TESTING/LIN/clqt02.f(3)

okay so bestie, welcome to the TESTING/LIN/clqt02.f(3) page from the Library Functions Manual — it’s giving LAPACK testing energy and it’s all about clqt02. 💅

🌸 NAME 🌸

TESTING/LIN/clqt02.f — that’s the manual page name, and the star of the show is the clqt02 subroutine. Periodt. ✨

✨ SYNOPSIS ✨

Functions/Subroutines

subroutine clqt02 (m, n, k, a, af, q, l, lda, tau, work, lwork, rwork,
    result)

CLQT02

🦋 Function/Subroutine Documentation 🦋

subroutine clqt02 (integer m, integer n, integer k, complex, dimension( lda,
    * ) a, complex, dimension( lda, * ) af, complex, dimension( lda, * ) q,
    complex, dimension( lda, * ) l, integer lda, complex, dimension( * )
    tau, complex, dimension( lwork ) work, integer lwork, real, dimension( *
    ) rwork, real, dimension( * ) result)

CLQT02

💖 Purpose 💖

okay so CLQT02 tests CUNGLQ, which generates an m-by-n matrix Q with orthonormal rows, and that Q is defined as the product of k elementary reflectors. no cap. 🫶

Given the LQ factorization of an m-by-n matrix A, CLQT02 generates the orthogonal matrix Q defined by the factorization of the first k rows of A. It compares L(1:k,1:m) with A(1:k,1:n)*Q(1:m,1:n)', and checks that the rows of Q are orthonormal. 💅

🎀 Parameters 🎀

• M — M is INTEGER. It’s the number of rows of the matrix Q to be generated. Constraint: M >= 0. 🌸
• N — N is INTEGER. It’s the number of columns of the matrix Q to be generated. Constraint: N >= M >= 0.
• K — K is INTEGER. It’s the number of elementary reflectors whose product defines the matrix Q. Constraint: M >= K >= 0.
• A — A is COMPLEX array, dimension (LDA,N). It’s the m-by-n matrix A which was factorized by CLQT01.
• AF — AF is COMPLEX array, dimension (LDA,N). It holds details of the LQ factorization of A, as returned by CGELQF. See CGELQF for further details.
• Q — Q is COMPLEX array, dimension (LDA,N).
• L — L is COMPLEX array, dimension (LDA,M).
• LDA — LDA is INTEGER. It’s the leading dimension of the arrays A, AF, Q and L. Constraint: LDA >= N.
• TAU — TAU is COMPLEX array, dimension (M). It holds the scalar factors of the elementary reflectors corresponding to the LQ factorization in AF.
• WORK — WORK is COMPLEX array, dimension (LWORK).
• LWORK — LWORK is INTEGER. It’s the dimension of the array WORK.
• RWORK — RWORK is REAL array, dimension (M).
• RESULT — RESULT is REAL array, dimension (2). It holds the test ratios:

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

👑 Author 👑

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

Definition at line 133 of file clqt02.f. ✨

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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footer vibe check, bestie: this is LAPACK Version 3.12.0 for TESTING/LIN/clqt02.f(3) — and nope, the footer doesn’t give a date line, so I’m not inventing one. 💖🎀