DLQT01(3)

✨ DLQT01(3) — the LQ factorization test girlie ✨

okay so bestie, let me tell you about DLQT01 from the LAPACK crew 💅 this one lives in /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/dlqt01.f and she is literally the vibe check for your LQ factorization, no cap 🎀

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🌸 SYNOPSIS 🌸

Functions/Subroutines — it's giving "one job, one subroutine":

subroutine DLQT01 (m, n, a, af, q, l, lda, tau, work, lwork, rwork, result)
    DLQT01

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🔥 Function/Subroutine Documentation 🔥

subroutine DLQT01 (integer m, integer n, double precision, dimension( lda, * ) a, double precision, dimension( lda, * ) af, double precision, dimension( lda, * ) q, double precision, dimension( lda, * ) l, integer lda, double precision, dimension( * ) tau, double precision, dimension( lwork ) work, integer lwork, double precision, dimension( * ) rwork, double precision, dimension( * ) result)
    DLQT01

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👑 Purpose 👑

ok so picture this: DLQT01 is the designated tester for DGELQF — that's the one that computes the LQ factorization of an m-by-n matrix A, iykyk. It also partially tests DORGLQ, which is the icon that forms the n-by-n orthogonal matrix Q. main character energy from both of them honestly 🦋

And what does our girl actually do? She compares L with A*Q', and checks that Q is orthogonal. That's it. That's the whole assignment. periodt 💖

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✨ Parameters ✨

• M — M is INTEGER. The number of rows of the matrix A. Constraint era: M >= 0. zero rows? allowed, we respect it 🙈
• N — N is INTEGER. The number of columns of the matrix A. Constraint: N >= 0. same energy, no negativity allowed 💀
• A — A is DOUBLE PRECISION array, dimension (LDA,N). The m-by-n matrix A herself. the original. the blueprint 🌸
• AF — AF is DOUBLE PRECISION array, dimension (LDA,N). Details of the LQ factorization of A, as returned by DGELQF. See DGELQF for further details — she's the receipts, basically 🧾
• Q — Q is DOUBLE PRECISION array, dimension (LDA,N). The n-by-n orthogonal matrix Q. iconic, orthogonal, everything 💅
• L — L is DOUBLE PRECISION array, dimension (LDA,max(M,N)). (that's the whole description, she's mysterious like that 🌈)
• LDA — LDA is INTEGER. The leading dimension of the arrays A, AF, Q and L. Constraint: LDA >= max(M,N). she's the boss of all four of them fr fr 👑
• TAU — TAU is DOUBLE PRECISION array, dimension (min(M,N)). The scalar factors of the elementary reflectors, as returned by DGELQF. cute little scalars, we love them 🎀
• WORK — WORK is DOUBLE PRECISION array, dimension (LWORK). the workspace, the grind, the behind-the-scenes 🫶
• LWORK — LWORK is INTEGER. The dimension of the array WORK. that's literally all it says, no notes 😭
• RWORK — RWORK is DOUBLE PRECISION array, dimension (max(M,N)). its own little world 💜
• RESULT — RESULT is DOUBLE PRECISION array, dimension (2). The test ratios, and bestie these are THE numbers:
  • RESULT(1) = norm( L - A*Q' ) / ( N * norm(A) * EPS )
  • RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )

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💖 Author 💖

the legends themselves:

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

Definition at line 124 of file dlqt01.f. slay 📍

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🦋 Author (yes again, that's how the page does it) 🦋

Generated automatically by Doxygen for LAPACK from the source code. the robots wrote this one, respectfully 🤖

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so yeah, that's DLQT01 — she tests DGELQF, she partially tests DORGLQ, she compares L with A*Q', she checks Q is orthogonal, and she reports exactly two ratios in RESULT. no cap, no filler, just factorization verification with immaculate vibes 🌟

LAPACK, Version 3.12.0 — this cutie came straight from /home/abui...IN/dlqt01.f(3) and honestly? she ate. 💅✨