SLQT02(3)

🎀 SLQT02(3) — Library Functions Manual 🎀

Okay bestie, welcome to the SLQT02(3) page from the LAPACK Library Functions Manual. The banner at the top is doing a little /home/abui...IN/slqt02.f(3) cameo situation, and we’re about to get into the whole subroutine. Buckle up, it’s giving numerical linear algebra 💅.

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📛 NAME 📛

Officially, the NAME section is just this file path, no cap:

/home/abuild/rpmbuild/BUILD/lapack-
static-3.12.0-build/lapack-3.12.0/TESTING/LIN/slqt02.f

📚 SYNOPSIS 📚

✨ Functions/Subroutines ✨

       subroutine SLQT02 (m, n, k, a, af, q, l, lda, tau, work, lwork, rwork,
           result)
           SLQT02

🧚 Function/Subroutine Documentation 🧚

   subroutine SLQT02 (integer m, integer n, integer k, real, dimension( lda, *
       ) a, real, dimension( lda, * ) af, real, dimension( lda, * ) q, real,
       dimension( lda, * ) l, integer lda, real, dimension( * ) tau, real,
       dimension( lwork ) work, integer lwork, real, dimension( * ) rwork,
       real, dimension( * ) result)
       SLQT02

🎯 Purpose 🎯

So SLQT02 tests SORGLQ, which generates an m-by-n matrix Q with orthonormal rows that is defined as the product of k elementary reflectors. Iconic behavior, honestly.

Given the LQ factorization of an m-by-n matrix A, SLQT02 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. Main character energy for a test routine, fr fr.

🎛️ 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 REAL array, dimension (LDA,N). The m-by-n matrix A which was factorized by SLQT01.
• AF — AF is REAL array, dimension (LDA,N). Details of the LQ factorization of A, as returned by SGELQF. See SGELQF for further details.
• Q — Q is REAL array, dimension (LDA,N). That’s the whole note, bestie.
• L — L is REAL array, dimension (LDA,M). Same vibe: that’s the note.
• LDA — LDA is INTEGER. The leading dimension of the arrays A, AF, Q and L. LDA >= N. 🦋
• TAU — TAU is REAL array, dimension (M). The scalar factors of the elementary reflectors corresponding to the LQ factorization in AF.
• WORK — WORK is REAL array, dimension (LWORK). Short and sweet.
• LWORK — LWORK is INTEGER. The dimension of the array WORK.
• RWORK — RWORK is REAL array, dimension (M). Also short and sweet.
• RESULT — RESULT is REAL array, dimension (2). The test ratios:
  • 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 slqt02.f.

📜 Author 📜

Generated automatically by Doxygen for LAPACK from the source code.

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And that’s the page, bestie 🫶. Cute little sign-off: the footer says LAPACK Version 3.12.0 and the path /home/abui...IN/slqt02.f(3) — no date shown, just version-and-path vibes. Periodt. 💖✨