DQRT03(3)

🌸 DQRT03(3) 🌸 — Library Functions Manual energy 💅

okay so bestie, welcome to the Library Functions Manual page for DQRT03(3) — the header label is /home/abui...IN/dqrt03.f(3), and this whole thing is LAPACK test-routine main character energy. ✨

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🎀 NAME 🎀

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/dqrt03.f

🦋 SYNOPSIS 🦋

Functions/Subroutines 💖

subroutine DQRT03 (m, n, k, af, c, cc, q, lda, tau, work, lwork, rwork,
           result)
           DQRT03

👑 Function/Subroutine Documentation 👑

subroutine DQRT03 (integer m, integer n, integer k, double precision,
       dimension( lda, * ) af, double precision, dimension( lda, * ) c, double
       precision, dimension( lda, * ) cc, double precision, dimension( lda, * )
       q, integer lda, double precision, dimension( * ) tau, double precision,
       dimension( lwork ) work, integer lwork, double precision, dimension( * )
       rwork, double precision, dimension( * ) result)
       DQRT03

🔥 Purpose 🔥

Okay so DQRT03 tests DORMQR, which computes Q*C, Q'*C, C*Q or C*Q'. Periodt. 💅

DQRT03 compares the results of a call to DORMQR with the results of forming Q explicitly by a call to DORGQR and then performing matrix multiplication by a call to DGEMM. It’s giving “check the math, bestie” energy. 🧠

🌈 Parameters 🌈

• M — M is INTEGER. The order of the orthogonal matrix Q. M >= 0.
• 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.
• K — K is INTEGER. The number of elementary reflectors whose product defines the orthogonal matrix Q. M >= K >= 0.
• AF — AF is DOUBLE PRECISION array, dimension (LDA,N). Details of the QR factorization of an m-by-n matrix, as returned by DGEQRF. See DGEQRF for further details.
• C — C is DOUBLE PRECISION array, dimension (LDA,N).
• CC — CC is DOUBLE PRECISION array, dimension (LDA,N).
• Q — Q is DOUBLE PRECISION array, dimension (LDA,M).
• LDA — LDA is INTEGER. The leading dimension of the arrays AF, C, CC, and Q.
• TAU — TAU is DOUBLE PRECISION array, dimension (min(M,N)). The scalar factors of the elementary reflectors corresponding to the QR factorization in AF.
• WORK — WORK is DOUBLE PRECISION array, dimension (LWORK).
• 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.
• RWORK — RWORK is DOUBLE PRECISION array, dimension (M).
• RESULT — RESULT is DOUBLE PRECISION array, dimension (4). The test ratios compare two techniques for multiplying a random matrix C by an m-by-m orthogonal matrix Q.

For RESULT, the formulas are exactly:

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 dqrt03.f.

✨ Author ✨

Generated automatically by Doxygen for LAPACK from the source code.

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💖 cute sign-off, bestie: this is LAPACK Version 3.12.0, source page /home/abui...IN/dqrt03.f(3) — no date is printed in this footer copy, so we’re not inventing one. Slay, bye! 🫶