TESTING/LIN/zsyt01_aa.f(3)

💖 TESTING/LIN/zsyt01_aa.f 💖

Okay so bestie, this is the manual page for TESTING/LIN/zsyt01_aa.f from the LAPACK library — it's giving very niche linear algebra energy and honestly? We're obsessed. 🧚✨

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✨ NAME ✨

TESTING/LIN/zsyt01_aa.f — no cap, that's literally the whole name, periodt. 💅

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💅 SYNOPSIS 💅

🎀 Functions/Subroutines 🎀

• subroutine zsyt01_aa (uplo, n, a, lda, afac, ldafac, ipiv, c, ldc, rwork, resid) — the main character of this whole page, fr fr.
  • ZSYT01 — yes queen, that's the short name and it ate. 👑

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🦋 Function/Subroutine Documentation 🦋

✨ subroutine zsyt01_aa ✨

subroutine zsyt01_aa (character uplo, integer n, complex*16, dimension( lda,
* ) a, integer lda, complex*16, dimension( ldafac, * ) afac, integer
ldafac, integer, dimension( * ) ipiv, complex*16, dimension( ldc, * ) c,
integer ldc, double precision, dimension( * ) rwork, double precision
resid)

ZSYT01 — that's the vibe check. 😌

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🌸 Purpose 🌸

!> !> ZSYT01 reconstructs a hermitian indefinite matrix A from its !> block L*D*L' or U*D*U' factorization and computes the residual !> norm( C - A ) / ( N * norm(A) * EPS ), !> where C is the reconstructed matrix and EPS is the machine epsilon. !>

So like, it takes the factored version of your matrix, puts it back together (reconstruction era 💖), and then checks how close it got. The residual formula is the whole point — it's literally norm( C - A ) / ( N * norm(A) * EPS ). Slay. 🔥

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💜 Parameters 💜

• UPLO — is a CHARACTER*1. It tells us whether we're storing the upper or lower triangular part of the hermitian matrix A. The options are:
  • = 'U': Upper triangular — the top half, iykyk. ⬆️
  • = 'L': Lower triangular — the bottom half, periodt. ⬇️
• N — is an INTEGER. The number of rows and columns of the matrix A. And bestie, N >= 0 — no negative dimensions allowed, that's not the vibe. 🚫
• A — is a COMPLEX*16 array, dimension (LDA,N). The original hermitian matrix A. The blueprint, the source material, the main character before reconstruction. 👑
• LDA — is an INTEGER. The leading dimension of the array A. Constraint: LDA >= max(1,N). Respect the leading dimension, okay? 💅
• AFAC — is a COMPLEX*16 array, dimension (LDAFAC,N). The factored form of the matrix A. AFAC contains the block diagonal matrix D and the multipliers used to obtain the factor L or U from the block L*D*L' or U*D*U' factorization as computed by ZSYTRF. So like, it's the already-glow-up version — we're just checking the reconstruction. ✨
• LDAFAC — is an INTEGER. The leading dimension of the array AFAC. Constraint: LDAFAC >= max(1,N). Again — respect it. 🫶
• IPIV — is an INTEGER array, dimension (N). The pivot indices from ZSYTRF. They're the receipts from the factorization, basically. 🧾
• C — is a COMPLEX*16 array, dimension (LDC,N). (No extra description needed, she's self-explanatory and that's iconic. 💁‍♀️)
• LDC — is an INTEGER. The leading dimension of the array C. Constraint: LDC >= max(1,N). You already know the drill. 🌈
• RWORK — is a COMPLEX*16 array, dimension (N). (Just vibes. No further notes. 🍓)
• RESID — is a COMPLEX*16. And here's where it gets juicy:
  • If UPLO = 'L', it returns norm(L*D*L' - A) / ( N * norm(A) * EPS )
  • If UPLO = 'U', it returns norm(U*D*U' - A) / ( N * norm(A) * EPS )

So it's literally the residual, based on which triangle you picked. Lowkey the most important part. 😭🔥

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👑 Author 👑

Shoutout to the brainiacs behind this:

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

They ate and left no crumbs. 💅✨

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⭐ Definition at line 122 of file zsyt01_aa.f. ⭐

That's the exact location if you wanna go read the source — go off, bestie. 📖

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💖 Author 💖

Generated automatically by Doxygen for LAPACK from the source code. So like, not me writing this by hand — the robots did it, and they understood the assignment. 🤖✨

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So yeah, that's the whole page. LAPACK Version 3.12.0, TESTING/LIN/zsyt01_aa.f(3) — brought to you by Doxygen and the LAPACK girlies. No cap, this was a journey. 💜🌸🦋

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