SSYCON(3)

💅 SSYCON(3) — the LAPACK manual page, bestie edition 🎀

ok so this is a page from the LAPACK Library Functions Manual, and the star of the show is ssycon.f — yes that whole path is the "name", she's extra like that:

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

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✨ SYNOPSIS ✨

Functions/Subroutines 🦋

• subroutine SSYCON (uplo, n, a, lda, ipiv, anorm, rcond, work, iwork, info) — like, that's her. that's the whole girl.
• SSYCON

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🔥 Function/Subroutine Documentation 🔥

subroutine SSYCON (character uplo, integer n, real, dimension( lda, * ) a,
    integer lda, integer, dimension( * ) ipiv, real anorm, real rcond, real,
    dimension( * ) work, integer, dimension( * ) iwork, integer info)

SSYCON — she's the one 💅

🌸 Purpose 🌸

ok so listen:

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

translation bestie: she estimates the reciprocal of the condition number, 1-norm edition, of a real symmetric matrix A, using the factorization A = U*D*U**T or A = L*D*L**T that SSYTRF already did for you. she gets an estimate for norm(inv(A)) and then the reciprocal of the condition number is literally RCOND = 1 / (ANORM * norm(inv(A))). math ate, no cap 🧮✨

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🫶 Parameters 🫶

• UPLO — UPLO is CHARACTER*1. tells her whether the factorization details are stored as an upper or lower triangular matrix, like:
  • = 'U': upper triangular, form is A = U*D*U**T;
  • = 'L': lower triangular, form is A = L*D*L**T.

pick one, bestie, she's not doing both 😭

• N — N is INTEGER. the order of the matrix A. N >= 0. that's it, that's the constraint, respect it 💀
• A — A is REAL array, dimension (LDA,N). the block diagonal matrix D plus the multipliers used to obtain the factor U or L, as computed by SSYTRF. yes, all of that lives in here 👑
• LDA — LDA is INTEGER. the leading dimension of the array A. LDA >= max(1,N). bestie, do NOT fumble this one 🙈
• IPIV — IPIV is INTEGER array, dimension (N). the details of the interchanges and the block structure of D, as determined by SSYTRF. she got it from SSYTRF, she's just passing the info along 💅
• ANORM — ANORM is REAL. the 1-norm of the original matrix A. the before picture, if you will 🌈
• RCOND — RCOND is REAL. 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. the whole point, the main character, the moment ⭐
• WORK — WORK is REAL array, dimension (2*N). scratch space. give her 2*N, she's hungry 🍓
• IWORK — IWORK is INTEGER array, dimension (N). integer scratch space. also N. don't mix them up 🎀
• INFO — INFO is INTEGER:
  • = 0: successful exit 🎉
  • < 0: if INFO = -i, the i-th argument had an illegal value 😭 (yeah, that's on you, not her)

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👑 Author 👑

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

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⭐ Author (yes, again) ⭐

Generated automatically by Doxygen for LAPACK from the source code. she's a bot-built icon, we stan 🤖💖

also for the record: Definition at line 128 of file ssycon.f. — line 128, note it, cite it, put it on a shirt 🔥

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💀 reminder bestie: INFO < 0 means an argument was illegal. go check your args before you come for her.

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and that's the whole page 🦋 this cutie was brought to you by LAPACK, Version 3.12.0, hot off /home/abui...RC/ssycon.f(3) — mwah, stan her, cite her, she slayed periodt 💅🎀✨