CQRT01(3)

💅 NAME 💅

ok so cqrt01.f — the manual for this one lives in the 3 section, and the file path is literally the whole vibe:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/cqrt01.f

like yes bestie, that's the name, that's the whole name, they really just gave us the file path and said "go off" 💖

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✨ SYNOPSIS ✨

Functions/Subroutines 🎀

• subroutine CQRT01 (m, n, a, af, q, r, lda, tau, work, lwork, rwork, result) — that's her. that's CQRT01.

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🦋 Function/Subroutine Documentation 🦋

subroutine CQRT01 (integer m, integer n, complex, dimension( lda, * ) a,
    complex, dimension( lda, * ) af, complex, dimension( lda, * ) q,
    complex, dimension( lda, * ) r, integer lda, complex, dimension( * )
    tau, complex, dimension( lwork ) work, integer lwork, real, dimension( *
    ) rwork, real, dimension( * ) result)

CQRT01 😌 the icon herself.

🌸 Purpose 🌸

!>
!> CQRT01 tests CGEQRF, which computes the QR factorization of an m-by-n
!> matrix A, and partially tests CUNGQR which forms the m-by-m
!> orthogonal matrix Q.
!>
!> CQRT01 compares R with Q'*A, and checks that Q is orthogonal.
!>

ok so real talk — CQRT01 is a tester. she tests CGEQRF (which computes the QR factorization of an m-by-n matrix A) and she partially tests CUNGQR (which forms the m-by-m orthogonal matrix Q). then she compares R with Q'*A and checks that Q is orthogonal. she's the one doing the vibe check on everybody else's math, no cap 💅

🧚 Parameters 🧚

• M

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

the row count of A, and she is an INTEGER, and M >= 0 — that's the rule, don't test her 🫶

• N

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

the column count of A. INTEGER, and N >= 0. same energy, same boundaries ✨

• A

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

it's A. it's COMPLEX, dimension (LDA,N), and it's the m-by-n matrix A. main character matrix fr 💖

• AF

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

COMPLEX array, dimension (LDA,N), holding the details of the QR factorization of A as returned by CGEQRF. for the full tea, see CGEQRF 👀

• Q

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

COMPLEX array, dimension (LDA,M) — the m-by-m orthogonal matrix Q. she's orthogonal and she's iconic 🌈

• R

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

COMPLEX array, dimension (LDA,max(M,N)). that's the whole description bestie, take it or leave it 😭

• LDA

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

INTEGER, the leading dimension of the arrays A, AF, Q and R — and it must satisfy LDA >= max(M,N). like, that's not a suggestion, that's the law 👑

• TAU

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

COMPLEX array, dimension (min(M,N)), holding the scalar factors of the elementary reflectors, as returned by CGEQRF ✨

• WORK

!>          WORK is COMPLEX array, dimension (LWORK)

COMPLEX array, dimension (LWORK). that's it. she works 💅

• LWORK

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

INTEGER, and she's literally just the dimension of the array WORK 🎀

• RWORK

!>          RWORK is REAL array, dimension (M)

REAL array, dimension (M). yes, REAL, not COMPLEX — she's different like that 💜

• RESULT

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

REAL array, dimension (2) — the test ratios, the moment of truth 🔥

RESULT(1) = norm( R - Q'*A ) / ( M * norm(A) * EPS )
RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )

two ratios, two receipts. RESULT(1) is the R vs Q'*A check, RESULT(2) is the orthogonality check. copy them exactly, do not freestyle 😤

🌟 Author 🌟

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

four institutions, one legend 🙌

⭐ Definition at line 124 of file cqrt01.f. ⭐

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🍓 Author 🍓

Generated automatically by Doxygen for LAPACK from the source code. (yes bestie, a robot wrote this one, not me 😭)

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and that's the whole page! 💖 this manual came to you from LAPACK, Version 3.12.0, dated /home/abui...IN/cqrt01.f(3) — that's the date, that's what it says, I don't make the rules 🎀 stay slay, stay orthogonal, periodt ✨