TESTING/LIN/cqlt02.f(3)

🌸 NAME 🌸

okay so this page is the iconic TESTING/LIN/cqlt02.f entry from the Library Functions Manual — and yes bestie, it's giving serious LAPACK test-routine energy. 🦋✨

✨ SYNOPSIS ✨

🌈 Functions/Subroutines 🌈

• subroutine cqlt02 (m, n, k, a, af, q, l, lda, tau, work, lwork, rwork, result) — CQLT02

💖 Function/Subroutine Documentation 💖

🫶 subroutine cqlt02 🫶

subroutine cqlt02 (integer m, integer n, integer k, complex, dimension( lda,
       * ) a, complex, dimension( lda, * ) af, complex, dimension( lda, * ) q,
       complex, dimension( lda, * ) l, integer lda, complex, dimension( * )
       tau, complex, dimension( lwork ) work, integer lwork, real, dimension( *
       ) rwork, real, dimension( * ) result)
       CQLT02

🌟 Purpose 🌟

okay so CQLT02 tests CUNGQL, 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, CQLT02 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. periodt. 🔥

🎀 Parameters 🎀

• M — M is INTEGER. It's the number of rows of the matrix Q to be generated, and it has to satisfy M >= 0. 🫶
• N — N is INTEGER. It's the number of columns of the matrix Q to be generated, with M >= N >= 0. 🌸
• K — K is INTEGER. It's the number of elementary reflectors whose product defines the matrix Q, and N >= K >= 0. ✨
• A — A is COMPLEX array, dimension (LDA,N). It's the m-by-n matrix A which was factorized by CQLT01. 💜
• AF — AF is COMPLEX array, dimension (LDA,N). It holds details of the QL factorization of A, as returned by CGEQLF. See CGEQLF for further details. 🦋
• Q — Q is COMPLEX array, dimension (LDA,N). 💖
• L — L is COMPLEX array, dimension (LDA,N). 🎀
• LDA — LDA is INTEGER. It's the leading dimension of the arrays A, AF, Q and L, and LDA >= M. 👑
• TAU — TAU is COMPLEX array, dimension (N). It holds the scalar factors of the elementary reflectors corresponding to the QL factorization in AF. 🌈
• WORK — WORK is COMPLEX array, dimension (LWORK). ⭐
• LWORK — LWORK is INTEGER. It's the dimension of the array WORK. 💅
• RWORK — RWORK is REAL array, dimension (M). 🍓
• RESULT — RESULT is REAL array, dimension (2). It holds 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 cqlt02.f. 💀✨

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💌 and that's the whole page, bestie — generated automatically by Doxygen for LAPACK from the source code. It's from LAPACK Version 3.12.0, and this absolute manual-page main character is TESTING/LIN/cqlt02.f(3). slay and goodbye 💅🫶