SRC/cung2l.f(3)

💅 SRC/cung2l.f — like, the whole entire manual page, bestie

Okay so real talk, this page is the docs for SRC/cung2l.f(3) from the LAPACK library manual, and it is literally about one (1) subroutine. One. And she's iconic for it. Let's get into it 🫶

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✨ NAME ✨

SRC/cung2l.f — that's her. That's the file. That's the name. Short, sweet, slays 💅

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🌸 SYNOPSIS 🌸

Functions/Subroutines

• subroutine cung2l (m, n, k, a, lda, tau, work, info) — CUNG2L generates all or part of the unitary matrix Q from a QL factorization determined by cgeqlf (unblocked algorithm).

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🦋 Function/Subroutine Documentation 🦋

subroutine cung2l (integer m, integer n, integer k, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( * ) work, integer info)

Full signature, verbatim, because we do not play fast and loose with signatures in this house:

subroutine cung2l (integer m, integer n, integer k, complex, dimension( lda,
* ) a, integer lda, complex, dimension( * ) tau, complex, dimension( * )
work, integer info)

CUNG2L generates all or part of the unitary matrix Q from a QL factorization determined by cgeqlf (unblocked algorithm). No cap 🧢

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🎀 Purpose 🎀

So here's the vibe: CUNG2L generates an m-by-n complex matrix Q with orthonormal columns. She is defined as the last n columns of a product of k elementary reflectors of order m — okay, slay, that's a mouthful, but the formula keeps it cute:

      Q  =  H(k) . . . H(2) H(1)

…just as returned by CGEQLF. Periodt. 👑

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💜 Parameters 💜

Buckle up bestie, here come all of them, in order, no skipping, no gatekeeping 🌈

• M — M is INTEGER. The number of rows of the matrix Q. M >= 0. Like, at minimum zero, okay? Zero rows is legal. Zero rows is valid. Zero rows is still a matrix. 🙈
• N — N is INTEGER. The number of columns of the matrix Q. M >= N >= 0. So N can never outgrow M and can never dip below zero — it's a whole mood, honestly, very balanced, main character energy ⭐
• K — K is INTEGER. The number of elementary reflectors whose product defines the matrix Q. N >= K >= 0. Sandwich constraint, love that for her 💖
• A — A is a COMPLEX array, dimension (LDA,N). On entry, the (n-k+i)-th column must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by CGEQLF in the last k columns of its array argument A. On exit, it's the m-by-n matrix Q. Glow-up arc, honestly — she goes from "input vectors" to "the whole entire Q" 🦋✨
• LDA — LDA is INTEGER. The first dimension of the array A. LDA >= max(1,M). Don't forget the max(1,...) bestie, she's not decorative 🔥
• TAU — TAU is a COMPLEX array, dimension (K). TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by CGEQLF. Keep her safe and correct or nothing works 😭
• WORK — WORK is a COMPLEX array, dimension (N). That's it. That's the whole description. She's a workspace, she works, she leaves. Respect 👑🫶
• INFO — INFO is INTEGER, and here's the tea 🍓:
  • = 0: successful exit — we love a happy ending 💖
  • < 0: if INFO = -i, the i-th argument has an illegal value — oop, somebody passed something sus 💀

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🧚 Author 🧚

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

Okay legends only, honestly 🌟

FYI, this is also the Definition at line 113 of file cung2l.f. — clocked it, wrote it down, not skipping it, iykyk 📌

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🍓 Author (yes, another one, and yes, we're keeping it) 🍓

Generated automatically by Doxygen for LAPACK from the source code. So technically the robot wrote this section and we're just vibing with it 🤖💅

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And that's the whole page, bestie — nothing skipped, nothing summarised, every flag and bound and dimension intact. ✨

Little sign-off from me to you: this manual page came from LAPACK Version 3.12.0, and we're reading it as SRC/cung2l.f(3) — ty for coming to my TED talk, mwah 💖🎀🌈