TESTING/LIN/drqt03.f(3)

🌸 TESTING/LIN/drqt03.f(3) 🌸

okay bestie, this page comes from the Library Functions Manual, and it’s the whole lore on drqt03 — a LAPACK testing routine that is very much giving “trust me, I checked the math” energy. 💅✨

✨ SYNOPSIS ✨

✨ Functions/Subroutines ✨

• subroutine drqt03 (m, n, k, af, c, cc, q, lda, tau, work, lwork, rwork, result) — DRQT03

🦋 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 💜

DRQT03 tests DORMRQ, which computes Q*C, Q'*C, C*Q or C*Q'. It’s the vibe-check routine for matrix multiplication with Q. 🫶

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. So yeah, it’s basically “did DORMRQ do the thing right, or do we need to compare notes with the explicit route?” 😭🔥

🎀 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. M >= 0.
• N — N is INTEGER. The order of the orthogonal matrix Q. N >= 0.
• K — K is INTEGER. The number of elementary reflectors whose product defines the orthogonal matrix Q. N >= K >= 0.
• 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.
• C — C is DOUBLE PRECISION array, dimension (LDA,N).
• CC — CC is DOUBLE PRECISION array, dimension (LDA,N).
• Q — Q is DOUBLE PRECISION array, dimension (LDA,N).
• LDA — LDA is INTEGER. The leading dimension of the arrays AF, C, CC, and Q.
• TAU — TAU is DOUBLE PRECISION array, dimension (min(M,N)). The scalar factors of the elementary reflectors corresponding to the RQ factorization in AF.
• WORK — WORK is DOUBLE PRECISION 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.

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 drqt03.f.

💖 Author 💖

Generated automatically by Doxygen for LAPACK from the source code.

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that’s the whole page, bestie — from LAPACK Version 3.12.0, page TESTING/LIN/drqt03.f(3). The footer doesn’t give a separate date, so we’re not inventing one; Doxygen just auto-made this cutie from the source code. 💖✨🎀