SRC/slarz.f(3)

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version 3.12.1 · 4 versions
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SRC/slarz.f 💅

Okay so bestie, this is literally the manual for SRC/slarz.f — a Fortran file in LAPACK that does some iconic matrix magic. It's giving "linear algebra but make it fashion" ✨

✨ SYNOPSIS ✨

Here's the function/subroutine tea:

subroutine slarz (side, m, n, l, v, incv, tau, c, ldc, work)

SLARZ applies an elementary reflector (as returned by stzrzf) to a general matrix. No cap, that's the whole vibe.

🎀 Function/Subroutine Documentation 🎀

subroutine slarz (character side, integer m, integer n, integer l, real, dimension( * ) v, integer incv, real tau, real, dimension( ldc, * ) c, integer ldc, real, dimension( * ) work)

SLARZ applies an elementary reflector (as returned by stzrzf) to a general matrix. Like, it literally takes a reflector and slaps it onto a matrix 💅

🌸 Purpose 🌸

!> SLARZ applies a real elementary reflector H to a real M-by-N !> matrix C, from either the left or the right. H is represented in the !> form ! !> H = I - tau * v * v**T ! !> where tau is a real scalar and v is a real vector. ! !> If tau = 0, then H is taken to be the unit matrix. ! !> H is a product of k elementary reflectors as returned by STZRZF.

So basically H is this fancy reflector thing made from tau and v. If tau is zero, H just becomes the identity matrix — like it's not even trying, periodt. And H is actually a whole product of k elementary reflectors from STZRZF. Obsessed 🔥

🌈 Parameters 🌈

  • SIDE — CHARACTER*1 — tells you which side the reflector goes on:
    • = 'L': form H * C (left side, left side, left side)
    • = 'R': form C * H (right side, right side, right side)
  • M — INTEGER — the number of rows of the matrix C. Like how tall it is 📏
  • N — INTEGER — the number of columns of the matrix C. How wide it is 📐
  • L — INTEGER — the number of entries of the vector V that contain the meaningful part of the Householder vectors. Constraints, bestie:
    • If SIDE = 'L', then M >= L >= 0
    • If SIDE = 'R', then N >= L >= 0
  • V — REAL array, dimension (1+(L-1)*abs(INCV)) — the vector v in the representation of H as returned by STZRZF. Lowkey important: V is not used if TAU = 0 💀
  • INCV — INTEGER — the increment between elements of v. And INCV <> 0 — no zero increments allowed, fr fr 🚫
  • TAU — REAL — the value tau in the representation of H. The main character of the equation ✨
  • C — REAL array, dimension (LDC,N) — on entry, the M-by-N matrix C. On exit, C is overwritten by:
    • H * C if SIDE = 'L'
    • C * H if SIDE = 'R' Like it literally gets replaced, no take-backsies 💅
  • LDC — INTEGER — the leading dimension of the array C. Must be LDC >= max(1,M). Respect the constraint, bestie 🫶
  • WORK — REAL array, dimension:
    • (N) if SIDE = 'L'
    • or (M) if SIDE = 'R' It's the workspace, doing the behind-the-scenes work 🧚

👑 Author 👑

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

💖 Contributors: 💖

  • A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

🦋 Further Details: 🦋

!>

(That's literally it — nothing else in the further details. Iconic minimalism 😭)

⭐ Definition at line 144 of file slarz.f. ⭐

🌟 Author 🌟

Generated automatically by Doxygen for LAPACK from the source code. Like the robots did this one, no cap 🤖✨

And that's the whole manual, bestie! LAPACK Version 3.12.0, SRC/slarz.f(3), slaying since forever. Periodt 💅🎀

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