TESTING/LIN/zrqt03.f(3)

💅 NAME

Okay bestie, this is the manual page for TESTING/LIN/zrqt03.f(3) — Library Functions Manual energy, and literally the whole name section. It’s giving “the file path is the main character,” and I’m obsessed. 👑

✨ SYNOPSIS

🌸 Functions/Subroutines

       subroutine zrqt03 (m, n, k, af, c, cc, q, lda, tau, work, lwork, rwork,
           result)
           ZRQT03

🎀 Function/Subroutine Documentation

Okay so here’s the full signature, fr fr:

       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

ZRQT03 tests ZUNMRQ, which computes Q*C, Q'*C, C*Q or C*Q'. ✨

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. 💅

Parameters

Vibe check on every argument, bestie — nothing skipped:

• M — M is INTEGER. It’s 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 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. 😭

The 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

These iconic institutions, no cap:

• 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. 👑

---

LAPACK Version 3.12.0 · TESTING/LIN/zrqt03.f(3) · footer date: none listed — that’s the whole manual page, bestie, periodt. 🫶✨