ZQLT03(3)

💅 ZQLT03(3) — Library Functions Manual

Hiii bestie 🫶 This is the ZQLT03(3) page from the Library Functions Manual — manual name folded in near the top so we don’t have to copy-paste the whole header line again. It’s giving “LAPACK test routine wants to check itself” energy, and we’re gonna go through every single detail together. No skips, no cap 💖

🌸 NAME

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/zqlt03.f

Ok so the NAME section is literally just that path, bestie — that’s the source file this page is about. Slay for absolute paths, I guess 🎀

🦋 SYNOPSIS

✨ Functions/Subroutines

subroutine ZQLT03 (m, n, k, af, c, cc, q, lda, tau, work, lwork, rwork,
    result)
    ZQLT03

That’s the short synopsis; the full typed-out signature is right below, don’t worry 🫶

🧚 Function/Subroutine Documentation

subroutine ZQLT03 (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)
    ZQLT03

Here’s the full signature, exactly as it appears, because we are not out here renaming a single parameter. Periodt.

🎀 Purpose

ZQLT03 is the test bestie for ZUNMQL 👑. ZUNMQL computes Q*C, Q'*C, C*Q, or C*Q'. And ZQLT03 compares the results of a call to ZUNMQL with the results of forming Q explicitly by a call to ZUNGQL, then performing matrix multiplication by a call to ZGEMM. Literally side-by-side vibes, no cap.

🌈 Parameters

• M — M is INTEGER. It’s the order of the orthogonal matrix Q. M >= 0.
• N — N is INTEGER. The number of rows or columns of the matrix C; C is m-by-n if Q is applied from the left, or n-by-m if Q is applied from the right. N >= 0.
• K — K is INTEGER. The number of elementary reflectors whose product defines the orthogonal matrix Q. M >= K >= 0.
• AF — AF is COMPLEX*16 array, dimension (LDA,N). Details of the QL factorization of an m-by-n matrix, as returned by ZGEQLF. See CGEQLF 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,M).
• 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 QL 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 m-by-m orthogonal matrix Q.

The formulas for RESULT, exactly as written, are:

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

👑 Author

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

Definition at line 134 of file zqlt03.f.

🦋 Author

Generated automatically by Doxygen for LAPACK from the source code.

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Ok that’s the whole page, bestie 💖✨ Footer tea: LAPACK Version 3.12.0, and the footer path is /home/abui...IN/zqlt03.f(3). There’s no date printed on that footer, so I’m not making one up — we respect the source 🎀👑