TESTING/LIN/dqrt01.f(3)

🌸 TESTING/LIN/dqrt01.f 🌸

Okay bestie, welcome to the Library Functions Manual page for TESTING/LIN/dqrt01.f — this one is lowkey a whole Fortran test-routine moment. 💅✨

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✨ NAME ✨

TESTING/LIN/dqrt01.f

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💖 SYNOPSIS 💖

🧚 Functions/Subroutines 🧚

subroutine dqrt01 (m, n, a, af, q, r, lda, tau, work, lwork, rwork,
    result)

DQRT01

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🎀 Function/Subroutine Documentation 🎀

Here's the full signature, fr fr — every type and dimension stays exactly where it lives:

subroutine dqrt01 (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)

DQRT01

🦋 Purpose 🦋

Okay so DQRT01 tests DGEQRF, 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. Iconic behavior. ✨

DQRT01 compares R with Q'*A, and checks that Q is orthogonal. Periodt. 💅

🍓 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 DGEQRF. See DGEQRF 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 DGEQRF.
• 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 )

Highkey important: those RESULT lines are the vibe check for whether the QR stuff is actually behaving. 👑

👑 Author 👑

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

Definition at line 124 of file dqrt01.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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That's the tea, bestie! Source/version sign-off: LAPACK Version 3.12.0; page label: TESTING/LIN/dqrt01.f(3). Slay and goodbye. 💖✨🎀