ZUNGR2(3)

🦋 ZUNGR2(3) — like, the RQ unitary matrix generator, bestie

okay so first things first: this lil page lives in the Library Functions Manual section, and the file it's yapping about is /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zungr2.f — yes that's the whole path, no I'm not shortening it, she's iconic like that 💅

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✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zungr2.f — that's the file, that's the whole name, we don't do nicknames here 🎀

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🌸 SYNOPSIS 🌸

Functions/Subroutines

subroutine ZUNGR2 (m, n, k, a, lda, tau, work, info)

ZUNGR2 generates all or part of the unitary matrix Q from an RQ factorization determined by cgerqf (unblocked algorithm). periodt. 💖

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👑 Function/Subroutine Documentation 👑

subroutine ZUNGR2 (integer m, integer n, integer k, complex*16, dimension(
    lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16,
    dimension( * ) work, integer info)

ZUNGR2 generates all or part of the unitary matrix Q from an RQ factorization determined by cgerqf (unblocked algorithm). literally the whole plot of this subroutine, right there 🫶

💜 Purpose:

!>
!> ZUNGR2 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 ZGERQF.
!>

so she builds an m-by-n complex matrix Q, orthonormal rows and all, and Q is defined as the last m rows of a product of k elementary reflectors of order n. slay ✨

🌈 Parameters

• M — no cap, this one matters:

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

the number of rows of Q. M >= 0. 💖

• N — the width queen:

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

the number of columns of Q. N >= M. note that, it's N greater than or equal to M, not the other way around 🎀

• K — the reflector count:

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

the number of elementary reflectors whose product defines Q. M >= K >= 0. yes bestie, sandwiched between M and 0 🦋

• A — main character energy, honestly:

!>          A is COMPLEX*16 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 ZGERQF in the last k rows of its array argument
!>          A.
!>          On exit, the m-by-n matrix Q.
!>

COMPLEX*16 array, dimension (LDA,N). on entry, the (m-k+i)-th row has GOT to contain the vector defining the elementary reflector H(i), for i = 1,2,...,k, exactly as ZGERQF returned it in the last k rows of its array argument A. on exit? boom, she's the m-by-n matrix Q now. glow-up 💅

• LDA — the leading dimension baddie:

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

INTEGER, the first dimension of the array A. LDA >= max(1,M). don't skip the max(1,M) part, iykyk 🔥

• TAU — the scalar factor stash:

!>          TAU is COMPLEX*16 array, dimension (K)
!>          TAU(i) must contain the scalar factor of the elementary
!>          reflector H(i), as returned by ZGERQF.
!>

COMPLEX*16 array, dimension (K). TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by ZGERQF. 💜

• WORK — the workspace, she's just vibing:

!>          WORK is COMPLEX*16 array, dimension (M)
!>

COMPLEX*16 array, dimension (M). that's it. that's the whole description. sometimes less is more 🧚

• INFO — the vibe check:

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

INTEGER. = 0: successful exit, we love to see it 🌸. < 0: if INFO = -i, the i-th argument has an illegal value — and you KNOW which one it is because she tells you the index, respectful king 😭

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⭐ Author ⭐

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

all four of them, credited, together, as it should be 👑

Definition at line 113 of file zungr2.f. 📍

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🍓 Author (yes, again, different author block, don't @ me)

Generated automatically by Doxygen for LAPACK from the source code. she didn't write her own bio, a robot did 🤖✨

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fr fr though: the array bounds, the dimension declarations, and every >= in here are load-bearing. treat them like the rules of the group chat — break them and it's chaos 💀

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and that's the whole page bestie!! this lil slice of the LAPACK docs is Version 3.12.0, and yes, the footer still points at /home/abui...RC/zungr2.f(3) — same file, same energy, mwah 💋🫶