DORG2L(3)

💅 dorg2l.f — like, the whole manual page, bestie

okay so this is a page from the Library Functions Manual, and the file it's documenting is literally this path right here:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dorg2l.f

(it's dorg2l.f(3) in the header if you're keeping track 🎀)

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✨ SYNOPSIS ✨

Functions/Subroutines

• subroutine DORG2L (m, n, k, a, lda, tau, work, info) — DORG2L generates all or part of the orthogonal matrix Q from a QL factorization determined by sgeqlf (unblocked algorithm).

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🦋 Function/Subroutine Documentation 🦋

subroutine DORG2L (integer m, integer n, integer k, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( * ) work, integer info)

DORG2L generates all or part of the orthogonal matrix Q from a QL factorization determined by sgeqlf (unblocked algorithm). no cap, that's the whole vibe 💜

🎀 Purpose:

!>
!> DORG2L generates an m by n real matrix Q with orthonormal columns,
!> which is defined as the last n columns of a product of k elementary
!> reflectors of order m
!>
!>       Q  =  H(k) . . . H(2) H(1)
!>
!> as returned by DGEQLF.
!>

like, it's giving "assemble the icon from the leftover reflector pieces" ✨

🌸 Parameters 🌸

• M

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

the row count, bestie. and it's gotta be M >= 0.

• N

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

column count, and note the sandwich: M >= N >= 0.

• K

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

how many elementary reflectors are multiplying together to make Q. constraint: N >= K >= 0.

• A

!>          A is DOUBLE PRECISION 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 DGEQLF in the last k columns of its array
!>          argument A.
!>          On exit, the m by n matrix Q.
!>

okay so on entry 👉 column (n-k+i) holds the vector defining H(i) for i = 1,2,...,k, exactly as DGEQLF handed it back in the last k columns of its A. on exit 👉 it's the full m by n matrix Q. glow-up fr fr 💅

• LDA

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

leading dimension of A, and it must satisfy LDA >= max(1,M).

• TAU

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

the scalar factor tea ☕ for each H(i), straight from DGEQLF.

• WORK

!>          WORK is DOUBLE PRECISION array, dimension (N)
!>

scratch space, dimension (N). it's just doing its little job 🫶

• INFO

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

the vibe check at the end: 0 means slay, we're done. and if INFO = -i (a negative number), then the i-th argument had an illegal value 😭

👑 Author

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

⭐ Definition at line 113 of file dorg2l.f.

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🌈 Author (the meta one) 🌈

Generated automatically by Doxygen for LAPACK from the source code. it literally wrote itself, main character energy ✨

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💖 that's the whole page, bestie — every flag, every constraint, every author. nothing skipped, periodt.

LAPACK · Version 3.12.0 · /home/abui...RC/dorg2l.f(3) — mwah, see u in the next manpage 🧚💜🎀