DLQT02(3)

hiii bestie, welcome to DLQT02(3) from the Library Functions Manual 💅✨ this is your girl's guide to a tiny but iconic LAPACK test routine. buckle up, it's giving numerical linear algebra with main character energy 🎀

💖 NAME 💖

okay so the name situation is literally this whole path, no cap:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/dlqt02.f

✨ SYNOPSIS ✨

under Functions/Subroutines, we have:

       subroutine DLQT02 (m, n, k, a, af, q, l, lda, tau, work, lwork, rwork,
           result)
           DLQT02

🦋 Function/Subroutine Documentation 🦋

here's the full signature in all its glory, bestie:

       subroutine DLQT02 (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, * )
           l, integer lda, double precision, dimension( * ) tau, double precision,
           dimension( lwork ) work, integer lwork, double precision, dimension( * )
           rwork, double precision, dimension( * ) result)
           DLQT02

🦋 Purpose 🦋

so DLQT02 tests DORGLQ, which generates an m-by-n matrix Q with orthonormal rows that is defined as the product of k elementary reflectors. obsessed with the clarity 💖

given the LQ factorization of an m-by-n matrix A, DLQT02 generates the orthogonal matrix Q defined by the factorization of the first k rows of A; it compares L(1:k,1:m) with A(1:k,1:n)*Q(1:m,1:n)', and checks that the rows 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. N >= M >= 0.
• K — K is INTEGER. the number of elementary reflectors whose product defines the matrix Q. M >= K >= 0.
• A — A is DOUBLE PRECISION array, dimension (LDA,N). the m-by-n matrix A which was factorized by DLQT01.
• AF — AF is DOUBLE PRECISION array, dimension (LDA,N). details of the LQ factorization of A, as returned by DGELQF. see DGELQF for further details.
• Q — Q is DOUBLE PRECISION array, dimension (LDA,N).
• L — L is DOUBLE PRECISION array, dimension (LDA,M).
• LDA — LDA is INTEGER. the leading dimension of the arrays A, AF, Q and L. LDA >= N.
• TAU — TAU is DOUBLE PRECISION array, dimension (M). the scalar factors of the elementary reflectors corresponding to the LQ 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 are:

RESULT(1) = norm( L - 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 133 of file dlqt02.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code. slay 💅

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xoxo, LAPACK 💖 — Version 3.12.0, with the footer path /home/abui...IN/dlqt02.f(3) 🫶✨