TESTING/LIN/sgbt02.f(3)

💅 TESTING/LIN/sgbt02.f(3) 💅

okay bestie, this page is straight outta the Library Functions Manual — no cap, it's the sgbt02 routine's moment. ✨

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🌸 NAME 🌸

TESTING/LIN/sgbt02.f

🎀 SYNOPSIS 🎀

Functions/Subroutines

subroutine sgbt02 (trans, m, n, kl, ku, nrhs, a, lda, x, ldx, b, ldb,
    rwork, resid)

SGBT02

🦋 Function/Subroutine Documentation 🦋

subroutine sgbt02 (character trans, integer m, integer n, integer kl,
    integer ku, integer nrhs, real, dimension( lda, * ) a, integer lda,
    real, dimension( ldx, * ) x, integer ldx, real, dimension( ldb, * ) b,
    integer ldb, real, dimension( * ) rwork, real resid)

SGBT02

✨ Purpose ✨

okay so SGBT02 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. 💖

🌈 Parameters 🌈

• TRANS — 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 = 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 REAL 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 REAL 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 REAL 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 REAL array, dimension (MAX(1,LRWORK)), where LRWORK >= M when TRANS = 'T' or 'C'; otherwise, RWORK is not referenced.
• RESID — RESID is REAL. The maximum over the number of right hand sides of:

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

💜 Author 💜

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

Definition at line 147 of file sgbt02.f.

🫶 Author 🫶

Generated automatically by Doxygen for LAPACK from the source code.

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that's the whole page, bestie — source/version: LAPACK, Version 3.12.0; page: TESTING/LIN/sgbt02.f(3). 💜✨