TESTING/LIN/zlqt03.f(3)

💖 NAME 💖

okay so bestie, this page is for TESTING/LIN/zlqt03.f, and it lives in the Library Functions Manual — section 3 energy, iykyk. It’s all about the zlqt03 subroutine, no cap.

🌸 SYNOPSIS 🌸

Under Functions/Subroutines, the whole flex is:

subroutine zlqt03 (m, n, k, af, c, cc, q, lda, tau, work, lwork, rwork,
    result)
    ZLQT03

🦋 Function/Subroutine Documentation 🦋

Full signature, bestie — every type and dimension exactly where it belongs:

subroutine zlqt03 (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)
    ZLQT03

🎀 Purpose 🎀

ZLQT03 tests ZUNMLQ, which computes Q*C, Q'*C, C*Q or C*Q' — yes, all four, she’s versatile. 💅

ZLQT03 compares the results of a call to ZUNMLQ with the results of forming Q explicitly by a call to ZUNGLQ and then performing matrix multiplication by a call to ZGEMM. Two techniques, one very serious test situation 🔥

💅 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 COMPLEX*16 array, dimension (LDA,N). Details of the LQ factorization of an m-by-n matrix, as returned by ZGELQF. See CGELQF 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 LQ 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 the test ratios are literally:

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.

And the source tea: Definition at line 134 of file zlqt03.f.

📜 Author 📜

This page was generated automatically by Doxygen for LAPACK from the source code. Cute.

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💖 cute sign-off: footer source/version is LAPACK / Version 3.12.0 / TESTING/LIN/zlqt03.f(3) — and the date slot is giving “no date shown on this page,” bestie 😭 byeee, go be iconic with those tests 🫶✨