DGBT02(3)

🎀 dgbt02.f — NAME 🎀

okay bestie, so this page is from the Library Functions Manual and it's all about /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/dgbt02.f — yes, that whole entire path, we're not shortening it, that's her full government name 💅

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✨ SYNOPSIS ✨

Functions/Subroutines

lowkey the main character:

subroutine DGBT02 (trans, m, n, kl, ku, nrhs, a, lda, x, ldx, b, ldb,
    rwork, resid)

and yeah, she's literally called DGBT02 🫶

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💖 Function/Subroutine Documentation 💖

here's the full glow-up of the signature, no details skipped, periodt:

subroutine DGBT02 (character trans, integer m, integer n, integer kl,
    integer ku, integer nrhs, double precision, dimension( lda, * ) a,
    integer lda, double precision, dimension( ldx, * ) x, integer ldx,
    double precision, dimension( ldb, * ) b, integer ldb, double precision,
    dimension( * ) rwork, double precision resid)

DGBT02 — she's iconic, she's a subroutine, she does the math 😌

🌸 Purpose 🌸

!> DGBT02 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 or A**T, depending on TRANS, and EPS is the !> machine epsilon. !> The norm used is the 1-norm. !>

so basically she's checking how good your solution actually is — computing that residual, with op(A) = A or op(A) = A**T depending on TRANS, EPS being the machine epsilon, and the norm being the 1-norm. no cap, that's the whole vibe check 🔥

🌈 Parameters 🌈

• TRANS — TRANS is CHARACTER*1, and she specifies the form of the system of equations:
  • = 'N': A * X = B (No transpose)
  • = 'T': A**T * X = B (Transpose)
  • = 'C': A**H * X = B (Conjugate transpose = Transpose)
• 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.
• KL — KL is INTEGER, the number of subdiagonals within the band of A. KL >= 0.
• KU — KU is INTEGER, the number of superdiagonals within the band of A. KU >= 0.
• NRHS — NRHS is INTEGER, the number of columns of B. NRHS >= 0.
• A — A is DOUBLE PRECISION array, dimension (LDA,N), the original matrix A in band storage, stored in rows 1 to KL+KU+1.
• LDA — LDA is INTEGER, the leading dimension of the array A. LDA >= max(1,KL+KU+1).
• X — X is DOUBLE PRECISION array, dimension (LDX,NRHS), the computed solution vectors for the system of linear equations.
• LDX — LDX is INTEGER, the leading dimension of the array X. If TRANS = 'N', LDX >= max(1,N); if TRANS = 'T' or 'C', LDX >= max(1,M).
• B — B is DOUBLE PRECISION array, dimension (LDB,NRHS). On entry, the right hand side vectors for the system of linear equations. On exit, B is overwritten with the difference B - A*X.
• LDB — LDB is INTEGER, the leading dimension of the array B. IF TRANS = 'N', LDB >= max(1,M); if TRANS = 'T' or 'C', LDB >= max(1,N).
• RWORK — RWORK is DOUBLE PRECISION array, dimension (MAX(1,LRWORK)), where LRWORK >= M when TRANS = 'T' or 'C'; otherwise, RWORK is not referenced.
• RESID — RESID is DOUBLE PRECISION, the maximum over the number of right hand sides of norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ).

bestie pls note: B gets overwritten with B - A*X on exit, and RWORK is literally not referenced unless TRANS = 'T' or 'C' 🙈

🦋 Author 🦋

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

Definition at line 147 of file dgbt02.f. 📍

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👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code. she's a bot-written baddie, we respect it 💜

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and that's the whole page, bestie — slay ✨ this was LAPACK Version 3.12.0, from /home/abui...IN/dgbt02.f(3), signing off 🎀🫶💖