DQRT01(3)

🌸 NAME 🌸

DQRT01(3) — Library Functions Manual, but make it cute. The page lives at /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/dqrt01.f. This is the DQRT01 function page, and honestly it’s giving “I test QR factorizations for breakfast” energy 💅.

✨ SYNOPSIS ✨

Functions/Subroutines

• subroutine DQRT01 (m, n, a, af, q, r, lda, tau, work, lwork, rwork, result) — DQRT01

🦋 Function/Subroutine Documentation 🦋

subroutine DQRT01

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 bestie, DQRT01 tests DGEQRF, which computes the QR factorization of an m-by-n matrix A, and it partially tests DORGQR which forms the m-by-m orthogonal matrix Q.

Then DQRT01 compares R with Q'*A, and checks that Q is orthogonal. That’s the whole plot: factorize, form Q, compare, and vibe-check the orthogonality ✨.

🌈 Parameters 🌈

• M — M is INTEGER. It’s the number of rows of the matrix A. M >= 0.
• N — N is INTEGER. It’s 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 )

👑 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.

Cute footer sign-off: source/version/date tea is LAPACK Version 3.12.0, dated /home/abui...IN/dqrt01.f(3). Bye bestie, go slay that QR test 💅✨