laed6(3)

💖 laed6(3) — Library Functions Manual 💖

okay bestie, welcome to the laed6(3) page — it’s giving LAPACK internal math, but make it cute. 💅 This whole page is about the D&C step that does one secular-equation Newton step. ✨

🌸 NAME 🌸

• laed6 — laed6: D&C step: secular equation Newton step. 🎀

🛠️ SYNOPSIS 🛠️

🧰 Functions

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

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

subroutine slaed6 (kniter, orgati, rho, d, z, finit, tau, info)

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

💫 Detailed Description 💫

This section is short and sweet, bestie: the detailed docs are the function documentation below. no cap. 🫶

🔥 Function Documentation 🔥

🧮 subroutine dlaed6 — the double-precision one 💅

Full signature, character-for-character:

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

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. 👑

🧾 Parameters

• KNITER — KNITER is INTEGER; refer to DLAED4 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 DLAED4 for further details.
• RHO — RHO is DOUBLE PRECISION; refer to the equation f(x) above.
• D — D is DOUBLE PRECISION array, dimension (3); D 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; 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. 📍

✨ subroutine slaed6 — the real one 🦋

Full signature, character-for-character:

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. 👑

🧾 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 🧚

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