TESTING/LIN/cgbt02.f(3)

💅 TESTING/LIN/cgbt02.f 💅

okay bestie, welcome to the <pink>TESTING/LIN/cgbt02.f(3)</pink> page — yes, straight from the <purple>Library Functions Manual</purple>, and she is here to explain CGBT02 in full, no skips, no cap. 💖

---

✨ NAME ✨

TESTING/LIN/cgbt02.f — the LAPACK testing routine CGBT02, and yes, she’s iconic. 🎀

---

🦋 SYNOPSIS 🦋

Functions/Subroutines

subroutine cgbt02 (trans, m, n, kl, ku, nrhs, a, lda, x, ldx, b, ldb,
    rwork, resid)

The routine name is CGBT02. 💅

---

🧚 Function/Subroutine Documentation 🧚

Here’s the full signature, character for character:

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

💖 Purpose 💖

okay so the whole point is this, bestie:

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.

So she’s computing that residual, exactly with the formula above. ✨

🎀 Parameters 🎀

• TRANS — is CHARACTER*1. 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)
• M — is INTEGER. The number of rows of the matrix A. M >= 0.
• N — is INTEGER. The number of columns of the matrix A. N >= 0.
• KL — is INTEGER. The number of subdiagonals within the band of A. KL >= 0.
• KU — is INTEGER. The number of superdiagonals within the band of A. KU >= 0.
• NRHS — is INTEGER. The number of columns of B. NRHS >= 0.
• A — is COMPLEX array, dimension (LDA,N). The original matrix A in band storage, stored in rows 1 to KL+KU+1.
• LDA — is INTEGER. The leading dimension of the array A. LDA >= max(1,KL+KU+1).
• X — is COMPLEX array, dimension (LDX,NRHS). The computed solution vectors for the system of linear equations.
• 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 — is COMPLEX 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 — 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 — is REAL array, dimension (MAX(1,LRWORK)), where LRWORK >= M when TRANS = 'T' or 'C'; otherwise, RWORK is not referenced.
• RESID — is REAL. The maximum over the number of right hand sides of norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ).

lowkey important: RWORK only gets referenced when TRANS = 'T' or 'C' — otherwise she’s literally not invited. 🫶

🌸 Author 🌸

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

Definition at line 146 of file cgbt02.f. 📌

---

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code. 💜

---

okay that’s the whole page, bestie! final footer vibe: <rainbow>LAPACK Version 3.12.0</rainbow>, source TESTING/LIN/cgbt02.f(3), no date printed, generated automatically by Doxygen for LAPACK from the source code. bye! 💖✨🎀