SQLT01(3)

🌸 NAME 🌸

okay so bestie, this is the page for /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/sqlt01.f — and yes, that whole entire path is the name, she's built different 💅 (it's from the Library Functions Manual, iykyk).

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✨ SYNOPSIS ✨

Functions/Subroutines

subroutine SQLT01 (m, n, a, af, q, l, lda, tau, work, lwork, rwork, result)

the one and only SQLT01 🔥

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🫶 Function/Subroutine Documentation 🫶

subroutine SQLT01 — the full glow-up signature

subroutine SQLT01 (integer m, integer n, real, dimension( lda, * ) a, real,
    dimension( lda, * ) af, real, dimension( lda, * ) q, real, dimension(
    lda, * ) l, integer lda, real, dimension( * ) tau, real, dimension(
    lwork ) work, integer lwork, real, dimension( * ) rwork, real,
    dimension( * ) result)

SQLT01 ✨

💖 Purpose

!>
!> SQLT01 tests SGEQLF, which computes the QL factorization of an m-by-n
!> matrix A, and partially tests SORGQL which forms the m-by-m
!> orthogonal matrix Q.
!>
!> SQLT01 compares L with Q'*A, and checks that Q is orthogonal.
!>

so real talk: this little icon is the vibe-check machine for two of her friends — SGEQLF (does the QL factorization of an m-by-n matrix A) and SORGQL (forms the m-by-m orthogonal matrix Q, but only partially tested, no cap). SQLT01 then compares L against Q'*A, and makes sure Q is actually orthogonal. literally the friend who checks receipts 👑

🎀 Parameters

• M — integer, bestie. the number of rows of the matrix A. constraint: M >= 0 💖
• N — integer. the number of columns of the matrix A. constraint: N >= 0 ✨
• A — REAL array, dimension (LDA,N). it's the m-by-n matrix A itself, main character energy 🌟
• AF — REAL array, dimension (LDA,N). the details of the QL factorization of A, exactly as returned by SGEQLF. check SGEQLF for further details, iykyk 🦋
• Q — REAL array, dimension (LDA,M). the m-by-m orthogonal matrix Q 💅
• L — REAL array, dimension (LDA,max(M,N)) 🎀 (the original says literally just this, and honestly? iconic minimalism)
• LDA — integer. the leading dimension of the arrays A, AF, Q and R. constraint: LDA >= max(M,N) ⭐
• TAU — REAL array, dimension (min(M,N)). the scalar factors of the elementary reflectors, as returned by SGEQLF 🌸
• WORK — REAL array, dimension (LWORK) 🧚
• LWORK — integer. the dimension of the array WORK. periodt 🫶
• RWORK — REAL array, dimension (M) 🌈
• RESULT — REAL array, dimension (2). the test ratios, and these are the receipts:

RESULT(1) = norm( L - Q'*A ) / ( M * norm(A) * EPS )
RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )

so RESULT(1) is the L vs Q'*A situation, and RESULT(2) is the I - Q'*Q orthogonality check. both divided by M (and EPS, and norm(A) for the first one) — keep the math exactly as written, don't come for me 💀

👑 Author

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

the whole squad showed up, we love a collaborative slay 🙈

Definition at line 124 of file sqlt01.f. 📍

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🌟 Author 🌟

Generated automatically by Doxygen for LAPACK from the source code. (not a human, just a very diligent little robot 🎀)

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ngl this whole page is auto-generated, so if something looks like it was copy-pasted by a machine, that's because it was 💀 — but the facts are all here, fr fr.

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LAPACK — Version 3.12.0 · signed off from /home/abui...IN/sqlt01.f(3) 🦋💜 stay orthogonal, bestie ✨