TESTING/LIN/dlqt03.f(3)

💅 NAME 💅

TESTING/LIN/dlqt03.f — hiii bestie, this is the TESTING/LIN/dlqt03.f(3) page from the Library Functions Manual, and it's all about the subroutine DLQT03. No cap. 🫶

✨ SYNOPSIS ✨

Functions/Subroutines

       subroutine dlqt03 (m, n, k, af, c, cc, q, lda, tau, work, lwork, rwork,
           result)
           DLQT03

DLQT03 — that's the subroutine, periodt. 💅

🧚 Function/Subroutine Documentation 🧚

   subroutine dlqt03 (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)

DLQT03 — okay so this is the full signature, and she's long but iconic. 👑

🎯 Purpose

okay so DLQT03 tests DORMLQ, which computes Q*C, Q'*C, C*Q or C*Q' — yes bestie, those are the four moods. ✨

DLQT03 compares the results of a call to DORMLQ with the results of forming Q explicitly by a call to DORGLQ and then performing matrix multiplication by a call to DGEMM. It's literally compare-and-contrast but make it matrices. 💖

📋 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 LQ factorization of an m-by-n matrix, as returned by DGELQF. See SGELQF for further details. 💜
• C — C is DOUBLE PRECISION array, dimension (LDA,N). That's the whole note, bestie. 🍓
• CC — CC is DOUBLE PRECISION array, dimension (LDA,N). Another simple icon. 🎀
• Q — Q is DOUBLE PRECISION array, dimension (LDA,N). Main character matrix energy. 👑
• 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 LQ 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 dlqt03.f. 🫶

🌟 Author 🌟

Generated automatically by Doxygen for LAPACK from the source code. no cap, the docs robots did their thing. 🤖💖

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xoxo, LAPACK Version 3.12.0, sliding in from TESTING/LIN/dlqt03.f(3) 💅✨