TESTING/LIN/dgbt02.f(3)

📦
version 3.12.1 · 2 versions
, in arch rolling

💅 TESTING/LIN/dgbt02.f 💅

ok so this is a page from the Library Functions Manual — it's the glow-up doc for TESTING/LIN/dgbt02.f, and honestly? she's a whole vibe. let's get into it bestie 🎀

✨ NAME ✨

TESTING/LIN/dgbt02.f — literally the file, that's the name, no notes 💅

🌸 SYNOPSIS 🌸

Functions/Subroutines

subroutine dgbt02 (trans, m, n, kl, ku, nrhs, a, lda, x, ldx, b, ldb,
    rwork, resid)

DGBT02 — that's her. that's the subroutine. 🦋

💖 Function/Subroutine Documentation 💖

🧚 the full signature, no cap

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

👑 Purpose 👑

ok so here's what she does — bestie, she computes the residual for a solution of a banded system of equations, and the system is:

op(A)*X = B

and the residual comes out as:

RESID = norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ),

where op(A) is either A or A**T (it depends on TRANS, iykyk), and EPS is the machine epsilon. 📐✨

and the norm in question? the 1-norm. periodt.

🔥 Parameters 🔥

  • TRANS — TRANS is CHARACTER*1. it's the main character that decides which form of the system we're solving, bestie:
    • = '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. and it better be M >= 0 or we're not doing this. 🙈
  • N — N is INTEGER. the number of columns of the matrix A. N >= 0, always. 💜
  • KL — KL is INTEGER. the number of subdiagonals chillin' within the band of A. KL >= 0. 🌸
  • KU — KU is INTEGER. the number of superdiagonals within the band of A. KU >= 0. she's above the diagonal, iconic. ⭐
  • NRHS — NRHS is INTEGER. the number of columns of B. NRHS >= 0. 🌈
  • A — A is DOUBLE PRECISION array, dimension (LDA,N). it's the original matrix A, but in band storage — stored in rows 1 to KL+KU+1. she's compressed, she's efficient, she ate. 💅
  • LDA — LDA is INTEGER. the leading dimension of the array A. requirement: LDA >= max(1,KL+KU+1). no shortcuts. 🎀
  • X — X is DOUBLE PRECISION array, dimension (LDX,NRHS). the computed solution vectors for the system of linear equations. the whole point, honestly. 🫶
  • LDX — LDX is INTEGER. the leading dimension of the array X. and it's conditional, so pay attention: if TRANS = 'N', then LDX >= max(1,N); if TRANS = 'T' or 'C', then LDX >= max(1,M). 😭
  • B — B is DOUBLE PRECISION array, dimension (LDB,NRHS). on entry, these are the right hand side vectors for the system of linear equations. on exit, B gets overwritten with the difference B - A*X. so yeah, she changes clothes mid-scene 💀
  • LDB — LDB is INTEGER. the leading dimension of the array B. conditional again, bestie: IF TRANS = 'N', LDB >= max(1,M); if TRANS = 'T' or 'C', LDB >= max(1,N). lowkey read it twice. 🙈
  • RWORK — RWORK is DOUBLE PRECISION array, dimension (MAX(1,LRWORK)), where LRWORK >= M when TRANS = 'T' or 'C'; otherwise, RWORK is not referenced. she's only here when she's needed, main character energy. ✨
  • 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 ). this is the final score, the vibe check, the verdict. 🔥

🦋 Author 🦋

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

⭐ Definition ⭐

Definition at line 147 of file dgbt02.f. slay. 💜

🌟 Author (the meta one) 🌟

Generated automatically by Doxygen for LAPACK from the source code. she was literally born this way, no cap. 🫶

ngl bestie, that's the whole page — every flag, every bound, every max(1,...) accounted for. no facts dropped, only vibes added. 💖

and that's a wrap, babe 🎀 — with love from LAPACK, Version 3.12.0, dated TESTING/LIN/dgbt02.f(3). go forth and compute residuals, queen. 👑✨

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