DRQT03(3)

💅 drqt03(3) — like, the LAPACK tester for DORMRQ, bestie

okay so first things first: this page lives in the Library Functions Manual (the <italic>drqt03.f(3)</italic> one, from the whole /home/abui...IN/drqt03.f(3) situation) and it's literally all about a Fortran subroutine that checks whether DORMRQ is doing its job. yes queen, quality assurance ✨

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✨ SYNOPSIS ✨

Functions/Subroutines 🫶

subroutine DRQT03 (m, n, k, af, c, cc, q, lda, tau, work, lwork, rwork,
    result)

DRQT03 — that's the whole name, no cap 💅

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🎀 Function/Subroutine Documentation 🎀

subroutine DRQT03 (integer m, integer n, integer k, double precision,
    dimension( lda, * ) af, double precision, dimension( lda, * ) c, double
    precision, dimension( lda, * ) cc, double precision, dimension( lda, * )
    q, integer lda, double precision, dimension( * ) tau, double precision,
    dimension( lwork ) work, integer lwork, double precision, dimension( * )
    rwork, double precision, dimension( * ) result)

DRQT03 👑

🌸 Purpose 🌸

ok so picture this: DRQT03 tests DORMRQ, which computes Q*C, Q'*C, C*Q or C*Q'. that's it, that's the vibe.

and how does it do the vibe check? DRQT03 compares the results of a call to DORMRQ with the results of forming Q explicitly by a call to DORGRQ and then performing matrix multiplication by a call to DGEMM. two techniques, one winner, we love a head-to-head 💀🔥

🦋 Parameters 🦋

• M — M is INTEGER. it's the number of rows or columns of the matrix C; C is n-by-m if Q is applied from the left, or m-by-n if Q is applied from the right. M >= 0. bestie it literally cannot be negative 🙈
• N — N is INTEGER. the order of the orthogonal matrix Q. N >= 0. again, zero is fine, negative is not ✨
• K — K is INTEGER. the number of elementary reflectors whose product defines the orthogonal matrix Q. N >= K >= 0. it's sandwiched, she's contained, periodt 👑
• AF — AF is DOUBLE PRECISION array, dimension (LDA,N). details of the RQ factorization of an m-by-n matrix, as returned by DGERQF. See SGERQF for further details. iykyk 🧚
• C — C is DOUBLE PRECISION array, dimension (LDA,N). yes. that's the whole description. she's mysterious, she's iconic 💅
• CC — CC is DOUBLE PRECISION array, dimension (LDA,N). same energy, different name 🎀
• Q — Q is DOUBLE PRECISION array, dimension (LDA,N). the main character herself 🌈
• LDA — LDA is INTEGER. the leading dimension of the arrays AF, C, CC, and Q. one number to rule all four arrays fr fr
• TAU — TAU is DOUBLE PRECISION array, dimension (min(M,N)). the scalar factors of the elementary reflectors corresponding to the RQ factorization in AF. the little guys behind the scenes 🍓
• WORK — WORK is DOUBLE PRECISION array, dimension (LWORK). the workspace. she works 💀
• LWORK — LWORK is INTEGER. the length of WORK. LWORK must be at least M, and should be M*NB, where NB is the blocksize for this environment. yes, "must" and "should" are different words, don't come for me 😭
• RWORK — RWORK is DOUBLE PRECISION array, dimension (M). okay so there's WORK and there's RWORK and you need both 🫶
• RESULT — RESULT is DOUBLE PRECISION array, dimension (4). the test ratios compare two techniques for multiplying a random matrix C by an n-by-n orthogonal matrix Q. like, the receipts:

RESULT(1) = norm( Q*C - Q*C )  / ( N * norm(C) * EPS )
RESULT(2) = norm( C*Q - C*Q )  / ( N * norm(C) * EPS )
RESULT(3) = norm( Q'*C - Q'*C )/ ( N * norm(C) * EPS )
RESULT(4) = norm( C*Q' - C*Q' )/ ( N * norm(C) * EPS )

💜 Author 💜

the whole squad behind this one:

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

Definition at line 134 of file drqt03.f. go look, she's right there 📍

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ngl this whole page was generated automatically by Doxygen for LAPACK from the source code. so if something reads weird, blame the robot, not me 🤖💀

and that's the tea, bestie — LAPACK, Version 3.12.0, dated /home/abui...IN/drqt03.f(3). mwah, slay, go test some matrices 💖✨🎀🦋