SRQT03(3)

🎀 NAME 🎀

okay bestie, this is the manpage for SRQT03(3) — aka /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/srqt03.f. That's the name section, no cap 💅.

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✨ SYNOPSIS ✨

Functions/Subroutines

subroutine SRQT03 (m, n, k, af, c, cc, q, lda, tau, work, lwork, rwork,
    result)
    SRQT03

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🧚 FUNCTION/SUBROUTINE DOCUMENTATION 🧚

🌈 SRQT03 🌈

subroutine SRQT03 (integer m, integer n, integer k, real, dimension( lda, * ) af, real, dimension( lda, * ) c, real, dimension( lda, * ) cc, real, dimension( lda, * ) q, integer lda, real, dimension( * ) tau, real, dimension( lwork ) work, integer lwork, real, dimension( * ) rwork, real, dimension( * ) result)

SRQT03 is the icon, the moment, the whole test routine 💖.

🌸 Purpose 🌸

okay so SRQT03 tests SORMRQ, which computes Q*C, Q'*C, C*Q or C*Q'. It's giving "let me verify that for you."

SRQT03 compares the results of a call to SORMRQ with the results of forming Q explicitly by a call to SORGRQ and then performing matrix multiplication by a call to SGEMM. literally comparing two techniques, bestie 🦋.

🎀 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. yes ma'am, dimension check 💅.
• N — N is INTEGER. It's the order of the orthogonal matrix Q. N >= 0. iconic square-ish energy ✨.
• K — K is INTEGER. It's the number of elementary reflectors whose product defines the orthogonal matrix Q. N >= K >= 0. the way that constraint sits there 🫶.
• AF — AF is REAL array, dimension (LDA,N). It holds details of the RQ factorization of an m-by-n matrix, as returned by SGERQF. See SGERQF for further details. iykyk, the factorization lore lives over there 🔥.
• C — C is REAL array, dimension (LDA,N). main-character matrix, no notes 🎀.
• CC — CC is REAL array, dimension (LDA,N). another matrix bestie, matching energy 💖.
• Q — Q is REAL array, dimension (LDA,N). the orthogonal matrix in question, slay ✨.
• LDA — LDA is INTEGER. It's the leading dimension of the arrays AF, C, CC, and Q. the group-chat leader, lowkey important 💅.
• TAU — TAU is REAL array, dimension (min(M,N)). It holds the scalar factors of the elementary reflectors corresponding to the RQ factorization in AF. tiny but powerful 🔥.
• WORK — WORK is REAL array, dimension (LWORK). workspace bestie, doing the behind-the-scenes work 🫶.
• LWORK — LWORK is INTEGER. It's the length of WORK. LWORK must be at least M, and should be M*NB, where NB is the blocksize for this environment. do not skimp on LWORK, bestie 😭.
• RWORK — RWORK is REAL array, dimension (M). another little helper array, living its truth 🌸.
• RESULT — RESULT is REAL array, dimension (4). The test ratios compare two techniques for multiplying a random matrix C by an n-by-n orthogonal matrix Q. Here's the exact formula lineup, and yes, we're keeping every character 👑:

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 👑

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

Definition at line 134 of file srqt03.f. periodt ✨.

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💖 AUTHOR 💖

Generated automatically by Doxygen for LAPACK from the source code. the auto-generated fairy godmother did her thing 🧚.

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okay that's the whole vibe check, bestie 💜 — this page is serving LAPACK Version 3.12.0 energy and the path /home/abui...IN/srqt03.f(3), and that's the cute little sign-off at the very end 🎀🦋💅.