TESTING/LIN/zqlt02.f(3)

🎀 TESTING/LIN/zqlt02.f(3) 🎀

okay so this is the Library Functions Manual page for TESTING/LIN/zqlt02.f — manual name folded in near the top, exactly as requested, bestie. 💅

✨ NAME ✨

TESTING/LIN/zqlt02.f

🌸 SYNOPSIS 🌸

Functions/Subroutines

• subroutine zqlt02 (m, n, k, a, af, q, l, lda, tau, work, lwork, rwork, result) — ZQLT02

🦋 Function/Subroutine Documentation 🦋

subroutine zqlt02 (integer m, integer n, integer k, complex*16, dimension( lda, * ) a, complex*16, dimension( lda, * ) af, complex*16, dimension( lda, * ) q, complex*16, dimension( lda, * ) l, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( lwork ) work, integer lwork, double precision, dimension( * ) rwork, double precision, dimension( * ) result)

ZQLT02

💖 Purpose 💖

ok so ZQLT02 tests ZUNGQL, 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, ZQLT02 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 COMPLEX*16 array, dimension (LDA,N). The m-by-n matrix A which was factorized by ZQLT01.
• AF — AF is COMPLEX*16 array, dimension (LDA,N). Details of the QL factorization of A, as returned by ZGEQLF. See ZGEQLF for further details.
• Q — Q is COMPLEX*16 array, dimension (LDA,N).
• L — L is COMPLEX*16 array, dimension (LDA,N).
• LDA — LDA is INTEGER. The leading dimension of the arrays A, AF, Q and L. LDA >= M.
• TAU — TAU is COMPLEX*16 array, dimension (N). The scalar factors of the elementary reflectors corresponding to the QL factorization in AF.
• WORK — WORK is COMPLEX*16 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( 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 zqlt02.f.

💜 Author 💜

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and that's the whole page, bestie — every detail is here, periodt 💖 The cute sign-off info: source LAPACK, Version 3.12.0, page TESTING/LIN/zqlt02.f(3). 🎀