TESTING/LIN/zqrt02.f(3)

okay so this is the TESTING/LIN/zqrt02.f(3) page from the Library Functions Manual — and it's literally the group chat for ZQRT02, a Fortran testing subroutine. Buckle up, bestie, because we're keeping every single detail 💖

💖 NAME 💖

TESTING/LIN/zqrt02.f — that's the file, and it's the main character of this page. Periodt.

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

subroutine zqrt02 (m, n, k, a, af, q, r, lda, tau, work, lwork, rwork,
           result)

ZQRT02

🦋 Function/Subroutine Documentation 🦋

subroutine zqrt02 (integer m, integer n, integer k, complex*16, dimension(
    lda, * ) a, complex*16, dimension( lda, * ) af, complex*16, dimension(
    lda, * ) q, complex*16, dimension( lda, * ) r, integer lda, complex*16,
    dimension( * ) tau, complex*16, dimension( lwork ) work, integer lwork,
    double precision, dimension( * ) rwork, double precision, dimension( * )
    result)

ZQRT02

🌸 Purpose 🌸

ZQRT02 tests ZUNGQR, which generates an m-by-n matrix Q with orthonormal columns that is defined as the product of k elementary reflectors.

Given the QR factorization of an m-by-n matrix A, ZQRT02 generates the orthogonal matrix Q defined by the factorization of the first k columns of A; it compares R(1:n,1:k) with Q(1:m,1:n)'*A(1:m,1:k), and checks that the columns of Q are orthonormal.

🎀 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. M >= N >= 0.
• K — K is INTEGER. The number of elementary reflectors whose product defines the matrix Q. N >= K >= 0.
• A — A is COMPLEX*16 array, dimension (LDA,N). The m-by-n matrix A which was factorized by ZQRT01.
• AF — AF is COMPLEX*16 array, dimension (LDA,N). Details of the QR factorization of A, as returned by ZGEQRF. See ZGEQRF for further details.
• Q — Q is COMPLEX*16 array, dimension (LDA,N).
• R — R is COMPLEX*16 array, dimension (LDA,N).
• LDA — LDA is INTEGER. The leading dimension of the arrays A, AF, Q and R. LDA >= M.
• TAU — TAU is COMPLEX*16 array, dimension (N). The scalar factors of the elementary reflectors corresponding to the QR factorization in AF.
• WORK — WORK is COMPLEX*16 array, dimension (LWORK).
• LWORK — LWORK is INTEGER. The dimension of the array WORK.
• RWORK — RWORK is DOUBLE PRECISION array, dimension (M).
• RESULT — RESULT is DOUBLE PRECISION array, dimension (2). The test ratios:

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

💖 Author 💖

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

Definition at line 133 of file zqrt02.f.

💖 Author 💖

Generated automatically by Doxygen for LAPACK from the source code.

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okay that's the whole page, bestie — cute sign-off time: LAPACK Version 3.12.0, source file TESTING/LIN/zqrt02.f(3). The original footer didn't hand me a date, so I'm not making one up — no cap, just the source/version tea 🫶💅