TESTING/LIN/zqrt01p.f(3)

💅 NAME

TESTING/LIN/zqrt01p.f — bestie, this is the page for that file, and it comes from the Library Functions Manual. Header folded in near the top, vibe check passed. ✨

✨ SYNOPSIS

Functions/Subroutines — okay so the synopsis is literally giving:

subroutine zqrt01p (m, n, a, af, q, r, lda, tau, work, lwork, rwork, result)
    ZQRT01P

🎀 Function/Subroutine Documentation

Here’s the full signature, exactly as printed, no edits, no games:

subroutine zqrt01p (integer m, integer n, 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)
    ZQRT01P

🌸 Purpose

Bestie, this routine is a test routine. It tests ZGEQRFP, which computes the QR factorization of an m-by-n matrix A, and it partially tests ZUNGQR, which forms the m-by-m orthogonal matrix Q.

ZQRT01P compares R with Q'*A, and checks that Q is orthogonal. That’s the assignment, periodt. 💅

🫶 Parameters

• M — INTEGER. The number of rows of the matrix A. M >= 0. 💖
• N — INTEGER. The number of columns of the matrix A. N >= 0. 🌸
• A — COMPLEX*16 array, dimension (LDA,N). The m-by-n matrix A. ✨
• AF — COMPLEX*16 array, dimension (LDA,N). Details of the QR factorization of A, as returned by ZGEQRFP. See ZGEQRFP for further details. 🦋
• Q — COMPLEX*16 array, dimension (LDA,M). The m-by-m orthogonal matrix Q. 👑
• R — COMPLEX*16 array, dimension (LDA,max(M,N)). That’s the whole note for R in this manpage, bestie — no extra lore invented. 🎀
• LDA — INTEGER. The leading dimension of the arrays A, AF, Q and R. LDA >= max(M,N). 🔥
• TAU — COMPLEX*16 array, dimension (min(M,N)). The scalar factors of the elementary reflectors, as returned by ZGEQRFP. 💜
• WORK — COMPLEX*16 array, dimension (LWORK). 🌈
• LWORK — INTEGER. The dimension of the array WORK. ⭐
• RWORK — DOUBLE PRECISION array, dimension (M). 🍓
• RESULT — DOUBLE PRECISION array, dimension (2). The test ratios are:

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 124 of file zqrt01p.f

For real, the definition is at line 124 of file zqrt01p.f. 💫

💖 Author

Generated automatically by Doxygen for LAPACK from the source code.

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Okay bestie, that’s the whole page, no details left behind, fr fr. 🫶 The footer sign-off says LAPACK Version 3.12.0 and the page tag is TESTING/LIN/zqrt01p.f(3); there’s no separate date printed there, so I’m not inventing one. Mwah 💋✨