CQLT02(3)

📦 version 3.12.0, in opensuse-leap 16.0

💖 NAME 💖

Okay bestie, welcome to CQLT02(3) from the Library Functions Manual. The file is:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/cqlt02.f

That's the whole name vibe for this page. 💅

✨ 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. That's the subroutine, bestie. 🫶

🎯 Purpose

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. Iconic behavior, honestly. ✨

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. That's the whole assignment. Periodt. 💅

🧸 Parameters

  • M — M is INTEGER. It's the number of rows of the matrix Q to be generated. M >= 0.
  • N — N is INTEGER. It's the number of columns of the matrix Q to be generated. M >= N >= 0.
  • K — K is INTEGER. It's the number of elementary reflectors whose product defines the matrix Q. N >= K >= 0.
  • A — A is COMPLEX array, dimension (LDA,N). The m-by-n matrix A which was factorized by CQLT01.
  • AF — AF is COMPLEX array, dimension (LDA,N). 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. The leading dimension of the arrays A, AF, Q and L. LDA >= M.
  • TAU — TAU is COMPLEX array, dimension (N). 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. 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 cqlt02.f.

🌸 Author

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💖 That's the footer tea: LAPACK, Version 3.12.0, page path /home/abui...IN/cqlt02.f(3) — and no extra date on this one. Mwah! 🎀

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