ZQRT01(3)

💅 NAME

okay so you're on the ZQRT01(3) page from the Library Functions Manual — header energy folded in right here, bestie. ✨ The NAME is literally this source file path: /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/zqrt01.f.

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✨ SYNOPSIS

Under Functions/Subroutines:

subroutine ZQRT01 (m, n, a, af, q, r, lda, tau, work, lwork, rwork,
    result)
    ZQRT01

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🫶 Function/Subroutine Documentation

here's the full signature, copied exact so nobody comes for me:

subroutine ZQRT01 (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)
    ZQRT01

🌸 Purpose

okay so ZQRT01 tests ZGEQRF, 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. Then ZQRT01 compares R with Q'*A, and checks that Q is orthogonal. slay. 💅

🎀 Parameters

• M — M is INTEGER. The number of rows of the matrix A. M >= 0.
• N — N is INTEGER. The number of columns of the matrix A. N >= 0.
• A — A is COMPLEX*16 array, dimension (LDA,N). The m-by-n matrix A.
• 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,M). The m-by-m orthogonal matrix Q.
• R — R is COMPLEX*16 array, dimension (LDA,max(M,N)).
• LDA — LDA is INTEGER. The leading dimension of the arrays A, AF, Q and R. LDA >= max(M,N).
• TAU — TAU is COMPLEX*16 array, dimension (min(M,N)). The scalar factors of the elementary reflectors, as returned by ZGEQRF.
• 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 124 of file zqrt01.f.

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👑 Author

Generated automatically by Doxygen for LAPACK from the source code.

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💖 and that's the whole page — signing off from LAPACK Version 3.12.0, source path /home/abui...IN/zqrt01.f(3). Periodt. 🫶