TESTING/LIN/crqt02.f(3)

💅 TESTING/LIN/crqt02.f 💅

okay bestie, welcome to the Library Functions Manual — this page is literally TESTING/LIN/crqt02.f, and it's all about the crqt02 subroutine. no cap, it's a LAPACK testing routine and it's giving “I check the math so you don't have to.” 💖

✨ NAME ✨

TESTING/LIN/crqt02.f — that's the file, bestie. 🎀

🦋 SYNOPSIS 🦋

🌼 Functions/Subroutines 🌼

subroutine crqt02 (m, n, k, a, af, q, r, lda, tau, work, lwork, rwork,
    result)

CRQT02 🔥

💖 Function/Subroutine Documentation 💖

subroutine crqt02 (integer m, integer n, integer k, complex, dimension( lda,
    * ) a, complex, dimension( lda, * ) af, complex, dimension( lda, * ) q,
    complex, dimension( lda, * ) r, integer lda, complex, dimension( * )
    tau, complex, dimension( lwork ) work, integer lwork, real, dimension( *
    ) rwork, real, dimension( * ) result)

CRQT02 ✨

🌸 Purpose 🌸

bestie, here's the tea: CRQT02 tests CUNGRQ, which generates an m-by-n matrix Q with orthonormal rows that is defined as the product of k elementary reflectors. 👑

Given the RQ factorization of an m-by-n matrix A, CRQT02 generates the orthogonal matrix Q defined by the factorization of the last k rows of A; it compares R(m-k+1:m,n-m+1:n) with A(m-k+1:m,1:n)*Q(n-m+1:n,1:n)', and checks that the rows of Q are orthonormal. periodt. 💅

🎀 Parameters 🎀

• M — M is INTEGER — the number of rows of the matrix Q to be generated. M >= 0. 🍓
• N — N is INTEGER — the number of columns of the matrix Q to be generated. N >= M >= 0. 🍓
• K — K is INTEGER — the number of elementary reflectors whose product defines the matrix Q. M >= K >= 0. 🍓
• A — A is COMPLEX array, dimension (LDA,N) — the m-by-n matrix A which was factorized by CRQT01. 🦋
• AF — AF is COMPLEX array, dimension (LDA,N) — details of the RQ factorization of A, as returned by CGERQF. See CGERQF for further details. 🦋
• Q — Q is COMPLEX array, dimension (LDA,N) — that's the array itself, no extra notes. 💖
• R — R is COMPLEX array, dimension (LDA,M) — the R array itself, living its best life. 💖
• LDA — LDA is INTEGER — the leading dimension of the arrays A, AF, Q and L. LDA >= N. 👑
• TAU — TAU is COMPLEX array, dimension (M) — the scalar factors of the elementary reflectors corresponding to the RQ factorization in AF. 🌈
• WORK — WORK is COMPLEX array, dimension (LWORK) — that's the spec, bestie. ⭐
• LWORK — LWORK is INTEGER — the dimension of the array WORK. ⭐
• RWORK — RWORK is REAL array, dimension (M) — that's the whole spec. 🌸
• RESULT — RESULT is REAL array, dimension (2) — the test ratios, and they are:

RESULT(1) = norm( R - A*Q' ) / ( N * norm(A) * EPS )
RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )

those are the exact ratios, no cap. 🔥

👑 Author 👑

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

Definition at line 134 of file crqt02.f. 💀

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code. 🫶

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mwah 💋 — that's the whole page, bestie! the footer says LAPACK Version 3.12.0 and TESTING/LIN/crqt02.f(3); no date listed, so I'm not inventing one. 🎀✨