TESTING/LIN/cqrt02.f(3)

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💅 TESTING/LIN/cqrt02.f(3) — Library Functions Manual 💅

okay bestie, welcome to the TESTING/LIN/cqrt02.f(3) page from the Library Functions Manual. It's giving “Fortran test routine with main character energy,” and we're gonna walk through it together, no cap. 🫶✨

✨ NAME ✨

TESTING/LIN/cqrt02.f

That's the name, bestie — the page is literally about this file. Slay. 💅

🌈 SYNOPSIS 🌈

🧚 Functions/Subroutines 🧚

subroutine cqrt02 (m, n, k, a, af, q, r, lda, tau, work, lwork, rwork,
    result)
    CQRT02

💖 Function/Subroutine Documentation 💖

subroutine cqrt02 (integer m, integer n, integer k, 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)
    CQRT02

🎀 Purpose 🎀

CQRT02 tests CUNGQR, which generates an m-by-n matrix Q with orthonormal columns that is defined as the product of k elementary reflectors. That's the whole vibe check. 🦋

Given the QR factorization of an m-by-n matrix A, CQRT02 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. Iconic behavior, honestly. 👑

🍓 Parameters 🍓

  • M — INTEGER. The number of rows of the matrix Q to be generated. Constraint: M >= 0. 💖
  • N — INTEGER. The number of columns of the matrix Q to be generated. Constraint: M >= N >= 0. 🌸
  • K — INTEGER. The number of elementary reflectors whose product defines the matrix Q. Constraint: N >= K >= 0. 🎀
  • A — COMPLEX array, dimension (LDA,N). The m-by-n matrix A which was factorized by CQRT01. 🫶
  • 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,N). That's it, bestie — the source just gives us the array and dimension. 💅
  • R — COMPLEX array, dimension (LDA,N). Same energy: array plus dimension, no extra lore. 🦋
  • LDA — INTEGER. The leading dimension of the arrays A, AF, Q and R. Constraint: LDA >= M. 🌈
  • TAU — COMPLEX array, dimension (N). The scalar factors of the elementary reflectors corresponding to the QR factorization in AF. ⭐
  • 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:
    • RESULT(1) = norm( R - Q'*A ) / ( M * norm(A) * EPS )
    • RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )

🔥 those formulas are the moment.

👑 Author 👑

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

The page literally says: Definition at line 133 of file cqrt02.f. Cute line reference, bestie. 🎀

🌸 Author 🌸

Generated automatically by Doxygen for LAPACK from the source code. The robot wrote it, and honestly? It ate. 💅✨

okay that's the whole page, bestie! 🫶 Source file: TESTING/LIN/cqrt02.f(3), LAPACK Version 3.12.0. The original footer doesn't show a separate date, so we're not inventing one — just source, version, and impeccable vibes. 🌈💖

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