ZQRT11(3)

📦 version 3.12.0, in opensuse-leap 16.0

💅 ZQRT11 — like, the whole manual, but make it make sense

Hey bestie 🫶 so this page lives in the Library Functions Manual (yes, that's the manual name, we're folding it in up top like a cute lil hair clip). It's a (3) man page, and the function is ZQRT11. It's giving LAPACK testing energy, and honestly? Iconic.

🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/zqrt11.f

That's the file. That's literally the whole NAME section. Periodt. 💅 (Yes, it's a path, and yes, you're gonna read it out loud in the group chat, sorry.)

✨ SYNOPSIS ✨

Functions/Subroutines

double precision function ZQRT11 (m, k, a, lda, tau, work, lwork)

ZQRT11

🦋 Function/Subroutine Documentation 🦋

double precision function ZQRT11 (integer m, integer k, complex*16,
    dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau,
    complex*16, dimension( lwork ) work, integer lwork)

ZQRT11

🎀 Purpose 🎀

okay so, bestie, pay attention, because this is the whole point of the function:

ZQRT11 computes the test ratio || Q'*Q - I || / (eps * m) where the orthogonal matrix Q is represented as a product of elementary transformations. Each transformation has the form H(k) = I - tau(k) v(k) v(k)' where tau(k) is stored in TAU(k) and v(k) is an m-vector of the form [ 0 ... 0 1 x(k) ]', where x(k) is a vector of length m-k stored in A(k+1:m,k).

Like, it's a test ratio — || Q'*Q - I || / (eps * m) — because Q should be orthogonal, and if Q'*Q isn't basically I, something is wrong, and this function is the one holding the mirror up. 🪞✨ It's the vibe check of the QR world, fr fr.

🍓 Parameters 🍓

M

M is INTEGER The number of rows of the matrix A.

So, like, how tall A is. 📏

K

K is INTEGER The number of columns of A whose subdiagonal entries contain information about orthogonal transformations.

i.e. how many columns are out here carrying the orthogonal-transformation lore. The subdiagonal entries are doing the heavy lifting, iykyk. 👑

A

A is COMPLEX*16 array, dimension (LDA,K) The (possibly partial) output of a QR reduction routine.

"Possibly partial" — she's a work in progress, and that's beautiful. 🫶

LDA

LDA is INTEGER The leading dimension of the array A.

The leading dimension, bestie. Don't skip it, don't question it. ⭐

TAU

TAU is COMPLEX*16 array, dimension (K) The scaling factors tau for the elementary transformations as computed by the QR factorization routine.

The scaling factors, straight from the QR factorization routine's own hands. 💖

WORK

WORK is COMPLEX*16 array, dimension (LWORK)

That's it. That's the description. It's a workspace array of size LWORK and nobody asked it to be more interesting than that. 💀

LWORK

LWORK is INTEGER The length of the array WORK. LWORK >= M*M + M.

⚠️ Important, no cap: LWORK >= M*M + M. That's the floor. Do not come in under that. 😭 It's M*M + M and it's not a suggestion.

👑 Author 👑

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

(i.e. the whole squad co-signed this one. 🌈)

Definition at line 97 of file zqrt11.f.

🧚 Author (yes, again) 🧚

Generated automatically by Doxygen for LAPACK from the source code.

Like, nobody hand-wrote this page, the machine did it, and honestly it ate. 🤖✨

💐 Sign-off 💐

This gorgeous lil page is LAPACK, Version 3.12.0 — and its footer path is /home/abui...IN/zqrt11.f(3), tucked in right there at the bottom like a signature on a love letter. 💌

Slay, bestie. Go orthogonalize something. 🔥💜

📦 where this page comes from