CGBT02(3)

💅 CGBT02(3) — like, the iconic LAPACK banded-residual checker 🎀

okay bestie, so you've stumbled into the Library Functions Manual (yes, that's the manual name, hi, welcome, make yourself comfy ✨) and the star of the show is a little Fortran file living its best life at:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/cgbt02.f

that's the whole NAME section, no notes 💀 she's literally just a path and a dream.

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✨ SYNOPSIS ✨

Functions/Subroutines 🦋

subroutine CGBT02 (trans, m, n, kl, ku, nrhs, a, lda, x, ldx, b, ldb,
    rwork, resid)

CGBT02

yeah that's it. that's the vibe check. 👑

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🌸 Function/Subroutine Documentation 🌸

subroutine CGBT02 (character trans, integer m, integer n, integer kl,
    integer ku, integer nrhs, complex, dimension( lda, * ) a, integer lda,
    complex, dimension( ldx, * ) x, integer ldx, complex, dimension( ldb, *
    ) b, integer ldb, real, dimension( * ) rwork, real resid)

CGBT02 — she's back, she's serving, she's the same girl as above 💖

🎯 Purpose

so here's the tea, and it's literally in a !> block in the original so you know it's official:

!>
!> CGBT02 computes the residual for a solution of a banded system of
!> equations op(A)*X = B:
!>    RESID = norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ),
!> where op(A) = A, A**T, or A**H, depending on TRANS, and EPS is the
!> machine epsilon.
!>

translation bestie: she checks how wrong your answer is. RESID = the size of B - op(A)*X, divided by norm(op(A)) * norm(X) * EPS. and op(A) is whatever TRANS tells her to be — plain A, A**T, or A**H. EPS is machine epsilon, no cap. 🧮✨

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💅 Parameters

• TRANS — girl, this one's a CHARACTER*1 and she picks the form of the system:

= 'N':  A    * X = B  (No transpose)
= 'T':  A**T * X = B  (Transpose)
= 'C':  A**H * X = B  (Conjugate transpose)

that's it, that's the whole menu 🍓

• M — INTEGER, the number of rows of the matrix A. and the rule is M >= 0, always. 🙏
• N — INTEGER, the number of columns of the matrix A. same energy: N >= 0. 💜
• KL — INTEGER, the number of subdiagonals within the band of A. KL >= 0 or don't even talk to me. 🦋
• KU — INTEGER, the number of superdiagonals within the band of A. KU >= 0, same rules apply. ✨
• NRHS — INTEGER, the number of columns of B. NRHS >= 0. we love a consistent queen. 👑
• A — COMPLEX array, dimension (LDA,N). it's the original matrix A in band storage, stored in rows 1 to KL+KU+1. band storage is that girl, it saves so much space fr fr. 🎀
• LDA — INTEGER, the leading dimension of the array A. gotta be LDA >= max(1,KL+KU+1). don't skimp on the leading dimension bestie, she will know. 💀
• X — COMPLEX array, dimension (LDX,NRHS). the computed solution vectors for the system of linear equations. she's the answer, allegedly. 😭
• LDX — INTEGER, the leading dimension of the array X. so: if TRANS = 'N', then LDX >= max(1,N); if TRANS = 'T' or 'C', then LDX >= max(1,M). got it? got it. 🫶
• B — COMPLEX array, dimension (LDB,NRHS). this one's doing a whole costume change:
  • on entry: the right hand side vectors for the system of linear equations 🧚
  • on exit: B is overwritten with the difference B - A*X (yes, she repurposes it, iconic behaviour, no notes) 🔥
• LDB — INTEGER, the leading dimension of the array B. IF TRANS = 'N', then LDB >= max(1,M); if TRANS = 'T' or 'C', then LDB >= max(1,N). 💖
• RWORK — REAL array, dimension (MAX(1,LRWORK)), where LRWORK >= M when TRANS = 'T' or 'C'. otherwise, RWORK is not referenced — she's off the clock, do not disturb. 🙈
• RESID — REAL, and this is the main character right here: the maximum over the number of right hand sides of

norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ).

like, the final score. the report card. the whole point of the exercise ⭐👑

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👑 Author

all of these absolute legends:

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

Definition at line 146 of file cgbt02.f. 📍 (iykyk — if you need the exact line, now you have it, you're welcome)

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🌈 Author (again, but the meta one)

Generated automatically by Doxygen for LAPACK from the source code. our robot overlord wrote this one, slay. 🤖✨

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💀 psst — this is test code (TESTING/LIN/), it computes residuals, it does not solve your system for you. don't @ me, that's literally just what the path says.

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okay that's the whole page bestie!! 🎀✨

cute little sign-off: this gorgeous document came from LAPACK, Version 3.12.0, and it's dated /home/abui...IN/cgbt02.f(3) — yes the date field is a truncated path, we don't question it, we just vibe 🦋💜