TESTING/LIN/zqrt01.f(3)

🌸 NAME 🌸

TESTING/LIN/zqrt01.f — bestie, this is the Library Functions Manual page for the zqrt01 test subroutine in the TESTING/LIN corner of LAPACK. 💅

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✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

subroutine zqrt01 (m, n, a, af, q, r, lda, tau, work, lwork, rwork,
     result)
     ZQRT01

That's the main-character signature, no cap. 🫶

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🔥 Function/Subroutine Documentation 🔥

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 is literally the vibe check for ZGEQRF, which computes the QR factorization of an m-by-n matrix A. It also 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. Iconic behavior, fr fr. 💖

🧾 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 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 zqrt01.f.

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🫶 Author 🫶

Generated automatically by Doxygen for LAPACK from the source code.

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Sign-off tea: source/version is LAPACK Version 3.12.0, manual page TESTING/LIN/zqrt01.f(3); date? not listed in this footer, so I'm not inventing one, bestie. 💅✨