SRC/dorgl2.f(3)

💅 SRC/dorgl2.f — the dorgl2 one (LAPACK, bestie)

okay so real talk, this page is from the LAPACK manual, and it's a Fortran thing, so buckle up 🎀

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✨ SYNOPSIS ✨

Functions/Subroutines 🦋

• subroutine dorgl2 (m, n, k, a, lda, tau, work, info) — literally the whole vibe, it's DORGL2

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🌸 Function/Subroutine Documentation 🌸

subroutine dorgl2 (integer m, integer n, integer k, double precision,
    dimension( lda, * ) a, integer lda, double precision, dimension( * )
    tau, double precision, dimension( * ) work, integer info)

DORGL2 👑

🫶 Purpose:

!>
!> DORGL2 generates an m by n real matrix Q with orthonormal rows,
!> which is defined as the first m rows of a product of k elementary
!> reflectors of order n
!>
!>       Q  =  H(k) . . . H(2) H(1)
!>
!> as returned by DGELQF.
!>

so basically it builds Q for you — an m-by-n real matrix with orthonormal rows, defined as the first m rows of that product of k elementary reflectors of order n, exactly the way DGELQF hands them back to you. no cap, it's giving "I do the math so you don't have to" energy 💅

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🌈 Parameters

🍓 M

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

the row count of Q. constraint: M >= 0 — negative rows are not a thing, bestie 😭

🧚 N

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

the column count of Q. constraint: N >= M — the columns gotta cover the rows, periodt.

⭐ K

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

how many elementary reflectors are multiplying together to define Q. constraint: M >= K >= 0 — sandwich it between zero and M, okay? 🥪

🦋 A

!>          A is DOUBLE PRECISION 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 DGELQF in the first k rows of its array argument A.
!>          On exit, the m-by-n matrix Q.
!>

DOUBLE PRECISION array, dimension (LDA,N). on entry, row i has to contain the vector defining the elementary reflector H(i) for i = 1,2,...,k, exactly as DGELQF returns them in the first k rows of its array argument A. on exit? it's literally Q, the m-by-n matrix. glow-up complete ✨

💜 LDA

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

the first dimension of A. constraint: LDA >= max(1,M) — don't try to be cute and shrink it, it will not slay 🙈

🎀 TAU

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

DOUBLE PRECISION array, dimension (K). TAU(i) must hold the scalar factor of the elementary reflector H(i), as returned by DGELQF. the little scalars behind the whole operation, iykyk 💖

🔥 WORK

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

DOUBLE PRECISION array, dimension (M). that's it, that's the whole description — it's the workspace, it works, slay.

👑 INFO

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

INTEGER, and here's the tea:

• = 0 — successful exit, we ate 🎉
• < 0 — if INFO = -i, the i-th argument had an illegal value 💀

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🧚 Author

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

Definition at line 112 of file dorgl2.f. 📍

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💖 Author (the meta one)

Generated automatically by Doxygen for LAPACK from the source code. yes, a robot wrote the page, and I'm just here to make it cute 🤖🎀

ngl, everything above is a spec — don't invent behaviour, just pass the right args and let DORGL2 cook 🔥

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and that's the whole page, bestie! this was LAPACK, Version 3.12.0, page SRC/dorgl2.f(3) — go forth and generate those orthonormal rows 💅✨🫶