TESTING/LIN/sqlt02.f(3)

💖 sqlt02 — the QL factorization test 💖

Okay so this is the manual page for TESTING/LIN/sqlt02.f(3) from the LAPACK Library Functions Manual, and it's all about the sqlt02 subroutine. It's giving "I test the QL factorization and I take that job very seriously" energy. 💅

✨ NAME ✨

TESTING/LIN/sqlt02.f

🎀 SYNOPSIS 🎀

🌸 Functions/Subroutines 🌸

• subroutine sqlt02 (m, n, k, a, af, q, l, lda, tau, work, lwork, rwork, result) — SQLT02.

🦋 Function/Subroutine Documentation 🦋

subroutine sqlt02 (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)

SQLT02

🌈 Purpose 🌈

SQLT02 tests SORGQL, which generates an m-by-n matrix Q with orthonormal columns that is defined as the product of k elementary reflectors.

Given the QL factorization of an m-by-n matrix A, SQLT02 generates the orthogonal matrix Q defined by the factorization of the last k columns of A; it compares L(m-n+1:m,n-k+1:n) with Q(1:m,m-n+1:m)'*A(1:m,n-k+1:n), and checks that the columns 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. M >= N >= 0.
• K — K is INTEGER. The number of elementary reflectors whose product defines the matrix Q. N >= K >= 0.
• A — A is REAL array, dimension (LDA,N). The m-by-n matrix A which was factorized by SQLT01.
• AF — AF is REAL array, dimension (LDA,N). Details of the QL factorization of A, as returned by SGEQLF. See SGEQLF for further details.
• Q — Q is REAL array, dimension (LDA,N).
• L — L is REAL array, dimension (LDA,N).
• LDA — LDA is INTEGER. The leading dimension of the arrays A, AF, Q and L. LDA >= M.
• TAU — TAU is REAL array, dimension (N). The scalar factors of the elementary reflectors corresponding to the QL factorization in AF.
• WORK — WORK is REAL array, dimension (LWORK).
• LWORK — LWORK is INTEGER. The dimension of the array WORK.
• RWORK — RWORK is REAL array, dimension (M).
• RESULT — RESULT is REAL array, dimension (2). The test ratios:

RESULT(1) = norm( L - 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 134 of file sqlt02.f.

🫶 Author 🫶

Generated automatically by Doxygen for LAPACK from the source code.

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Okay bestie, that's the whole vibe check. This page is from LAPACK Version 3.12.0, manual page TESTING/LIN/sqlt02.f(3) — no separate date appears on this one, and yes, the Doxygen-generated footer energy is included. 💖✨🎀