larmm(3)

okay bestie, this is larmm(3) from the Library Functions Manual — yes, the manual name is literally “Library Functions Manual,” and this page is about larmm. It’s giving tiny-but-useful auxiliary-routine energy 💅✨.

💖 NAME 💖

larmm — larmm: scale factor to avoid overflow, step in latrs.

✨ SYNOPSIS ✨

🦋 Functions 🦋

• double precision function dlarmm (anorm, bnorm, cnorm) — DLARMM
• real function slarmm (anorm, bnorm, cnorm) — SLARMM

🌈 DETAILED DESCRIPTION 🌈

This page is all about larmm, and the detailed function docs are right below. There are two versions: a double precision one and a real one. It’s auxiliary-routine core, so there’s no argument checking — the source says it, not me 😭.

🔥 FUNCTION DOCUMENTATION 🔥

💫 DLARMM 💫

       double precision function dlarmm (double precision anorm, double precision
       bnorm, double precision cnorm)

DLARMM

Purpose:

           !>
           !> DLARMM returns a factor s in (0, 1] such that the linear updates
           !>
           !>    (s * C) - A * (s * B)  and  (s * C) - (s * A) * B
           !>
           !> cannot overflow, where A, B, and C are matrices of conforming
           !> dimensions.
           !>
           !> This is an auxiliary routine so there is no argument checking.
           !>

So s lands in (0, 1], and those two linear updates cannot overflow. Iconic. 🫶

🍓 Parameters 🍓

ANORM

           !>          ANORM is DOUBLE PRECISION
           !>          The infinity norm of A. ANORM >= 0.
           !>          The number of rows of the matrix A.  M >= 0.
           !>

BNORM

           !>          BNORM is DOUBLE PRECISION
           !>          The infinity norm of B. BNORM >= 0.
           !>

CNORM

           !>          CNORM is DOUBLE PRECISION
           !>          The infinity norm of C. CNORM >= 0.
           !>

References: C. C. Kjelgaard Mikkelsen and L. Karlsson, Blocked Algorithms for Robust Solution of Triangular Linear Systems. In: International Conference on Parallel Processing and Applied Mathematics, pages 68--78. Springer, 2017.

Definition at line 60 of file dlarmm.f.

💫 SLARMM 💫

       real function slarmm (real anorm, real bnorm, real cnorm)

SLARMM

Purpose:

           !>
           !> SLARMM returns a factor s in (0, 1] such that the linear updates
           !>
           !>    (s * C) - A * (s * B)  and  (s * C) - (s * A) * B
           !>
           !> cannot overflow, where A, B, and C are matrices of conforming
           !> dimensions.
           !>
           !> This is an auxiliary routine so there is no argument checking.
           !>

Same energy, real precision edition: s is in (0, 1], and the updates can’t overflow. Slay. 💅

🍓 Parameters 🍓

ANORM

           !>          ANORM is REAL
           !>          The infinity norm of A. ANORM >= 0.
           !>          The number of rows of the matrix A.  M >= 0.
           !>

BNORM

           !>          BNORM is REAL
           !>          The infinity norm of B. BNORM >= 0.
           !>

CNORM

           !>          CNORM is REAL
           !>          The infinity norm of C. CNORM >= 0.
           !>

References: C. C. Kjelgaard Mikkelsen and L. Karlsson, Blocked Algorithms for Robust Solution of Triangular Linear Systems. In: International Conference on Parallel Processing and Applied Mathematics, pages 68--78. Springer, 2017.

Definition at line 60 of file slarmm.f.

💖 AUTHOR 💖

Generated automatically by Doxygen for LAPACK from the source code.

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okay that’s the whole page, bestie 🫶. Footer sign-off: LAPACK, Version 3.12.0, and larmm(3) — that’s the source/version and page tag, and the date slot is giving empty on this one, so don’t come for me 💅✨.