SRC/zunglq.f(3)

✨ SRC/zunglq.f ✨

okay so this is a page from the Library Functions Manual for LAPACK, and today's main character is zunglq 💅 buckle up bestie, she's a Fortran subroutine and she's iconic.

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🎀 SYNOPSIS 🎀

Functions/Subroutines

• subroutine zunglq (m, n, k, a, lda, tau, work, lwork, info) — literally ZUNGLQ, that's her name, no notes 🫶

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🌸 Function/Subroutine Documentation 🌸

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

ZUNGLQ 💖 (yes the full signature is right up there, we love a thorough girlie)

🦋 Purpose 🦋

okay so the way that ZUNGLQ generates an M-by-N complex matrix Q with orthonormal rows — and she defines it as the first M rows of a product of K elementary reflectors of order N, no cap:

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

...exactly as returned by ZGELQF. periodt. ✨

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🍓 Parameters 🍓

• M — M is INTEGER. it's the number of rows of the matrix Q. M >= 0. simple as that, bestie.
• N — N is INTEGER. the number of columns of the matrix Q. constraint check: N >= M. 💜
• K — K is INTEGER. the number of elementary reflectors whose product defines the matrix Q. rules: M >= K >= 0. yes both of those, she's strict 😌
• A — A is COMPLEX*16 array, dimension (LDA,N).
  • on entry: the i-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by ZGELQF in the first k rows of its array argument A. 👀
  • on exit: the M-by-N matrix Q. glow-up complete, she ate 💅
• LDA — LDA is INTEGER. the first dimension of the array A. LDA >= max(1,M). don't skip the max, fr fr.
• TAU — TAU is COMPLEX*16 array, dimension (K). TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by ZGELQF. she's the supporting cast but she's essential 🎀
• WORK — WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)). on exit, if INFO = 0, WORK(1) returns the optimal LWORK. cute little bonus info 💫
• LWORK — LWORK is INTEGER. the dimension of the array WORK. LWORK >= max(1,M). for optimum performance LWORK >= M*NB, where NB is the optimal blocksize. highkey she wants room to breathe 😤
  • > ⚠️ if LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. so like, don't panic when nothing yells at you, that's the whole point 🫶
• INFO — INFO is INTEGER:
  • = 0: successful exit; slay 🎉
  • < 0: if INFO = -i, the i-th argument has an illegal value 💀 rude but valid

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👑 Author 👑

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

such a stacked collab, honestly 🌈

Definition at line 126 of file zunglq.f. ✨

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🌺 Author 🌺

generated automatically by Doxygen for LAPACK from the source code. the robots did this one, we just added the sparkle 🧚

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💖 and that's the whole page bestie, no cap. go forth and make your orthonormal rows.

LAPACK — Version 3.12.0 🌸 bye lovie, drink some water, and remember: LWORK >= max(1,M) 🫶💅