SORG2R(3)

💅 SORG2R(3) — like, the manual page, bestie

okay so first things first: this page lives in the Library Functions Manual (yes, that's the manual name, keep up 💖) and the file we're talking about is, like, sorg2r.f — full path /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/sorg2r.f, or as the header shows it, /home/abui...RC/sorg2r.f(3). Cute. Truncated. Iconic. 🎀

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✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/sorg2r.f — that's the whole name section, no cap, it's literally just the file path. LAPACK said "the name IS the address" and honestly? slay. 🦋

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🌸 SYNOPSIS 🌸

Functions/Subroutines

subroutine SORG2R (m, n, k, a, lda, tau, work, info)

SORG2R generates all or part of the orthogonal matrix Q from a QR factorization determined by sgeqrf (unblocked algorithm). that's the whole vibe 💫

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👑 Function/Subroutine Documentation 👑

subroutine SORG2R (integer m, integer n, integer k, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( * ) work, integer info)

SORG2R generates all or part of the orthogonal matrix Q from a QR factorization determined by sgeqrf (unblocked algorithm). (yes I said it twice, it's that important, periodt 💅)

🧚 Purpose:

!>
!> SORG2R generates an m by n real matrix Q with orthonormal columns,
!> which is defined as the first n columns of a product of k elementary
!> reflectors of order m
!>
!>       Q  =  H(1) H(2) . . . H(k)
!>
!> as returned by SGEQRF.
!>

so like, you hand it the reflector data and it hands you back Q, the first n columns of that big product of k elementary reflectors of order m, exactly as SGEQRF gave them to you. math but make it fashion ✨

🌈 Parameters

• M — M is INTEGER, the number of rows of the matrix Q. constraint: M >= 0. no negative rows bestie, we don't do that here 🙈
• N — N is INTEGER, the number of columns of the matrix Q. constraint: M >= N >= 0. (yep, it's sandwiched between M and zero 😭)
• K — K is INTEGER, the number of elementary reflectors whose product defines the matrix Q. constraint: N >= K >= 0.
• A — A is REAL array, dimension (LDA,N).
  • On entry: the i-th column must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by SGEQRF in the first k columns of its array argument A. 🫶
  • On exit: the m-by-n matrix Q. glow-up complete 💖
• LDA — LDA is INTEGER, the first dimension of the array A. constraint: LDA >= max(1,M). respect the leading dimension or perish 🔥
• TAU — TAU is REAL array, dimension (K). TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by SGEQRF. the little scalar that could ⭐
• WORK — WORK is REAL array, dimension (N). scratch space, doing the most behind the scenes, main character energy fr fr 🎀
• WORK... no wait, INFO — INFO is INTEGER:
  • = 0: successful exit 🎉
  • < 0: if INFO = -i, the i-th argument has an illegal value. 💀 somebody passed a bad arg, it happens

🦋 Author

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

(the whole squad, we love a collab 👑)

⭐ Definition at line 113 of file sorg2r.f.

like, go look at line 113 if you want the receipts, iykyk.

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🍓 Author (yeah there's a second one, don't @ me)

Generated automatically by Doxygen for LAPACK from the source code. a robot wrote this and honestly it ate 🤖✨

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lowkey reminder bestie: M >= N >= 0, N >= K >= 0, and LDA >= max(1,M) — break those and INFO will come for you with a negative number 😭

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and that's the page! 🌸 brought to you by LAPACK, Version 3.12.0, dated /home/abui...RC/sorg2r.f(3) — mwah, drink water, and go generate some orthonormal columns 💜🫶