TESTING/LIN/zlqt01.f(3)

🎀 NAME 🎀

This is the TESTING/LIN/zlqt01.f(3) page from the Library Functions Manual, and the NAME is TESTING/LIN/zlqt01.f. Bestie, it’s giving very specific LAPACK manual page energy, and we’re gonna read it together. 💅✨

✨ SYNOPSIS ✨

Functions/Subroutines

• subroutine zlqt01 (m, n, a, af, q, l, lda, tau, work, lwork, rwork, result) — ZLQT01

🧚 Function/Subroutine Documentation 🧚

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   subroutine zlqt01 (integer m, integer n, 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)

ZLQT01 👑

Purpose

Okay so ZLQT01 tests ZGELQF, which computes the LQ factorization of an m-by-n matrix A, and partially tests ZUNGLQ which forms the n-by-n orthogonal matrix Q.

ZLQT01 compares L with A*Q', and checks that Q is orthogonal. Literally the whole vibe check. 💖

Parameters

• M — M is INTEGER. The number of rows of the matrix A. M >= 0.
• N — N is INTEGER. The number of columns of the matrix A. N >= 0.
• A — A is COMPLEX*16 array, dimension (LDA,N). The m-by-n matrix A.
• AF — AF is COMPLEX*16 array, dimension (LDA,N). Details of the LQ factorization of A, as returned by ZGELQF. See ZGELQF for further details.
• Q — Q is COMPLEX*16 array, dimension (LDA,N). The n-by-n orthogonal matrix Q.
• L — L is COMPLEX*16 array, dimension (LDA,max(M,N)).
• LDA — LDA is INTEGER. The leading dimension of the arrays A, AF, Q and L. LDA >= max(M,N).
• TAU — TAU is COMPLEX*16 array, dimension (min(M,N)). The scalar factors of the elementary reflectors, as returned by ZGELQF.
• 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 (max(M,N)).
• RESULT — RESULT is DOUBLE PRECISION array, dimension (2). The test ratios:
  • RESULT(1) = norm( L - A*Q' ) / ( N * norm(A) * EPS )
  • RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )

Author

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

Definition at line 124 of file zlqt01.f.

Author

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