TESTING/LIN/cqrt01.f(3)

🌸 NAME 🌸

okay so this page is TESTING/LIN/cqrt01.f(3), from the Library Functions Manual — and it’s all about the CQRT01 subroutine, bestie. 💅

✨ SYNOPSIS ✨

Functions/Subroutines

here’s the whole callable situation:

subroutine cqrt01 (m, n, a, af, q, r, lda, tau, work, lwork, rwork,
    result)
    CQRT01

🦋 Function/Subroutine Documentation 🦋

the full signature is giving “I know exactly what I’m doing” energy:

subroutine cqrt01 (integer m, integer n, complex, dimension( lda, * ) a,
    complex, dimension( lda, * ) af, complex, dimension( lda, * ) q,
    complex, dimension( lda, * ) r, integer lda, complex, dimension( * )
    tau, complex, dimension( lwork ) work, integer lwork, real, dimension( *
    ) rwork, real, dimension( * ) result)
    CQRT01

Purpose

so CQRT01 is out here testing CGEQRF, which computes the QR factorization of an m-by-n matrix A, and it also partially tests CUNGQR, which forms the m-by-m orthogonal matrix Q. 🫶

and then it compares R with Q'*A, and checks that Q is orthogonal. that’s the whole vibe check, no cap.

Parameters

• M — INTEGER; the number of rows of the matrix A. it has to satisfy M >= 0. ✨
• N — INTEGER; the number of columns of the matrix A. it has to satisfy N >= 0. 🌸
• A — COMPLEX array, dimension (LDA,N); this is the m-by-n matrix A. 👑
• AF — COMPLEX array, dimension (LDA,N); details of the QR factorization of A, as returned by CGEQRF. see CGEQRF for further details. 🦋
• Q — COMPLEX array, dimension (LDA,M); the m-by-m orthogonal matrix Q. 💖
• R — COMPLEX array, dimension (LDA,max(M,N)). that’s it, that’s the whole description. 💀
• LDA — INTEGER; the leading dimension of the arrays A, AF, Q and R. must satisfy LDA >= max(M,N). ⭐
• TAU — COMPLEX array, dimension (min(M,N)); the scalar factors of the elementary reflectors, as returned by CGEQRF. 🎀
• WORK — COMPLEX array, dimension (LWORK). 🧚
• LWORK — INTEGER; the dimension of the array WORK. 💜
• RWORK — REAL array, dimension (M). 🌈
• RESULT — REAL array, dimension (2); the test ratios, and they are literally these:

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 cqrt01.f.

💜 Author 💜

this page was generated automatically by Doxygen for LAPACK from the source code, so it’s giving auto-generated but still iconic. 💅

---

💖 sign-off time: the footer is LAPACK Version 3.12.0 + TESTING/LIN/cqrt01.f(3), and there’s no separate date printed on this footer — just that source/version and page-name combo, periodt 💅