ZSYT03(3)

💅 NAME

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/zsyt03.f

okay so bestie, this page is from the Library Functions Manual (section 3, iykyk) and it's literally just... the full file path of a Fortran file. that's the name. that's it. she said "my name is my address" and honestly? iconic. ✨

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🦋 SYNOPSIS

Functions/Subroutines

• subroutine ZSYT03 (uplo, n, a, lda, ainv, ldainv, work, ldwork, rwork, rcond, resid) — the girl herself, ZSYT03 🎀

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🌸 Function/Subroutine Documentation

the full signature, no crumbs 💖

subroutine ZSYT03 (character uplo, integer n, complex*16, dimension( lda, * ) a,
    integer lda, complex*16, dimension( ldainv, * ) ainv, integer ldainv,
    complex*16, dimension( ldwork, * ) work, integer ldwork,
    double precision, dimension( * ) rwork, double precision rcond,
    double precision resid)

ZSYT03 — say it with your chest 🗣️

🔥 Purpose:

!>
!> ZSYT03 computes the residual for a complex symmetric matrix times
!> its inverse:
!>    norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * EPS )
!> where EPS is the machine epsilon.
!>

so basically she's the vibe-checker: she multiplies a complex symmetric matrix by its inverse and measures how close you actually got to the identity. the smaller that residual, the more slay. 👑

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✨ Parameters

• UPLO — is CHARACTER*1, no cap. tells us which triangle of the complex symmetric matrix A is stored:
  • = 'U': Upper triangular 🌈
  • = 'L': Lower triangular 🦋
• N — is INTEGER, and it's the number of rows and columns of the matrix A (square queen 👑). N >= 0.
• A — is COMPLEX*16 array, dimension (LDA,N). it's the original complex symmetric matrix A, like the before photo. 📸
• LDA — is INTEGER, the leading dimension of the array A. LDA >= max(1,N) — respect the constraint fr fr.
• AINV — is COMPLEX*16 array, dimension (LDAINV,N). on entry, this is the inverse of the matrix A, stored as a symmetric matrix in the same format as A. ⚠️ but heads up: in this version, AINV is expanded into a full matrix and multiplied by A, so the opposing triangle of AINV will be changed — i.e., if the upper triangular part of AINV is stored, the lower triangular part will be used as work space. so yeah, she's not a girls' girl about your data, she will rearrange it. 💀
• LDAINV — is INTEGER, the leading dimension of the array AINV. LDAINV >= max(1,N). don't test her.
• WORK — is COMPLEX*16 array, dimension (LDWORK,N). the designated scratch space, doing the most so the rest of y'all don't have to. 🫶
• LDWORK — is INTEGER, the leading dimension of the array WORK. LDWORK >= max(1,N).
• RWORK — is DOUBLE PRECISION array, dimension (N). real ones only. ✨
• RCOND — is DOUBLE PRECISION, the reciprocal of the condition number of A, computed as

RCOND = 1/ (norm(A) * norm(AINV)).

• RESID — is DOUBLE PRECISION, and it's the final answer bestie:

norm(I - A*AINV) / ( N * norm(A) * norm(AINV) * EPS )

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👑 Author

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

the whole group chat contributed, we love a collab. 🫶💜

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⭐ Definition at line 124 of file zsyt03.f.

like, literally line 124. go look. i'll wait. 🙈

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🎀 Author (again, but make it meta)

Generated automatically by Doxygen for LAPACK from the source code. no thoughts, just vibes and a parser. 🧚

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okay bye bestie!! this page is brought to you by LAPACK, Version 3.12.0, and it lives at /home/abui...IN/zsyt03.f(3) — mwah 💋 go read the actual source, zsyt03.f, and stan a real one. periodt. 💅🔥🌈