TESTING/LIN/sqrt03.f(3)

🎀 TESTING/LIN/sqrt03.f 🎀

okay bestie, welcome to the group chat of LAPACK test files — the manual name is TESTING/LIN/sqrt03.f and honestly it's giving "humble little Fortran file that does the most". let's get into it 💅

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✨ SYNOPSIS ✨

🦋 Functions/Subroutines

• subroutine sqrt03 (m, n, k, af, c, cc, q, lda, tau, work, lwork, rwork, result) — the one and only, SQRT03 itself 🫶

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💖 Function/Subroutine Documentation 💖

🌸 the actual signature (no cap, type it right)

subroutine sqrt03 (integer m, integer n, integer k, real, dimension( lda, *
) af, real, dimension( lda, * ) c, real, dimension( lda, * ) cc, real,
dimension( lda, * ) q, integer lda, real, dimension( * ) tau, real,
dimension( lwork ) work, integer lwork, real, dimension( * ) rwork,
real, dimension( * ) result)

SQRT03 — that's the name, and yes she's iconic 👑

⭐ Purpose ⭐

okay so SQRT03 tests SORMQR, which computes Q*C, Q'*C, C*Q or C*Q'. literally its whole job 💀

and then — this is the best part — SQRT03 compares the results of a call to SORMQR with the results of forming Q explicitly by a call to SORGQR and then performing matrix multiplication by a call to SGEMM. two techniques, one vibe check, whoever disagrees loses 🫶

🌈 Parameters 🌈

• M — M is INTEGER. the order of the orthogonal matrix Q. M >= 0. main character energy fr ✨
• N — N is INTEGER. the number of rows or columns of the matrix C; C is m-by-n if Q is applied from the left, or n-by-m if Q is applied from the right. N >= 0. pick a side bestie 💅
• K — K is INTEGER. the number of elementary reflectors whose product defines the orthogonal matrix Q. M >= K >= 0. sandwiched, but like, respectfully 🎀
• AF — AF is REAL array, dimension (LDA,N). details of the QR factorization of an m-by-n matrix, as returned by SGEQRF. see SGEQRF for further details 👀
• C — C is REAL array, dimension (LDA,N). that's it, that's the description, she said what she said 🙈
• CC — CC is REAL array, dimension (LDA,N). same energy, different name 💀
• Q — Q is REAL array, dimension (LDA,M). and here's Q living her best life, (LDA,M) 🦋
• LDA — LDA is INTEGER. the leading dimension of the arrays AF, C, CC, and Q. all four. she's the group mom 🔥
• TAU — TAU is REAL array, dimension (min(M,N)). the scalar factors of the elementary reflectors corresponding to the QR factorization in AF. tiny but crucial 🌸
• WORK — WORK is REAL array, dimension (LWORK). the workspace. the grind. the behind-the-scenes queen 👑
• LWORK — LWORK is INTEGER. the length of WORK. LWORK must be at least M, and should be M*NB, where NB is the blocksize for this environment. note the "should" bestie, don't come for me 😭
• RWORK — RWORK is REAL array, dimension (M). no note, just vibes ✨
• RESULT — RESULT is REAL array, dimension (4). the test ratios compare two techniques for multiplying a random matrix C by an m-by-m orthogonal matrix Q. and here's the receipts:

RESULT(1) = norm( Q*C - Q*C )  / ( M * norm(C) * EPS )
RESULT(2) = norm( C*Q - C*Q )  / ( M * norm(C) * EPS )
RESULT(3) = norm( Q'*C - Q'*C )/ ( M * norm(C) * EPS )
RESULT(4) = norm( C*Q' - C*Q' )/ ( M * norm(C) * EPS )

four ratios, four chances to slay 💅✨

🧚 Author 🧚

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

absolute legends, all of them 🫶

Definition at line 134 of file sqrt03.f. — yes, line one-three-four, go look, she's there 🎀

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💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code. not a human, just a very diligent little robot doing her thing 🤖✨

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and that's the whole page bestie!! LAPACK, Version 3.12.0 — mwah, drink some water, and remember: the vibe changes, the facts do not 💖🌸🦋👑