ZRQT03(3)

okay bestie, welcome to ZRQT03(3) — the manual name is Library Functions Manual, and the header path is /home/abui...IN/zrqt03.f(3). This is the docs page for the ZRQT03 subroutine, and yes, we’re gonna get through every single parameter together 💅✨

💖 NAME

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/zrqt03.f

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📚 SYNOPSIS

✨ Functions/Subroutines

subroutine ZRQT03 (m, n, k, af, c, cc, q, lda, tau, work, lwork, rwork,
    result)

ZRQT03

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🧚 Function/Subroutine Documentation

subroutine ZRQT03 (integer m, integer n, integer k, complex*16, dimension(
    lda, * ) af, complex*16, dimension( lda, * ) c, complex*16, dimension(
    lda, * ) cc, complex*16, dimension( lda, * ) q, integer lda, complex*16,
    dimension( * ) tau, complex*16, dimension( lwork ) work, integer lwork,
    double precision, dimension( * ) rwork, double precision, dimension( * )
    result)

ZRQT03

🎯 Purpose

okay so here’s the tea: ZRQT03 tests ZUNMRQ, which computes Q*C, Q'*C, C*Q or C*Q' 🔥

Then ZRQT03 compares the results of a call to ZUNMRQ with the results of forming Q explicitly by a call to ZUNGRQ and then performing matrix multiplication by a call to ZGEMM. Literally the whole vibe is “did these two ways of doing the thing line up?” 👑

🫶 Parameters

• M — M is INTEGER. 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. Constraint: M >= 0.
• N — N is INTEGER. The order of the orthogonal matrix Q. Constraint: N >= 0.
• K — K is INTEGER. The number of elementary reflectors whose product defines the orthogonal matrix Q. Constraint: N >= K >= 0.
• AF — AF is COMPLEX*16 array, dimension (LDA,N). Details of the RQ factorization of an m-by-n matrix, as returned by ZGERQF. See CGERQF for further details.
• C — C is COMPLEX*16 array, dimension (LDA,N).
• CC — CC is COMPLEX*16 array, dimension (LDA,N).
• Q — Q is COMPLEX*16 array, dimension (LDA,N).
• LDA — LDA is INTEGER. The leading dimension of the arrays AF, C, CC, and Q.
• TAU — TAU is COMPLEX*16 array, dimension (min(M,N)). The scalar factors of the elementary reflectors corresponding to the RQ factorization in AF.
• WORK — WORK is COMPLEX*16 array, dimension (LWORK).
• 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.
• RWORK — RWORK is DOUBLE PRECISION array, dimension (M).
• 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.

And here are the exact ratio formulas, bestie — copy-paste energy only:

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 zrqt03.f.

🌈 Author

Generated automatically by Doxygen for LAPACK from the source code.

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That’s the whole page, bestie 💜 — footer says LAPACK Version 3.12.0 and /home/abui...IN/zrqt03.f(3). The footer line has no separate date, so I’m not inventing one 🙈 slay ✨