DQRT02(3)

🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/dqrt02.f — okay so bestie, that whole path is the name, and this page is dqrt02.f(3) from the Library Functions Manual. We're in our Fortran-testing era 💅

✨ SYNOPSIS ✨

Functions/Subroutines

• subroutine DQRT02 (m, n, k, a, af, q, r, lda, tau, work, lwork, rwork, result) — DQRT02

💖 Function/Subroutine Documentation 💖

subroutine DQRT02

subroutine DQRT02 (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)

DQRT02 ✨

🎯 Purpose

Okay so DQRT02 tests DORGQR, which generates an m-by-n matrix Q with orthonormal columns that is defined as the product of k elementary reflectors.

Given the QR factorization of an m-by-n matrix A, DQRT02 generates the orthogonal matrix Q defined by the factorization of the first k columns of A; it compares R(1:n,1:k) with Q(1:m,1:n)'*A(1:m,1:k), and checks that the columns of Q are orthonormal. Periodt. 🌈

🧸 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. M >= N >= 0.
• K — K is INTEGER; the number of elementary reflectors whose product defines the matrix Q. N >= K >= 0.
• A — A is DOUBLE PRECISION array, dimension (LDA,N); the m-by-n matrix A which was factorized by DQRT01.
• AF — AF is DOUBLE PRECISION array, dimension (LDA,N); details of the QR factorization of A, as returned by DGEQRF. See DGEQRF for further details.
• Q — Q is DOUBLE PRECISION array, dimension (LDA,N).
• R — R is DOUBLE PRECISION array, dimension (LDA,N).
• LDA — LDA is INTEGER; the leading dimension of the arrays A, AF, Q and R. LDA >= M.
• TAU — TAU is DOUBLE PRECISION array, dimension (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 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 - Q'*A ) / ( M * norm(A) * EPS )
  • RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )

🫶 Author

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

Definition at line 133 of file dqrt02.f. ✨

🌈 Author

Generated automatically by Doxygen for LAPACK from the source code.

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Cute sign-off time: LAPACK Version 3.12.0, source /home/abui...IN/dqrt02.f(3) — the footer doesn't give us a date, so no cap, just vibes 💖🎀