TESTING/LIN/zsyt01.f(3)

💅 TESTING/LIN/zsyt01.f — from the LAPACK manual, bestie

okay so this is zsyt01.f, page 3 of the manual, and it lives in TESTING/LIN/ — yes it's a test routine, main character energy but for checking other people's math 💖

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✨ SYNOPSIS ✨

Functions/Subroutines

subroutine zsyt01 (uplo, n, a, lda, afac, ldafac, ipiv, c, ldc, rwork,
    resid)

ZSYT01 🫶

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🌸 Function/Subroutine Documentation 🌸

subroutine zsyt01 (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 ✨

🎀 Purpose:

!>
!> ZSYT01 reconstructs a complex symmetric 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, EPS is the machine epsilon,
!> L' is the transpose of L, and U' is the transpose of U.
!>

so basically it rebuilds A from its factorization — literally reverse-engineering the glow-up — and then checks how close it got. iconic behavior 👑

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💜 Parameters

• UPLO — UPLO is CHARACTER*1. tells it which triangular half of the complex symmetric matrix A you actually stored: = 'U' means upper triangular, = 'L' means lower triangular 🔼🔽
• N — N is INTEGER. how many rows and columns the matrix A has. N >= 0 (zero is allowed, no judgement 💀)
• A — A is COMPLEX*16 array, dimension (LDA,N). the original complex symmetric matrix A, the one and only 🌟
• LDA — LDA is INTEGER. the leading dimension of the array A. needs LDA >= max(1,N) ⚠️
• AFAC — AFAC is COMPLEX*16 array, dimension (LDAFAC,N). the factored form of A, fr fr — it holds the block diagonal matrix D plus the multipliers that build the factor L or U from the block L*D*L' or U*D*U' factorization, exactly as computed by ZSYTRF 🧚
• LDAFAC — LDAFAC is INTEGER. the leading dimension of the array AFAC. LDAFAC >= max(1,N). ✨
• IPIV — IPIV is INTEGER array, dimension (N). the pivot indices from ZSYTRF, straight from the source 🎯
• C — C is COMPLEX*16 array, dimension (LDC,N). the reconstructed matrix goes here, no notes 💅
• LDC — LDC is INTEGER. the leading dimension of the array C. LDC >= max(1,N). 🌈
• RWORK — RWORK is DOUBLE PRECISION array, dimension (N). scratch space, doing its quiet little job 🍓
• RESID — RESID is DOUBLE PRECISION. the tea ☕ — the actual residual:
  • if UPLO = 'L': norm(L*D*L' - A) / ( N * norm(A) * EPS )
  • if UPLO = 'U': norm(U*D*U' - A) / ( N * norm(A) * EPS )

watch ur LDA, LDAFAC and LDC bestie — they all gotta be >= max(1,N) or it's over for you 😭

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👑 Author

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

Definition at line 123 of file zsyt01.f.

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🦋 Author (meta edition)

Generated automatically by Doxygen for LAPACK from the source code. yes the docs generate themselves, we love a self-sufficient queen 💖

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and that's the whole page bestie, no cap, every flag and every caveat intact 💅✨

signing off — LAPACK, Version 3.12.0, and this little zsyt01.f(3) page 🎀🫶 see u in the next one 🌸