TESTING/LIN/dpbt02.f(3)

✨ TESTING/LIN/dpbt02.f(3) ✨

okay bestie, this is the TESTING/LIN/dpbt02.f page from the Library Functions Manual — the dpbt02 subroutine is serving residual-computation main character energy, and she has receipts. 🎀

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🌸 NAME 🌸

TESTING/LIN/dpbt02.f — the file that brings you the dpbt02 subroutine. No cap. 🦋

💅 SYNOPSIS 💅

🧚 Functions/Subroutines 🧚

• subroutine dpbt02 (uplo, n, kd, nrhs, a, lda, x, ldx, b, ldb, rwork, resid)
  • DPBT02 — that's the name, iconic behavior only. 💖

👑 Function/Subroutine Documentation 👑

✨ subroutine dpbt02 ✨

subroutine dpbt02 (character uplo, integer n, integer kd, 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)

DPBT02 🫶

🎀 Purpose 🎀

okay so DPBT02 computes the residual for a solution of a symmetric banded system of equations A*x = b:

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

where EPS is the machine precision. That's the whole assignment, literally. 💀

🌈 Parameters 🌈

• UPLO — UPLO is CHARACTER*1. Specifies whether the upper or lower triangular part of the symmetric matrix A is stored:
  • = 'U': Upper triangular
  • = 'L': Lower triangular
• N — N is INTEGER. The number of rows and columns of the matrix A. N >= 0.
• KD — KD is INTEGER. The number of super-diagonals of the matrix A if UPLO = 'U', or the number of sub-diagonals if UPLO = 'L'. KD >= 0.
• NRHS — NRHS is INTEGER. The number of right hand sides. NRHS >= 0.
• A — A is DOUBLE PRECISION array, dimension (LDA,N). The original symmetric band matrix A. If UPLO = 'U', the upper triangular part of A is stored as a band matrix; if UPLO = 'L', the lower triangular part of A is stored. The columns of the appropriate triangle are stored in the columns of A and the diagonals of the triangle are stored in the rows of A. See DPBTRF for further details.
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,KD+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. LDX >= max(1,N).
• 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. LDB >= max(1,N).
• RWORK — RWORK is DOUBLE PRECISION array, dimension (N).
• RESID — RESID is DOUBLE PRECISION. The maximum over the number of right hand sides of norm(B - A*X) / ( norm(A) * norm(X) * EPS ).

🫶 Author 🫶

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

🧾 Definition at line 🧾

Definition at line 134 of file dpbt02.f.

🤖 Author 🤖

Generated automatically by Doxygen for LAPACK from the source code.

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and that's the tea, bestie: the footer signs off with LAPACK, Version 3.12.0, and TESTING/LIN/dpbt02.f(3) — the source/version/date energy, periodt. 💖✨🎀