SRC/slaed6.f(3)

💖 SRC/slaed6.f(3) 💖

okay so bestie, this is the SRC/slaed6.f(3) page from the Library Functions Manual, and we are getting into the slaed6 subroutine together. stay with me, it's actually iconic 💅

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🌸 NAME 🌸

SRC/slaed6.f

that's the page name, no notes needed 🎀

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

• subroutine slaed6 (kniter, orgati, rho, d, z, finit, tau, info) — SLAED6 used by SSTEDC. Computes one Newton step in solution of the secular equation.

🦋 Function/Subroutine Documentation 🦋

slaed6 subroutine

subroutine slaed6 (integer kniter, logical orgati, real rho, real, dimension( 3 ) d, real, dimension( 3 ) z, real finit, real tau, integer info)

SLAED6 used by SSTEDC. Computes one Newton step in solution of the secular equation.

🎀 Purpose 🎀

SLAED6 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 SLAED4 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 what they said, bestie — not the usual vibe but it happens 🙈

🌈 Parameters 🌈

• KNITER — KNITER is INTEGER. Refer to SLAED4 for its significance.
• 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 SLAED4 for further details.
• RHO — RHO is REAL. Refer to the equation f(x) above.
• D — D is REAL array, dimension (3). D satisfies d(1) < d(2) < d(3).
• Z — Z is REAL array, dimension (3). Each of the elements in z must be positive.
• FINIT — FINIT is REAL. 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 REAL. 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 slaed6.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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and that's the whole page, bestie — LAPACK Version 3.12.0, from SRC/slaed6.f(3) 💜✨