DSPCON(3)

💅 DSPCON(3) — like, the Library Functions Manual, but make it cute 🎀

okay so bestie, welcome to the Library Functions Manual entry for DSPCON(3), straight out of the LAPACK-verse ✨ the file lives at /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dspcon.f and honestly? it's giving "quietly doing the most important math in the room" 👑

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✨ SYNOPSIS ✨

Functions/Subroutines — the cast 💖

subroutine DSPCON (uplo, n, ap, ipiv, anorm, rcond, work, iwork, info)

DSPCON — that's her, that's the main character 🌟

Function/Subroutine Documentation 📜

subroutine DSPCON (character uplo, integer n, double precision, dimension( * )
    ap, integer, dimension( * ) ipiv, double precision anorm, double
    precision rcond, double precision, dimension( * ) work, integer,
    dimension( * ) iwork, integer info)

yep, DSPCON again — she said "billing twice, I earned it" 💅

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🌸 PURPOSE 🌸

so what does she do? DSPCON estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric packed matrix A, using the factorization A = U*D*U**T or A = L*D*L**T computed by DSPTRF 🫶

an estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))) — that's the whole formula, no cap, it's literally right there 📐✨

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🦋 PARAMETERS 🦋

every single one of them, bestie, no skips 👇

• UPLO — UPLO is CHARACTER*1. Specifies whether the details of the factorization 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. Constraint, and she's strict about it: N >= 0 🚨
• AP — AP is DOUBLE PRECISION array, dimension (N*(N+1)/2). The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by DSPTRF, stored as a packed triangular matrix 🧩 (packed!! like a little suitcase of math)
• IPIV — IPIV is INTEGER array, dimension (N). Details of the interchanges and the block structure of D as determined by DSPTRF 🔀
• 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 💫
• WORK — WORK is DOUBLE PRECISION array, dimension (2*N) 🛠️
• IWORK — IWORK is INTEGER array, dimension (N) 🔢
• INFO — INFO is INTEGER 📣
  • = 0: successful exit 🎉
  • < 0: if INFO = -i, the i-th argument had an illegal value 💀 (so like… check your inputs, bestie)

⚠️ heads up: that INFO < 0 situation means you passed something illegal into the i-th argument. it's not a "vibe", it's an error. respect the constraint 🙈

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👑 AUTHOR 👑

iconic institutions only, we stan credentialed excellence:

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

📍 Definition at line 123 of file dspcon.f.

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🎀 AUTHOR (the meta one) 🎀

Generated automatically by Doxygen for LAPACK from the source code 🤖✨ (yes bestie, even the docs have docs)

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and that's the whole page!! 💜 this lovely little document is LAPACK, Version 3.12.0, and it signs off from /home/abui...RC/dspcon.f(3) — mwah, drink water, and may your RCOND always be reasonable 🌈💖