ZGBT02(3)

✨ NAME ✨

Welcome to ZGBT02(3) from the Library Functions Manual, bestie 💖. The header tag is /home/abui...IN/zgbt02.f(3) — twice in the original header, iconic — and the NAME line points at the full source file path: /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/zgbt02.f.

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🦋 SYNOPSIS 🦋

🦋 Functions/Subroutines 🦋

subroutine ZGBT02 (trans, m, n, kl, ku, nrhs, a, lda, x, ldx, b, ldb,
    rwork, resid)

And the function itself is ZGBT02, periodt.

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🧚 Function/Subroutine Documentation 🧚

Here's the full signature, character for character, no cap:

subroutine ZGBT02 (character trans, integer m, integer n, integer kl,
    integer ku, integer nrhs, complex*16, dimension( lda, * ) a, integer
    lda, complex*16, dimension( ldx, * ) x, integer ldx, complex*16,
    dimension( ldb, * ) b, integer ldb, double precision, dimension( * )
    rwork, double precision resid)

This is the ZGBT02 star of the show.

🌸 Purpose 🌸

Ok so ZGBT02 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. Literally the whole vibe of this routine.

💅 Parameters 💅

• TRANS — 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 — INTEGER. The number of rows of the matrix A. M >= 0.
• N — INTEGER. The number of columns of the matrix A. N >= 0.
• KL — INTEGER. The number of subdiagonals within the band of A. KL >= 0.
• KU — INTEGER. The number of superdiagonals within the band of A. KU >= 0.
• NRHS — INTEGER. The number of columns of B. NRHS >= 0.
• A — COMPLEX*16 array, dimension (LDA,N). The original matrix A in band storage, stored in rows 1 to KL+KU+1.
• LDA — INTEGER. The leading dimension of the array A. LDA >= max(1,KL+KU+1).
• X — COMPLEX*16 array, dimension (LDX,NRHS). The computed solution vectors for the system of linear equations.
• LDX — 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 — COMPLEX*16 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 — 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 — DOUBLE PRECISION array, dimension (MAX(1,LRWORK)), where LRWORK >= M when TRANS = 'T' or 'C'; otherwise, RWORK is not referenced.
• RESID — DOUBLE PRECISION. The maximum over the number of right hand sides of norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ).

Bestie, those dimension conditions are mandatory, not a suggestion 💀.

👑 Author 👑

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

Definition at line 146 of file zgbt02.f.

💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code.

And that's the cute little sign-off, bestie: LAPACK, Version 3.12.0, from /home/abui...IN/zgbt02.f(3). The page doesn't give a date, so I'm not inventing one — periodt. Mwah 💋