SQRT02(3)

💅 SQRT02(3) — Library Functions Manual 💅

okay so bestie, this is the sqrt02.f(3) page from the Library Functions Manual, and it’s lowkey a LAPACK test routine with main-character energy. no cap. 💖

🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/sqrt02.f

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

subroutine SQRT02 (m, n, k, a, af, q, r, lda, tau, work, lwork, rwork,
    result)
    SQRT02

🦋 Function/Subroutine Documentation 🦋

subroutine SQRT02 (integer m, integer n, integer k, 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)

and the routine name is literally SQRT02, bestie 💅

💖 Purpose 💖

Here’s the vibe: SQRT02 tests SORGQR, which generates an m-by-n matrix Q with orthonormal columns that is defined as the product of k elementary reflectors. 🫶

Given the QR factorization of an m-by-n matrix A, SQRT02 generates the orthogonal matrix Q defined by the factorization of the first k columns of A; it compares R(1:n,1:k) with Q(1:m,1:n)'*A(1:m,1:k), and checks that the columns of Q are orthonormal. ✨

🎀 Parameters 🎀

🌟 M

M is INTEGER — the number of rows of the matrix Q to be generated. Constraint: M >= 0.

🌟 N

N is INTEGER — the number of columns of the matrix Q to be generated. Constraint: M >= N >= 0.

🌟 K

K is INTEGER — the number of elementary reflectors whose product defines the matrix Q. Constraint: N >= K >= 0.

🌟 A

A is REAL array, dimension (LDA,N) — the m-by-n matrix A which was factorized by SQRT01.

🌟 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,N).

🌟 R

R is REAL array, dimension (LDA,N).

🌟 LDA

LDA is INTEGER — the leading dimension of the arrays A, AF, Q and R. Constraint: LDA >= M.

🌟 TAU

TAU is REAL array, dimension (N) — the scalar factors of the elementary reflectors corresponding to the QR factorization in AF.

🌟 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 133 of file sqrt02.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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mwah 💋 — signed off with LAPACK, Version 3.12.0, and the footer path /home/abui...IN/sqrt02.f(3). no separate date field in this footer, bestie — that’s the whole footer vibe. 🫶