TESTING/LIN/dqlt02.f(3)

💅 TESTING/LIN/dqlt02.f(3) — the DQLT02 glow-up 🎀

okay so bestie, welcome to the TESTING/LIN/dqlt02.f page from the LAPACK manual ✨ this one's a testing routine, and honestly? it's giving "quietly holding the whole QL factorization together" energy 👑

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✨ SYNOPSIS ✨

🌸 Functions/Subroutines

• subroutine dqlt02 (m, n, k, a, af, q, l, lda, tau, work, lwork, rwork, result) — DQLT02 🫶

💖 Function/Subroutine Documentation 💖

🧚 subroutine dqlt02 (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)

DQLT02 ⭐

🦋 Purpose:

!>
!> DQLT02 tests DORGQL, 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, DQLT02 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.
!>

so basically, it's lowkey the vibe-check routine for DORGQL 💅 it generates that m-by-n Q with orthonormal columns made from k elementary reflectors, then it compares L(m-n+1:m,n-k+1:n) against Q(1:m,m-n+1:m)'*A(1:m,n-k+1:n) — and on top of that it checks that Q's columns are actually orthonormal. no cap, that's the whole assignment 🫶

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💜 Parameters 💜

• M — M is INTEGER 🌸 The number of rows of the matrix Q to be generated. M >= 0. like, how tall Q is, and it's gotta be at least 0.
• N — N is INTEGER ✨ The number of columns of the matrix Q to be generated. and M >= N >= 0. so N can never ghost past M, periodt.
• K — K is INTEGER 🎀 The number of elementary reflectors whose product defines the matrix Q. N >= K >= 0. the reflector count, sandwiched between N and 0.
• A — A is DOUBLE PRECISION array, dimension (LDA,N) 🦋 The m-by-n matrix A which was factorized by DQLT01. the original matrix, already been through DQLT01's whole thing.
• AF — AF is DOUBLE PRECISION array, dimension (LDA,N) 💖 Details of the QL factorization of A, as returned by DGEQLF. See DGEQLF for further details. iykyk, the factorization receipts live in here.
• Q — Q is DOUBLE PRECISION array, dimension (LDA,N) 🌈 the star of the show, bestie 👑
• L — L is DOUBLE PRECISION array, dimension (LDA,N) ⭐ also iconic, also living its LDA by N life.
• LDA — LDA is INTEGER 🌸 The leading dimension of the arrays A, AF, Q and L. LDA >= M. it's the leading-dim glow-up for all four of those arrays, and LDA better be >= M or we riot 😭
• TAU — TAU is DOUBLE PRECISION array, dimension (N) 🧚 The scalar factors of the elementary reflectors corresponding to the QL factorization in AF. the little scalar-factor besties chilling with the AF factorization.
• WORK — WORK is DOUBLE PRECISION array, dimension (LWORK) 💜 scratch space, dimension (LWORK).
• LWORK — LWORK is INTEGER 🎀 The dimension of the array WORK. literally just that, bestie.
• RWORK — RWORK is DOUBLE PRECISION array, dimension (M) 🦋 another workspace, dimension (M) this time.
• RESULT — RESULT is DOUBLE PRECISION array, dimension (2) 🔥 The test ratios: the tea ☕, two of them:

!>          RESULT(1) = norm( L - Q'*A ) / ( M * norm(A) * EPS )
!>          RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )

like, RESULT(1) is the accuracy ratio for the L vs Q'*A comparison, and RESULT(2) is the orthonormality check on Q — the I - Q'*Q ratio. both scaled by M and EPS of course 💅

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👑 Author 👑

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

💀 Definition at line 134 of file dqlt02.f.

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🌟 Author 🌟

Generated automatically by Doxygen for LAPACK from the source code. 🙈 yes it's autogenerated, don't come for her 😭

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and that's a wrap, bestie! 🫶 the footer energy is giving LAPACK, Version 3.12.0, and this little page is dated back to its TESTING/LIN/dqlt02.f(3) era — mwah 💋 go forth and test those QL factorizations, queen 👑💖