TESTING/LIN/sqrt02.f(3)

💅 TESTING/LIN/sqrt02.f — from the Library Functions Manual files, bestie 🎀

okay so picture this: you're deep in LAPACK land, everybody's talking about QR factorizations, and somebody has to be the one to actually check that the Q matrix is behaving. that someone is sqrt02. she's the vibe check for SORGQR. periodt. ✨

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🌸 SYNOPSIS 🌸

Functions/Subroutines

• subroutine sqrt02 (m, n, k, a, af, q, r, lda, tau, work, lwork, rwork, result) — the whole squad, one call. this is what we call a full house 💖

subroutine sqrt02 (m, n, k, a, af, q, r, lda, tau, work, lwork, rwork, result)

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🦋 Function/Subroutine Documentation 🦋

the actual signature (yes, all of it, no skips 💅)

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)

SQRT02 👑 — main character subroutine, no notes.

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✨ Purpose ✨

!> !> 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. !>

so lowkey what she's doing: SQRT02 puts SORGQR through its paces. she builds that m-by-n matrix Q with the orthonormal columns — you know, the one that's defined as the product of k elementary reflectors — and then she does the receipts 💀. given the QR factorization of an m-by-n matrix A, she generates the orthogonal matrix Q defined by the factorization of the first k columns of A, compares R(1:n,1:k) with Q(1:m,1:n)'*A(1:m,1:k), and then double checks that the columns of Q are actually orthonormal. she's thorough. she's that girl. 🫶

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🍓 Parameters 🍓

• M — M is INTEGER. the number of rows of the matrix Q to be generated. requirement: M >= 0. ✨
• N — N is INTEGER. the number of columns of the matrix Q to be generated. requirement: M >= N >= 0. 💜
• K — K is INTEGER. the number of elementary reflectors whose product defines the matrix Q. requirement: N >= K >= 0. 🌸
• A — A is REAL array, dimension (LDA,N). this is the m-by-n matrix A which was factorized by SQRT01. she's the original, the source material 💖
• AF — AF is REAL array, dimension (LDA,N). all the details of the QR factorization of A, as returned by SGEQRF. see SGEQRF for further details 👀
• Q — Q is REAL array, dimension (LDA,N). (the star of the show, honestly — this is where the generated Q lives) ⭐
• R — R is REAL array, dimension (LDA,N). 🌈
• LDA — LDA is INTEGER. the leading dimension of the arrays A, AF, Q and R. requirement: LDA >= M. don't skimp on this one bestie 😭
• 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). the workspace, doing workspace things ✨
• 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, and they are:
  • RESULT(1) = norm( R - Q'*A ) / ( M * norm(A) * EPS )
  • RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )

these two numbers are the whole personality of the routine ngl — they tell you if the factorization actually slayed or if it flopped 💀

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👑 Author 👑

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

Definition at line 133 of file sqrt02.f. (iykyk 📍)

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🧚 Author (the meta one) 🧚

Generated automatically by Doxygen for LAPACK from the source code.

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and that's the whole page, bestie 🫶 LAPACK, Version 3.12.0 — written way back when, still out here validating your Q matrices today. go forth and be orthonormal 💅✨🎀