CPOT05(3)

✨ CPOT05 ✨

okay so bestie, buckle up 💖 this is a page from the LAPACK manual — the <pink>Library Functions Manual</pink> — and it's all about one lil Fortran subroutine called CPOT05. It lives at /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/cpot05.f and honestly? she's a tester, not a solver. she checks other people's homework. iconic behavior tbh 🎀

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🌸 SYNOPSIS 🌸

Functions/Subroutines

subroutine CPOT05 (uplo, n, nrhs, a, lda, b, ldb, x, ldx, xact, ldxact,
    ferr, berr, reslts)

CPOT05 — that's the whole name, no notes 💅

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🦋 Function/Subroutine Documentation 🦋

subroutine CPOT05 (character uplo, integer n, integer nrhs, complex,
    dimension( lda, * ) a, integer lda, complex, dimension( ldb, * ) b,
    integer ldb, complex, dimension( ldx, * ) x, integer ldx, complex,
    dimension( ldxact, * ) xact, integer ldxact, real, dimension( * ) ferr,
    real, dimension( * ) berr, real, dimension( * ) reslts)

CPOT05 ✨ (yes she gets her own heading, main character energy 👑)

💜 Purpose 💜

!> !> CPOT05 tests the error bounds from iterative refinement for the !> computed solution to a system of equations A*X = B, where A is a !> Hermitian n by n matrix. !> !> RESLTS(1) = test of the error bound !> = norm(X - XACT) / ( norm(X) * FERR ) !> !> A large value is returned if this ratio is not less than one. !> !> RESLTS(2) = residual from the iterative refinement routine !> = the maximum of BERR / ( (n+1)EPS + () ), where !> (*) = (n+1)*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i ) !>

so basically: she takes your solution, takes the actual answer, and is like "girl. how far off are we." 😭 and if <hotpink>RESLTS(1)</hotpink> comes back large (i.e. the ratio is not less than one), that's your red flag bestie 💀

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🎀 Parameters 🎀

• UPLO — CHARACTER*1. Tells us which triangle of the Hermitian matrix A is actually stored. = 'U': Upper triangular 🌸. = 'L': Lower triangular 🦋. (pick one, she needs to know!)
• N — INTEGER. The number of rows of the matrices X, B, and XACT, and also the order of matrix A. Requirement: N >= 0. no negatives, we don't do that here ✨
• NRHS — INTEGER. The number of columns of the matrices X, B, and XACT. Requirement: NRHS >= 0. same vibe check 🫶
• A — COMPLEX array, dimension (LDA,N). The Hermitian matrix A herself 👑. If UPLO = 'U', the leading n by n upper triangular part of A holds the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced (she simply doesn't look, ngl 🙈). If UPLO = 'L', the leading n by n lower triangular part of A holds the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced.
• LDA — INTEGER. The leading dimension of the array A. Requirement: LDA >= max(1,N). don't skimp on this one 💅
• B — COMPLEX array, dimension (LDB,NRHS). The right hand side vectors for the system of linear equations 💖
• LDB — INTEGER. The leading dimension of the array B. Requirement: LDB >= max(1,N).
• X — COMPLEX array, dimension (LDX,NRHS). The computed solution vectors. Each vector is stored as a column of the matrix X 🌈
• LDX — INTEGER. The leading dimension of the array X. Requirement: LDX >= max(1,N).
• XACT — COMPLEX array, dimension (LDX,NRHS). The exact solution vectors, fr fr. Each vector is stored as a column of the matrix XACT ⭐
• LDXACT — INTEGER. The leading dimension of the array XACT. Requirement: LDXACT >= max(1,N).
• FERR — REAL array, dimension (NRHS). The estimated forward error bounds for each solution vector X. If XTRUE is the true solution, FERR bounds the magnitude of the largest entry in (X - XTRUE) divided by the magnitude of the largest entry in X. it's giving "how wrong could you possibly be" energy 😭
• BERR — REAL array, dimension (NRHS). The componentwise relative backward error of each solution vector — that's the smallest relative change in any entry of A or B that makes X an exact solution 🧚 (yes, she'll move the goalposts just enough. respectfully.)
• RESLTS — REAL array, dimension (2). The maximum over the NRHS solution vectors of the ratios:
  • RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
  • RESLTS(2) = BERR / ( (n+1)*EPS + (*) )

like the purpose said, (*) = (n+1)*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i ) 💀

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👑 Author 👑

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

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Definition at line 163 of file cpot05.f. 📍 (go look, it's right there)

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💅 Author (the meta one) 💅

Generated automatically by Doxygen for LAPACK from the source code. yes she was built by a robot, and yes she still ate 🤖✨

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okay that's the whole page bestie, you're officially smarter than you were three minutes ago 🫶 this was LAPACK, Version 3.12.0, served fresh from /home/abui...IN/cpot05.f(3) — go forth and check those error bounds, mwah 💖🎀🦋