ZRQT02(3)

💖 NAME 💖

okay so bestie, welcome to the zrqt02.f(3) manual page — it's from the Library Functions Manual — and the file it's documenting is literally:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/zrqt02.f

that's the whole NAME moment. slay. 💅

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✨ SYNOPSIS ✨

Functions/Subroutines

subroutine ZRQT02 (m, n, k, a, af, q, r, lda, tau, work, lwork, rwork,
    result)
    ZRQT02

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🫶 Function/Subroutine Documentation 🫶

the full signature, no cap:

   subroutine ZRQT02 (integer m, integer n, integer k, complex*16, dimension(
       lda, * ) a, complex*16, dimension( lda, * ) af, complex*16, dimension(
       lda, * ) q, complex*16, dimension( lda, * ) r, integer lda, complex*16,
       dimension( * ) tau, complex*16, dimension( lwork ) work, integer lwork,
       double precision, dimension( * ) rwork, double precision, dimension( * )
       result)
       ZRQT02

🌸 Purpose 🌸

ZRQT02 tests ZUNGRQ, which generates an m-by-n matrix Q with orthonormal rows that is defined as the product of k elementary reflectors.

Given the RQ factorization of an m-by-n matrix A, ZRQT02 generates the orthogonal matrix Q defined by the factorization of the last k rows of A; 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 checks that the rows of Q are orthonormal. 🦋

🎀 Parameters 🎀

• M — M is INTEGER; the number of rows of the matrix Q to be generated. M >= 0.
• N — N is INTEGER; the number of columns of the matrix Q to be generated. N >= M >= 0.
• K — K is INTEGER; the number of elementary reflectors whose product defines the matrix Q. M >= K >= 0.
• A — A is COMPLEX*16 array, dimension (LDA,N); the m-by-n matrix A which was factorized by ZRQT01.
• AF — AF is COMPLEX*16 array, dimension (LDA,N); details of the RQ factorization of A, as returned by ZGERQF. See ZGERQF for further details.
• Q — Q is COMPLEX*16 array, dimension (LDA,N).
• R — R is COMPLEX*16 array, dimension (LDA,M).
• LDA — LDA is INTEGER; the leading dimension of the arrays A, AF, Q and L. LDA >= N.
• TAU — TAU is COMPLEX*16 array, dimension (M); the scalar factors of the elementary reflectors corresponding to the RQ factorization in AF.
• WORK — WORK is COMPLEX*16 array, dimension (LWORK).
• LWORK — LWORK is INTEGER; the dimension of the array WORK.
• RWORK — RWORK is DOUBLE PRECISION array, dimension (M).
• RESULT — RESULT is 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 zrqt02.f.

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💖 Author 💖

Generated automatically by Doxygen for LAPACK from the source code.

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mwah 💋 that's the whole page, bestie. sign-off: LAPACK Version 3.12.0 — footer path /home/abui...IN/zrqt02.f(3). The original footer's only source/version-date-ish line is that version/path combo, so I'm not inventing extra date info. periodt. 💅✨