DPOT06(3)

🌸 DPOT06(3) 🌸

okay so bestie, welcome to the Library Functions Manual entry for dpot06.f — yes that's a whole manual page for one little test subroutine, and honestly? she deserves it 💅

✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/dpot06.f

that's it. that's the name. full path and everything, no cap 💀 that's literally how this file identifies itself.

🦋 SYNOPSIS 🦋

Functions/Subroutines

• subroutine DPOT06 (uplo, n, nrhs, a, lda, x, ldx, b, ldb, rwork, resid) — DPOT06, bestie. it's her.

🎀 Function/Subroutine Documentation 🎀

subroutine DPOT06 (character uplo, integer n, 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)

DPOT06 💖

Purpose:

!>
!> DPOT06 computes the residual for a solution of a system of linear
!> equations  A*x = b :
!>    RESID = norm(B - A*X,inf) / ( norm(A,inf) * norm(X,inf) * EPS ),
!> where EPS is the machine epsilon.
!>

so like — she's a residual checker. she takes how wrong your answer is, divides it by how big your matrix and your solution are, and then divides by machine epsilon so the number is normalized instead of being a tiny unreadable sliver. iconic behavior fr fr ✨

💜 Parameters 💜

• UPLO — UPLO is CHARACTER*1, and she tells you whether the upper or lower triangular part of the symmetric matrix A is the one being stored:

= 'U':  Upper triangular
= 'L':  Lower triangular

pick one, bestie, she's not doing both 🌸

• N — N is INTEGER. the number of rows and columns of the matrix A, so it's a square situation. constraint: N >= 0 🫶
• NRHS — NRHS is INTEGER. the number of columns of B, which is the matrix of right hand sides. constraint: NRHS >= 0 ⭐
• A — A is DOUBLE PRECISION array, dimension (LDA,N). the original M x N matrix A. yes the doc literally says M x N even though there's no M anywhere else on this page — i don't make the rules, i just report them 🙈
• LDA — LDA is INTEGER. the leading dimension of the array A. constraint: LDA >= max(1,N) 💀
• X — X is DOUBLE PRECISION array, dimension (LDX,NRHS). the computed solution vectors for the system of linear equations. i.e. the answer you're trying to check 👑
• LDX — LDX is INTEGER. the leading dimension of the array X. and here's the vibe check: if TRANS = 'N', LDX >= max(1,N); if TRANS = 'T' or 'C', LDX >= max(1,N). yeah — it's the same condition either way, and TRANS isn't even a parameter of this routine. that's just how the doc is written. we love consistency-ish 💅
• 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 if you needed your original B, she's gone, hope you made a copy.
• 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). again with the TRANS and the M — copied straight from the source doc, and again TRANS is not one of her arguments. iykyk 🌀
• RWORK — RWORK is DOUBLE PRECISION array, dimension (N). workspace. no further comment. she's mysterious like that 🧚
• RESID — RESID is DOUBLE PRECISION. the maximum over the number of right hand sides of:

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

so she loops over every right hand side, computes that ratio, and hands you back the biggest one. one number to rule them all 🔥

🌈 Author

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

four whole institutions, and they all signed off on this. group project energy but make it prestigious 🎓

⭐ Definition at line 125 of file dpot06.f.

💫 Author (the metadata one)

Generated automatically by Doxygen for LAPACK from the source code. so nobody wrote this page, a robot did, and honestly the robot ate 🤖✨

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heads up bestie: those TRANS and M references in the LDX and LDB descriptions? they're in the original doc verbatim. i'm not inventing anything, i'm just holding the door open for you while you read them 🙈

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okay that's the whole page, mwah 💖 this was LAPACK, Version 3.12.0, dated /home/abui...IN/dpot06.f(3) — and that's the sign-off, bestie, go check your residuals 🫶🎀🦋