ZSYCON(3)

🦋 ZSYCON(3) — Library Functions Manual 🦋

Okay bestie, so this page lives in the Library Functions Manual and it's literally the doc for /home/abui...RC/zsycon.f(3). Buckle up, we're getting into some LAPACK lore 💅

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✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zsycon.f

Yep, that's the whole name. It's a .f file, she's a Fortran girlie, and that's the entire vibe. 🎀

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🌸 SYNOPSIS 🌸

Functions/Subroutines

subroutine ZSYCON (uplo, n, a, lda, ipiv, anorm, rcond, work, info)

ZSYCON — that's her name, don't wear it out ✨

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👑 Function/Subroutine Documentation 👑

subroutine ZSYCON (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, double precision anorm, double precision rcond, complex*16, dimension( * ) work, integer info)

ZSYCON 💖 (yes, again, it's giving full government name energy)

🧚 Purpose:

!> ZSYCON estimates the reciprocal of the condition number (in the 1-norm) of a complex symmetric matrix A using the factorization A = U*D*UT or A = L*D*LT computed by ZSYTRF. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).

So like, fr fr, ZSYCON takes your complex symmetric matrix A, which you already factored with ZSYTRF into either A = U*D*U**T or A = L*D*L**T, and it estimates the reciprocal of the condition number in the 1-norm. It gets an estimate for norm(inv(A)) and then does the math: RCOND = 1 / (ANORM * norm(inv(A))). Lowkey iconic 🫶

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💜 Parameters 💜

• UPLO — UPLO is CHARACTER*1. Tells us whether the factorization details are stored as an upper or lower triangular matrix:
  • = 'U': Upper triangular, form is A = U*D*U**T;
  • = 'L': Lower triangular, form is A = L*D*L**T.
• N — N is INTEGER. The order of the matrix A. Requirement: N >= 0. 👑
• A — A is COMPLEX*16 array, dimension (LDA,N). This is the block diagonal matrix D plus the multipliers used to obtain the factor U or L, exactly as computed by ZSYTRF. 💅
• LDA — LDA is INTEGER. The leading dimension of the array A. Requirement: LDA >= max(1,N). Don't skip the vibe check on this one 🙈
• IPIV — IPIV is INTEGER array, dimension (N). All the deets about the interchanges and the block structure of D, as determined by ZSYTRF. 🍓
• ANORM — ANORM is DOUBLE PRECISION. The 1-norm of the original matrix A. ✨
• RCOND — RCOND is DOUBLE PRECISION. The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an estimate of the 1-norm of inv(A) computed in this routine. She's the main character of the output, honestly 🌟
• WORK — WORK is COMPLEX*16 array, dimension (2*N). The scratch space. Not glamorous but we love her anyway 💀
• INFO — INFO is INTEGER:
  • = 0: successful exit 🎉
  • < 0: if INFO = -i, the i-th argument had an illegal value 😭

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🌈 Author 🌈

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

Four whole institutions, we stan a collaborative icon 👑

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⭐ Definition at line 123 of file zsycon.f. ⭐

That's the receipt, no cap. 🔥

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🎀 Author (again, because she's extra) 🎀

Generated automatically by Doxygen for LAPACK from the source code. Not me writing by hand, it's giving robot-typed slay 🤖✨

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Heads up bestie: this whole page is machine-generated documentation, so if something looks weird, blame Doxygen, not me 🫶

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And that's a wrap, babes 🌸 — this page is from LAPACK, Version 3.12.0, and it came straight out of /home/abui...RC/zsycon.f(3). Periodt. 💖