SRC/dlaed6.f(3)

💅 NAME 💅

okay so picture it: SRC/dlaed6.f(3), from the Library Functions Manual, and it’s giving main character Fortran subroutine energy. The file is SRC/dlaed6.f. That’s the name, that’s the icon, that’s the moment. ✨

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✨ SYNOPSIS ✨

Functions/Subroutines

subroutine dlaed6 (kniter, orgati, rho, d, z, finit, tau, info)

DLAED6 used by DSTEDC. Computes one Newton step in solution of the secular equation.

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🦋 Function/Subroutine Documentation 🦋

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)

DLAED6 used by DSTEDC. Computes one Newton step in solution of the secular equation.

✨ Purpose ✨

okay bestie, here’s the whole point: 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.

rare situations said “not today, bestie” — the smallest-in-magnitude thing is most cases, not every case. periodt.

🎀 Parameters 🎀

• KNITER — KNITER is INTEGER. Refer to DLAED4 for its significance. iykyk.
• 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 — that’s the vibe.
• D — D is DOUBLE PRECISION array, dimension (3). D satisfies d(1) < d(2) < d(3). strict ordering, no chaos.
• Z — Z is DOUBLE PRECISION array, dimension (3). Each of the elements in z must be positive. no negatives allowed, bestie 💅
• FINIT — FINIT is DOUBLE PRECISION. 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. The root of the equation f(x).
• INFO — INFO is INTEGER.
  • = 0: successful exit
  • > 0: if INFO = 1, failure to converge

👑 Author 👑

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

💜 Further Details 💜

• 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 🌸

Generated automatically by Doxygen for LAPACK from the source code.

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sign-off bestie: this whole page is SRC/dlaed6.f(3), LAPACK Version 3.12.0, with the 10/02/03 and 05/10/06 notes living their best life above. 💖✨🫶