TESTING/LIN/cqrt01p.f(3)

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💖 NAME 💖

okay so this is the page for TESTING/LIN/cqrt01p.f, bestie — living in the Library Functions Manual — and it's all about the CQRT01P subroutine. iconic little test routine behavior, no cap. 🫶✨

✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

subroutine cqrt01p (m, n, a, af, q, r, lda, tau, work, lwork, rwork,
    result)
    CQRT01P

🧚 Function/Subroutine Documentation 🧚

subroutine cqrt01p (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)

CQRT01P 💅

🌸 Purpose 🌸

CQRT01P tests CGEQRFP, which computes the QR factorization of an m-by-n matrix A, and partially tests CUNGQR which forms the m-by-m orthogonal matrix Q. 🔥

CQRT01P compares R with Q'*A, and checks that Q is orthogonal. ✨

🎀 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 array, dimension (LDA,N). The m-by-n matrix A. 🦋
  • AF — AF is COMPLEX array, dimension (LDA,N). Details of the QR factorization of A, as returned by CGEQRFP. See CGEQRFP for further details. 🫶
  • Q — Q is COMPLEX array, dimension (LDA,M). The m-by-m orthogonal matrix Q. 👑
  • R — R is COMPLEX 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 array, dimension (min(M,N)). The scalar factors of the elementary reflectors, as returned by CGEQRFP. 🌸
  • WORK — WORK is COMPLEX array, dimension (LWORK). 🧚
  • LWORK — LWORK is INTEGER. The dimension of the array WORK. 🎀
  • RWORK — RWORK is REAL array, dimension (M). 💜
  • RESULT — RESULT is 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 )

👑 Author 👑

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

Definition at line 124 of file cqrt01p.f. 📌

👑 Author 👑

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