TESTING/LIN/clqt01.f(3)

💅 TESTING/LIN/clqt01.f(3) — a.k.a. the LAPACK manual, Library Functions Manual, bestie edition 🎀

okay so real talk, this page is literally all about one Fortran subroutine and she is iconic. no cap.

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✨ NAME ✨

TESTING/LIN/clqt01.f — yes queen, that's the file, that's the whole name, we love a straightforward main character 🦋

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🌸 SYNOPSIS 🌸

Functions/Subroutines

• subroutine clqt01 (m, n, a, af, q, l, lda, tau, work, lwork, rwork, result) — CLQT01 💖

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👑 Function/Subroutine Documentation 👑

🫶 subroutine clqt01

subroutine clqt01 (integer m, integer n, 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)

CLQT01 ⭐

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💜 Purpose 💜

!>
!> CLQT01 tests CGELQF, which computes the LQ factorization of an m-by-n
!> matrix A, and partially tests CUNGLQ which forms the n-by-n
!> orthogonal matrix Q.
!>
!> CLQT01 compares L with A*Q', and checks that Q is orthogonal.
!>

so basically she's the vibe-check subroutine 🧚: CLQT01 tests CGELQF (which computes the LQ factorization of an m-by-n matrix A), and she partially tests CUNGLQ (which forms the n-by-n orthogonal matrix Q). and then, the actual flex: CLQT01 compares L with A*Q', and checks that Q is orthogonal. slay 🔥

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🎀 Parameters 🎀

• M

!>          M is INTEGER
!>          The number of rows of the matrix A.  M >= 0.
!>

M is INTEGER, and she's the number of rows of the matrix A. the rule? M >= 0. periodt 💅

• N

!>          N is INTEGER
!>          The number of columns of the matrix A.  N >= 0.
!>

N is INTEGER and she's the number of columns of the matrix A. constraint bestie: N >= 0 ✨

• A

!>          A is COMPLEX array, dimension (LDA,N)
!>          The m-by-n matrix A.
!>

A is a COMPLEX array, dimension (LDA,N). it's literally the m-by-n matrix A 💖

• AF

!>          AF is COMPLEX array, dimension (LDA,N)
!>          Details of the LQ factorization of A, as returned by CGELQF.
!>          See CGELQF for further details.
!>

AF is a COMPLEX array, dimension (LDA,N). she holds the details of the LQ factorization of A, as returned by CGELQF — and if you want further details, see CGELQF (iykyk) 🦋

• Q

!>          Q is COMPLEX array, dimension (LDA,N)
!>          The n-by-n orthogonal matrix Q.
!>

Q is a COMPLEX array, dimension (LDA,N) — the n-by-n orthogonal matrix Q. orthogonal queen 👑

• L

!>          L is COMPLEX array, dimension (LDA,max(M,N))
!>

L is a COMPLEX array, dimension (LDA,max(M,N)). that's it, that's the whole note 😌

• LDA

!>          LDA is INTEGER
!>          The leading dimension of the arrays A, AF, Q and L.
!>          LDA >= max(M,N).
!>

LDA is INTEGER: the leading dimension of the arrays A, AF, Q and L. and the rule is LDA >= max(M,N) — no exceptions bestie 🌸

• TAU

!>          TAU is COMPLEX array, dimension (min(M,N))
!>          The scalar factors of the elementary reflectors, as returned
!>          by CGELQF.
!>

TAU is a COMPLEX array, dimension (min(M,N)): the scalar factors of the elementary reflectors, as returned by CGELQF 💫

• WORK

!>          WORK is COMPLEX array, dimension (LWORK)
!>

WORK is a COMPLEX array, dimension (LWORK). she works hard, obviously 💅

• LWORK

!>          LWORK is INTEGER
!>          The dimension of the array WORK.
!>

LWORK is INTEGER: the dimension of the array WORK. simple, cute, done 🎀

• RWORK

!>          RWORK is REAL array, dimension (max(M,N))
!>

RWORK is a REAL array, dimension (max(M,N)). yes she's the real one 🫶

• RESULT

!>          RESULT is REAL array, dimension (2)
!>          The test ratios:
!>          RESULT(1) = norm( L - A*Q' ) / ( N * norm(A) * EPS )
!>          RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )
!>

RESULT is a REAL array, dimension (2), and she carries the test ratios, verbatim:

• RESULT(1) = norm( L - A*Q' ) / ( N * norm(A) * EPS )
• RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )

those are the receipts, and the receipts are math 😭🔥

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🌈 Author 🌈

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

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Definition at line 124 of file clqt01.f. 🧚

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⭐ Author ⭐

Generated automatically by Doxygen for LAPACK from the source code. (the robots did this one, not me 💀)

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