.f.

🪄 Author

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That’s the page, bestie — this is LAPACK, Version 3.12.0, and the source page is SRC/slartgs.f(3). Go forth and rotate those vectors, periodt 💖✨🫶

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