DPBT02(3)

🦋 DPBT02(3) — like, the residual checker for symmetric banded systems 💅

okay so real talk: this page lives in the Library Functions Manual, and it's all about a Fortran subroutine that goes by DPBT02. And the path is a whole journey, bestie — /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/dpbt02.f. We love a girl with a long address. 👑

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✨ SYNOPSIS ✨

Functions/Subroutines 🎀

subroutine DPBT02 (uplo, n, kd, nrhs, a, lda, x, ldx, b, ldb, rwork,
    resid)

DPBT02 — yes that's her name, that's her whole name, no notes. 💖

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🌸 Function/Subroutine Documentation 🌸

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

!> 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.

So basically she's the vibe-checker for your linear solve 🧚 — she takes A*x = b, measures how far B - A*X is from zero, and normalizes it by norm(A) * norm(X) * EPS. If your answer's slaying, RESID is tiny. If it's giving chaos, RESID is big. No cap. 🔥

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💜 Parameters

• UPLO — UPLO is CHARACTER*1. Tells you which half of the symmetric matrix A we're storing, bestie:
  • = 'U': Upper triangular ⬆️
  • = 'L': Lower triangular ⬇️
• N — N is INTEGER. The number of rows and columns of the matrix A. N >= 0. Square queen behavior only. 👑
• 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. It's giving "how thick is the band" energy. 🎀
• NRHS — NRHS is INTEGER. The number of right hand sides. NRHS >= 0. Yes she can handle multiple at once, multi-tasking icon. ✨
• A — A is DOUBLE PRECISION array, dimension (LDA,N). The original symmetric band matrix A, fr fr. 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). Respect the constraint or else. 💀
• X — X is DOUBLE PRECISION array, dimension (LDX,NRHS). The computed solution vectors for the system of linear equations. This is your answer, your moment, your main character vector. 🌟
• 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. So she does NOT ask permission, she just replaces B with the leftover 👀 — plan accordingly.
• LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,N). ⭐
• RWORK — RWORK is DOUBLE PRECISION array, dimension (N). Workspace. It's her little scratchpad, we don't ask questions. 🌈
• RESID — RESID is DOUBLE PRECISION. The maximum over the number of right hand sides of

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

The final grade. The moment of truth. The report card. 😭💖

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👑 Author

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

Four institutions, one subroutine, absolutely iconic collab. 🫶

Definition at line 134 of file dpbt02.f.

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💅 Author (the meta one)

Generated automatically by Doxygen for LAPACK from the source code. Not a human, just a very diligent robot doing her thing. 🤖✨

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okay that's the whole page, bestie — and for the cute sign-off: this one's stamped by LAPACK, Version 3.12.0, served fresh from /home/abui...IN/dpbt02.f(3). Go forth and check those residuals. Periodt. 💜🎀🌷