SQRT03(3)

✨ SQRT03(3) ✨

okay bestie, welcome to the Library Functions Manual page for SQRT03 — it’s giving “LAPACK test routine energy” and we’re gonna get through every single detail together, no cap 💅

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🎀 NAME

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/sqrt03.f

that’s the file this page is about, bestie 🫶

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🌸 SYNOPSIS

🦋 Functions/Subroutines

       subroutine SQRT03 (m, n, k, af, c, cc, q, lda, tau, work, lwork, rwork,
           result)
           SQRT03

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💜 Function/Subroutine Documentation

   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

🔥 Purpose

okay so SQRT03 tests SORMQR, which computes Q*C, Q'*C, C*Q or C*Q' ✨

and 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. iconic comparison behavior, fr fr 👑

🌈 Parameters

• M — M is INTEGER and it’s the order of the orthogonal matrix Q. M >= 0 💖
• N — N is INTEGER and it’s 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 🌸
• K — K is INTEGER and it’s the number of elementary reflectors whose product defines the orthogonal matrix Q. M >= K >= 0 ✨
• AF — AF is REAL array, dimension (LDA,N) and it holds 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) 💅
• CC — CC is REAL array, dimension (LDA,N) 💅
• Q — Q is REAL array, dimension (LDA,M) 💅
• LDA — LDA is INTEGER and it’s the leading dimension of the arrays AF, C, CC, and Q 🎀
• TAU — TAU is REAL array, dimension (min(M,N)) and it holds 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 and it’s the length of WORK. LWORK must be at least M, and should be M*NB, where NB is the blocksize for this environment 🔥
• RWORK — RWORK is REAL array, dimension (M) 🌸
• 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:

           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 )

👑 Author

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

Definition at line 134 of file sqrt03.f.

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🧚 Author

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