DRQT02(3)

💖 DRQT02(3) — Library Functions Manual 💖

okay so bestie, welcome to the Library Functions Manual corner where we're talking about DRQT02(3), and I promise this is gonna be way less cursed than it looks. 🫶

🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/drqt02.f — that's the file this page is serving, periodt. It's a Fortran source file in the LAPACK testing lineup. 💅

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🦋 SYNOPSIS 🦋

✨ Functions/Subroutines ✨

subroutine DRQT02 (m, n, k, a, af, q, r, lda, tau, work, lwork, rwork,
    result)
    DRQT02

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🌈 Function/Subroutine Documentation 🌈

Here's the whole argument squad in all its glory:

subroutine DRQT02 (integer m, integer n, integer k, double precision,
     dimension( lda, * ) a, double precision, dimension( lda, * ) af, double
     precision, dimension( lda, * ) q, double precision, dimension( lda, * )
     r, integer lda, double precision, dimension( * ) tau, double precision,
     dimension( lwork ) work, integer lwork, double precision, dimension( * )
     rwork, double precision, dimension( * ) result)
     DRQT02

✨ Purpose ✨

okay so the purpose is literally this: DRQT02 is the test bestie for DORGRQ. DORGRQ generates an m-by-n matrix Q with orthonormal rows, and that Q is defined as the product of k elementary reflectors. 🫶

Now, given the RQ factorization of an m-by-n matrix A, DRQT02 generates the orthogonal matrix Q defined by the factorization of the last k rows of A. Then it compares R(m-k+1:m,n-m+1:n) with A(m-k+1:m,1:n)*Q(n-m+1:n,1:n)', and it checks that the rows of Q are orthonormal. That's the whole slay. ✨

🧸 Parameters 🧸

Every parameter is here, no skips, no cap:

• M — INTEGER. The number of rows of the matrix Q to be generated. M >= 0.
• N — INTEGER. The number of columns of the matrix Q to be generated. N >= M >= 0.
• K — INTEGER. The number of elementary reflectors whose product defines the matrix Q. M >= K >= 0.
• A — DOUBLE PRECISION array, dimension (LDA,N). The m-by-n matrix A which was factorized by DRQT01.
• AF — DOUBLE PRECISION array, dimension (LDA,N). Details of the RQ factorization of A, as returned by DGERQF. See DGERQF for further details.
• Q — DOUBLE PRECISION array, dimension (LDA,N).
• R — DOUBLE PRECISION array, dimension (LDA,M).
• LDA — INTEGER. The leading dimension of the arrays A, AF, Q and L. LDA >= N.
• TAU — DOUBLE PRECISION array, dimension (M). The scalar factors of the elementary reflectors corresponding to the RQ factorization in AF.
• WORK — DOUBLE PRECISION array, dimension (LWORK).
• LWORK — INTEGER. The dimension of the array WORK.
• RWORK — DOUBLE PRECISION array, dimension (M).
• RESULT — DOUBLE PRECISION array, dimension (2). The test ratios:
  • RESULT(1) = norm( R - A*Q' ) / ( N * norm(A) * EPS )
  • RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )

👑 Author 👑

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

Definition at line 134 of file drqt02.f.

👑 Author 👑 (the auto-generated one)

Generated automatically by Doxygen for LAPACK from the source code.

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mwah 💅 this page was auto-generated by Doxygen for LAPACK from the source code, and the footer info is LAPACK Version 3.12.0 plus the file path /home/abui...IN/drqt02.f(3). Byeee, go test those orthonormal rows 🫶✨