DLAED6(3)

💖 DLAED6(3) — Library Functions Manual 💖

okay so bestie, welcome to the DLAED6(3) glow-up. The header is from the Library Functions Manual, and the source path up top is /home/abui...RC/dlaed6.f(3). We're keeping it cute but every single technical crumb is staying. periodt. 💅

🌸 NAME 🌸

The name section is just this absolute unit of a path:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dlaed6.f

✨ SYNOPSIS ✨

🌟 Functions/Subroutines 🌟

The callable is DLAED6, and the short synopsis is:

subroutine DLAED6 (kniter, orgati, rho, d, z, finit, tau, info)

Quick vibe check: DLAED6 used by DSTEDC. Computes one Newton step in solution of the secular equation. That's the official energy. 💅

📚 Function/Subroutine Documentation 📚

Here's the full signature, no cap:

       subroutine DLAED6 (integer kniter, logical orgati, double precision rho,
       double precision, dimension( 3 ) d, double precision, dimension( 3 ) z,
       double precision finit, double precision tau, integer info)

And again, just so it's in the group chat: DLAED6 used by DSTEDC. Computes one Newton step in solution of the secular equation. 🫶

🎯 Purpose 🎯

This is what DLAED6 is doing, bestie — it computes the positive or negative root (closest to the origin) of the following, and yes the formatting is part of the slay:

!>
!> DLAED6 computes the positive or negative root (closest to the origin)
!> of
!>                  z(1)        z(2)        z(3)
!> f(x) =   rho + --------- + ---------- + ---------
!>                 d(1)-x      d(2)-x      d(3)-x
!>
!> It is assumed that
!>
!>       if ORGATI = .true. the root is between d(2) and d(3);
!>       otherwise it is between d(1) and d(2)
!>
!> This routine will be called by DLAED4 when necessary. In most cases,
!> the root sought is the smallest in magnitude, though it might not be
!> in some extremely rare situations.
!>

Translation for the besties: if ORGATI = .true., the root is between d(2) and d(3); otherwise it's between d(1) and d(2). DLAED4 calls this routine when necessary, and in most cases the root sought is the smallest in magnitude — though it might not be in some extremely rare situations. No extra lore added, that's literally the page. 🔥

🔧 Parameters 🔧

• KNITER — KNITER is INTEGER. For its significance, refer to DLAED4.
• ORGATI — ORGATI is LOGICAL. If ORGATI is true, the needed root is between d(2) and d(3); otherwise it is between d(1) and d(2). See DLAED4 for further details.
• RHO — RHO is DOUBLE PRECISION. Refer to the equation f(x) above. (You know, the whole z(1), z(2), z(3) situation.)
• D — D is DOUBLE PRECISION array, dimension (3). It satisfies d(1) < d(2) < d(3).
• Z — Z is DOUBLE PRECISION array, dimension (3). Each of the elements in z must be positive.
• FINIT — FINIT is DOUBLE PRECISION. This is the value of f at 0. It is more accurate than the one evaluated inside this routine (if someone wants to do so).
• TAU — TAU is DOUBLE PRECISION. This is the root of the equation f(x).
• INFO — INFO is INTEGER. The exit status tea is:
  • = 0: successful exit
  • > 0: if INFO = 1, failure to converge

✍️ Author ✍️

Give these institutions their flowers:

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

🧐 Further Details: 🧐

The literal receipts:

!>
!>  10/02/03: This version has a few statements commented out for thread
!>  safety (machine parameters are computed on each entry). SJH.
!>
!>  05/10/06: Modified from a new version of Ren-Cang Li, use
!>     Gragg-Thornton-Warner cubic convergent scheme for better stability.
!>

🫶 Contributors: 🫶

Ren-Cang Li, Computer Science Division, University of California at Berkeley, USA

Definition at line 139 of file dlaed6.f. 💅

🤖 Author 🤖

This last Author block is the auto-generated one: Generated automatically by Doxygen for LAPACK from the source code. ✨

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okay bestie, that's the whole page. Cute sign-off time: this is LAPACK Version 3.12.0, and the footer path is /home/abui...RC/dlaed6.f(3). Byeee! 💖🎀🦋