SQRT01(3)

💖 SQRT01(3) — LAPACK Library Functions Manual 💖

okay bestie, this is the <sqrt01.f> page from the LAPACK Library Functions Manual, and it’s here to test some QR factorization behavior. Let’s get into it 🫶

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🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/sqrt01.f

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✨ SYNOPSIS ✨

🌈 Functions/Subroutines 🌈

subroutine SQRT01 (m, n, a, af, q, r, lda, tau, work, lwork, rwork,
    result)
    SQRT01

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🦋 Function/Subroutine Documentation 🦋

💅 subroutine SQRT01

subroutine SQRT01 (integer m, integer n, real, dimension( lda, * ) a, real,
    dimension( lda, * ) af, real, dimension( lda, * ) q, real, dimension(
    lda, * ) r, integer lda, real, dimension( * ) tau, real, dimension(
    lwork ) work, integer lwork, real, dimension( * ) rwork, real,
    dimension( * ) result)
    SQRT01

🎀 Purpose 🎀

So basically, SQRT01 tests SGEQRF, which computes the QR factorization of an m-by-n matrix A, and it also partially tests SORGQR, which forms the m-by-m orthogonal matrix Q.

SQRT01 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 REAL array, dimension (LDA,N). The m-by-n matrix A.
• AF — AF is REAL array, dimension (LDA,N). Details of the QR factorization of A, as returned by SGEQRF. See SGEQRF for further details.
• Q — Q is REAL array, dimension (LDA,M). The m-by-m orthogonal matrix Q.
• R — R is REAL 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 REAL array, dimension (min(M,N)). The scalar factors of the elementary reflectors, as returned by SGEQRF.
• WORK — WORK is REAL 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 sqrt01.f.

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🌟 Author 🌟

Generated automatically by Doxygen for LAPACK from the source code.

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