CSYT01(3)

💅 CSYT01(3) — like, the whole entire manual page, bestie

Okay so first things first, the title is CSYT01(3) and the manual it lives in is Library Functions Manual — and the source file is this absolute journey of a path, no cap:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/csyt01.f

That's it. That's the file. She's long, she's slaying, she's in the LAPACK testing directory. Periodt. 🎀

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✨ SYNOPSIS ✨

Functions/Subroutines — the cast 💖

subroutine CSYT01 (uplo, n, a, lda, afac, ldafac, ipiv, c, ldc, rwork,
    resid)
    CSYT01

Literally one subroutine, one name, ten arguments. Main character energy fr fr. 👑

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🌸 Function/Subroutine Documentation 🌸

subroutine CSYT01 🦋

Here's the full signature so you can see exactly what she's working with:

subroutine CSYT01 (character uplo, integer n, complex, dimension( lda, * )
    a, integer lda, complex, dimension( ldafac, * ) afac, integer ldafac,
    integer, dimension( * ) ipiv, complex, dimension( ldc, * ) c, integer
    ldc, real, dimension( * ) rwork, real resid)

Yep, still CSYT01. Iconic.

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🎯 Purpose 🎯

So what does she do? Bestie, she reconstructs a complex symmetric indefinite matrix A from its block L*D*L' or U*D*U' factorization, and then computes the residual:

norm( C - A ) / ( N * norm(A) * EPS ),

where C is the reconstructed matrix, EPS is the machine epsilon, L' is the transpose of L, and U' is the transpose of U.

That's the whole vibe check. Rebuild the matrix, measure how far off you are, divide by N * norm(A) * EPS. Math girlies rise up. ✨

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🧚 Parameters 🧚 (every single one, don't worry)

• UPLO — is CHARACTER*1. It specifies whether the upper or lower triangular part of the complex symmetric matrix A is stored:
  • = 'U': Upper triangular
  • = 'L': Lower triangular
• N — is INTEGER. The number of rows and columns of the matrix A. Constraint: N >= 0.
• A — is COMPLEX array, dimension (LDA,N). The original complex symmetric matrix A. The source material, the blueprint, the original before the glow-up. 💜
• LDA — is INTEGER. The leading dimension of the array A. Constraint: LDA >= max(1,N).
• AFAC — is COMPLEX 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 CSYTRF.
• LDAFAC — is INTEGER. The leading dimension of the array AFAC. Constraint: LDAFAC >= max(1,N).
• IPIV — is INTEGER array, dimension (N). The pivot indices from CSYTRF. She's not inventing these, she's receiving them. 🫶
• C — is COMPLEX array, dimension (LDC,N). That's the whole description. She's the reconstructed one, and honestly she speaks for herself.
• LDC — is INTEGER. The leading dimension of the array C. Constraint: LDC >= max(1,N).
• RWORK — is REAL array, dimension (N). That's it. That's the whole entry. Scratch space doing scratch space things. 🍓
• RESID — is REAL. The actual result, and it depends on UPLO:
  • If UPLO = 'L', it's norm(L*D*L' - A) / ( N * norm(A) * EPS )
  • If UPLO = 'U', it's norm(U*D*U' - A) / ( N * norm(A) * EPS )

Heads up bestie, the RESID descriptions in the original are written in terms of the factorization minus A while the Purpose section says the residual is norm( C - A ) / ( N * norm(A) * EPS ) — both are in there, so I'm giving you both, exactly as written. No editorializing, no cap. 🙈

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👑 Author 👑

The whole squad of institutions behind this:

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

Legends, all of them. Collaborating across state lines to bring you linear algebra. We love to see it. 🌈

Definition at line 123 of file csyt01.f. Line one-two-three, look at her go. 🔥

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💫 Author (again, but the meta one) 💫

This page was generated automatically by Doxygen for LAPACK from the source code. Not a human, not a group chat, a documentation generator. Respect the machine. ⭐

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Alright bestie, that's the page — every flag, every array, every constraint, all accounted for. 😭💖

Sign-off time: this was LAPACK, Version 3.12.0, dated /home/abui...IN/csyt01.f(3) — okay the date field is genuinely just that truncated path, but she's doing her best. Bye, ily, go call CSYTRF first. 🧚💅