TESTING/EIG/dlarfy.f(3)

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version 3.12.1 · 4 versions
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💅 TESTING/EIG/dlarfy.f — from the Library Functions Manual, bestie

okay so this is TESTING/EIG/dlarfy.f(3), and it's literally the glow-up page for one single subroutine: dlarfy. she's a LAPACK testing-zone icon, she applies a Householder reflector to a symmetric matrix from both sides, and yes she ate. let's get into it 🎀

✨ NAME ✨

TESTING/EIG/dlarfy.f — that's the file, that's the whole name, no notes 💖

🌸 SYNOPSIS 🌸

Functions/Subroutines

  • subroutine dlarfy (uplo, n, v, incv, tau, c, ldc, work) — DLARFY

🦋 Function/Subroutine Documentation 🦋

subroutine dlarfy (character uplo, integer n, double precision, dimension( * ) v, integer incv, double precision tau, double precision, dimension( ldc, * ) c, integer ldc, double precision, dimension( * ) work)

DLARFY 👑 — that's her, that's the whole signature, memorize it fr fr.

🎯 Purpose 🎯

!> !> DLARFY applies an elementary reflector, or Householder matrix, H, !> to an n x n symmetric matrix C, from both the left and the right. !> !> H is represented in the form !> !> H = I - tau * v * v' !> !> where tau is a scalar and v is a vector. !> !> If tau is zero, then H is taken to be the unit matrix. !>

so basically: H shows up on both sides of C — left and right — which is giving main character energy for a matrix operation, honestly. and the H = I - tau * v * v' form? iconic. if tau is zero, H just becomes the unit matrix, no drama, we move on 💅

🧚 Parameters 🧚

  • UPLO — UPLO is CHARACTER*1. tells us which triangular half of the symmetric matrix C is the one actually being stored. = 'U': Upper triangle, = 'L': Lower triangle. pick a lane, bestie 🌈
  • N — N is INTEGER. how many rows and columns matrix C has (square vibes only). constraint check: N >= 0 ✨
  • V — V is DOUBLE PRECISION array, dimension (1 + (N-1)*abs(INCV)). this is the vector v from the whole H = I - tau * v * v' situation described above, no cap 🫶
  • INCV — INCV is INTEGER. the increment between successive elements of v. and listen: INCV must not be zero. like, at all. that's the vibe check and you will fail it 💀
  • TAU — TAU is DOUBLE PRECISION. the scalar tau from the formula above, exactly as described 😌
  • C — C is DOUBLE PRECISION array, dimension (LDC, N). on entry: the actual matrix C, the moment. on exit: C is overwritten by H * C * H' — so she gets fully replaced, hope you didn't need the original 🙈
  • LDC — LDC is INTEGER. the leading dimension of the array C. LDC >= max( 1, N ) — required, non-negotiable 🎀
  • WORK — WORK is DOUBLE PRECISION array, dimension (N). scratch space, the backstage area, the get-ready room ⭐

👑 Author 👑

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

(iconic institutions only, we love a credentialed squad 🌸)

📍 Definition 📍

Definition at line 107 of file dlarfy.f.

🌟 Author 🌟

Generated automatically by Doxygen for LAPACK from the source code. — so yes, a robot wrote this page, but the lore is real, iykyk 🤖💜

okay that's the whole page, bestie, every flag and every constraint accounted for, no details dropped, periodt 🍓

LAPACK — Version 3.12.0 — that's the version, that's the date stamp, so this page is certified vintage-adjacent. stay slay, go call dlarfy responsibly 💅✨🔥
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