CUNGR2(3)

💜 CUNGR2 (3) — like, the whole vibe

okay bestie, so you know how LAPACK has approximately one billion subroutines and half of them are named like someone fell asleep on a keyboard? Yeah. This one lives at:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/cungr2.f

That's the whole file path, no cap. That's the "NAME" energy here — it's a Fortran source file, and this page is its little friendship bracelet of documentation. 🎀

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✨ SYNOPSIS ✨

Under "Functions/Subroutines" we got exactly one icon:

subroutine CUNGR2 (m, n, k, a, lda, tau, work, info)

CUNGR2 generates all or part of the unitary matrix Q from an RQ factorization determined by cgerqf (unblocked algorithm).

That's the elevator pitch. Iconic. 🫶

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💅 Function/Subroutine Documentation 💅

subroutine CUNGR2 (integer m, integer n, integer k, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( * ) work, integer info)

CUNGR2 generates all or part of the unitary matrix Q from an RQ factorization determined by cgerqf (unblocked algorithm).

🌸 Purpose 🌸

!> !> CUNGR2 generates an m by n complex matrix Q with orthonormal rows, !> which is defined as the last m rows of a product of k elementary !> reflectors of order n !> !> Q = H(1)**H H(2)**H . . . H(k)**H !> !> as returned by CGERQF. !>

So basically — those reflectors? We're conjugating-transposing them and multiplying them all together, and that's your Q. It's giving row-orthonormal, not column, bestie. Notice the difference. 👑

🦋 Parameters 🦋

• M

!> M is INTEGER !> The number of rows of the matrix Q. M >= 0. !>

Number of rows. Cannot be negative, not even a little.

• N

!> N is INTEGER !> The number of columns of the matrix Q. N >= M. !>

Number of columns, and yes N >= M is a whole requirement. It's not optional, it's a lifestyle.

• K

!> K is INTEGER !> The number of elementary reflectors whose product defines the !> matrix Q. M >= K >= 0. !>

How many elementary reflectors are in the group chat, essentially. Constraint is M >= K >= 0 and we respect it. ✨

• A

!> A is COMPLEX array, dimension (LDA,N) !> On entry, the (m-k+i)-th row must contain the vector which !> defines the elementary reflector H(i), for i = 1,2,...,k, as !> returned by CGERQF in the last k rows of its array argument !> A. !> On exit, the m-by-n matrix Q. !>

Okay so on entry the (m-k+i)-th row holds the vector defining H(i), for i = 1,2,...,k, exactly as CGERQF handed it over in the last k rows of its array argument A. On exit? It's Q. Glow-up complete. 💖 Don't forget the dimension is (LDA,N).

• LDA

!> LDA is INTEGER !> The first dimension of the array A. LDA >= max(1,M). !>

The first dimension of the array A, and the rule is LDA >= max(1,M). Write it down, memorize it, put it on a sticky note. 🎀

• TAU

!> TAU is COMPLEX array, dimension (K) !> TAU(i) must contain the scalar factor of the elementary !> reflector H(i), as returned by CGERQF. !>

Dimension (K). TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by CGERQF. No improvising, bestie. 🦋

• WORK

!> WORK is COMPLEX array, dimension (M) !>

Just a COMPLEX array of dimension (M). She works. That's the whole description. Respect. 💅

• INFO

!> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument has an illegal value !>

Exit status icon: = 0 means successful exit (slay), and < 0 means if INFO = -i, the i-th argument has an illegal value (not slay, go fix your argument). 😭

👑 Author 👑

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

All four of them. Group project that actually got finished. 🌟

Definition at line 113 of file cungr2.f.

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⭐ Author (yes, again) ⭐

Generated automatically by Doxygen for LAPACK from the source code. Classic Doxygen behavior. It literally said "I'll do it myself." 💀

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🌈💜 that's the whole page, bestie — LAPACK Version 3.12.0, page footer from /home/abui...RC/cungr2.f(3), and yes, the timestamp in the footer got abbreviated into that ellipsis-laden path because that's exactly how it's printed. fr fr. 🧚✨