TESTING/LIN/dqrt01p.f(3)

💖 TESTING/LIN/dqrt01p.f(3) — Library Functions Manual 💖

okay bestie, this is the manual page for TESTING/LIN/dqrt01p.f, and it is literally all about testing QR factorization energy. Let’s get into it. 🦋

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✨ NAME ✨

TESTING/LIN/dqrt01p.f

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🌀 SYNOPSIS 🌀

💅 Functions/Subroutines 💅

       subroutine dqrt01p (m, n, a, af, q, r, lda, tau, work, lwork, rwork,
           result)
           DQRT01P

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🌸 Function/Subroutine Documentation 🌸

   subroutine dqrt01p (integer m, integer n, double precision, dimension( lda,
       * ) a, double precision, dimension( lda, * ) af, double precision,
       dimension( lda, * ) q, double precision, dimension( lda, * ) r, integer
       lda, double precision, dimension( * ) tau, double precision, dimension(
       lwork ) work, integer lwork, double precision, dimension( * ) rwork,
       double precision, dimension( * ) result)
       DQRT01P

🎀 Purpose 🎀

DQRT01P tests DGEQRFP, which computes the QR factorization of an m-by-n matrix A, and partially tests DORGQR which forms the m-by-m orthogonal matrix Q.

DQRT01P 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 DOUBLE PRECISION array, dimension (LDA,N). The m-by-n matrix A.
• AF — AF is DOUBLE PRECISION array, dimension (LDA,N). Details of the QR factorization of A, as returned by DGEQRFP. See DGEQRFP for further details.
• Q — Q is DOUBLE PRECISION array, dimension (LDA,M). The m-by-m orthogonal matrix Q.
• R — R is DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (min(M,N)). The scalar factors of the elementary reflectors, as returned by DGEQRFP.
• WORK — WORK is DOUBLE PRECISION 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 dqrt01p.f.

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👑 Author 👑

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