lartgs(3)

📦
version 3.12.1 · 9 versions
, in arch rolling

💅 lartgs — the group-chat guide to a LAPACK manual page

ok so this is the lartgs page from the Library Functions Manual — it's the C/Fortran library reference for LAPACK, and honestly? It's short, it's sweet, and it does exactly one (1) thing. Let's get into it, bestie 🎀

✨ NAME ✨

lartgs — like, the whole vibe is: generate a plane rotation for bidiag SVD. That's it. That's the function. 😌

🌸 SYNOPSIS 🌸

🫶 Functions

subroutine dlartgs (x, y, sigma, cs, sn)

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

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.

notice how the two are literally twins 💀 same args, same job — the only glow-up is the precision. d = double precision, s = real. iconic sibling energy fr fr.

🦋 Detailed Description 🦋

ok there's genuinely nothing here, the heading is doing all the work 😭 — the actual content lives in the Function Documentation section right below. scroll with me 🫡

👑 Function Documentation 👑

💜 subroutine dlartgs (double precision x, double precision y, double precision sigma, double precision cs, double precision sn)

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

⭐ Purpose:

!>
!> DLARTGS 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.
!>

so yeah — <italic>X</italic> and <italic>Y</italic> are the top-row entries, <italic>SIGMA</italic> is the shift, and the <italic>CS</italic> / <italic>SN</italic> they compute out are the plane rotation that satisfies that matrix equation up there ⬆️. And note: <italic>R</italic> is nonnegative. Also, if X^2 - SIGMA and X * Y are both 0, then the rotation is by PI/2. no cap, that's the special case 🎯

🌈 Parameters

  • X — !> X is DOUBLE PRECISION !> The (1,1) entry of an upper bidiagonal matrix. !>
  • Y — !> Y is DOUBLE PRECISION !> The (1,2) entry of an upper bidiagonal matrix. !>
  • SIGMA — !> SIGMA is DOUBLE PRECISION !> The shift. !>
  • CS — !> CS is DOUBLE PRECISION !> The cosine of the rotation. !>
  • SN — !> SN is DOUBLE PRECISION !> 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 dlartgs.f.

💜 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:

!>
!> 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.
!>

same story, single-precision edition 🫶 <italic>X</italic> and <italic>Y</italic> = top-row entries, <italic>SIGMA</italic> = the shift, <italic>CS</italic> and <italic>SN</italic> = the rotation. <italic>R</italic> stays nonnegative, and if X^2 - SIGMA and X * Y are both 0, the rotation is by PI/2. periodt 💅

🌈 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 🔥

Generated automatically by Doxygen for LAPACK from the source code.

ok that's the whole page, you ate that 💖 and for the sign-off: this masterpiece is LAPACK, Version 3.12.0, stamped with the date on the original footer. go forth and rotate those planes, bestie 🌟👑

📦 where this page comes from