ZPPCON(3)

💅 ZPPCON(3) — the zppcon.f era ✨

okay so bestie, this whole page is literally about one file: /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zppcon.f — that's the NAME section, that's the whole vibe. it's a Library Functions Manual entry, LAPACK edition. slay.

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✨ SYNOPSIS ✨

Functions/Subroutines section, and here's the moment:

subroutine ZPPCON (uplo, n, ap, anorm, rcond, work, rwork, info)
    ZPPCON

that's it. that's the icon.

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🫶 Function/Subroutine Documentation 🫶

🌸 subroutine ZPPCON 🌸

the full signature, character for character, don't @ me:

subroutine ZPPCON (character uplo, integer n, complex*16, dimension( * ) ap,
    double precision anorm, double precision rcond, complex*16, dimension( *
    ) work, double precision, dimension( * ) rwork, integer info)
    ZPPCON

💖 Purpose:

!> !> ZPPCON estimates the reciprocal of the condition number (in the !> 1-norm) of a complex Hermitian positive definite packed matrix using !> the Cholesky factorization A = UH*U or A = L*LH computed by !> ZPPTRF. !> !> An estimate is obtained for norm(inv(A)), and the reciprocal of the !> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). !>

like, it's giving "how badly-conditioned is my matrix" energy. it estimates norm(inv(A)) and then does RCOND = 1 / (ANORM * norm(inv(A))). math girlboss behavior fr fr.

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🎀 Parameters 🎀

• UPLO — it's CHARACTER*1, cute little one-character king. tells you which triangle of A is stored:
  • = 'U': Upper triangle of A is stored;
  • = 'L': Lower triangle of A is stored.

the full quote, verbatim:

!> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored. !>

• N — INTEGER, the order of the matrix A. and bestie, N >= 0, non-negotiable.

!> N is INTEGER !> The order of the matrix A. N >= 0. !>

• AP — COMPLEX*16 array, dimension (N*(N+1)/2). this is the triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, packed columnwise in a linear array. and the way the j-th column of U or L gets stored? iconic:

!> AP is COMPLEX*16 array, dimension (N*(N+1)/2) !> The triangular factor U or L from the Cholesky factorization !> A = UH*U or A = L*LH, packed columnwise in a linear !> array. The j-th column of U or L is stored in the array AP !> as follows: !> if UPLO = 'U', AP(i + (j-1)j/2) = U(i,j) for 1<=i<=j; !> if UPLO = 'L', AP(i + (j-1)(2n-j)/2) = L(i,j) for j<=i<=n. !>

• ANORM — DOUBLE PRECISION, the 1-norm (or infinity-norm) of the Hermitian matrix A. yes she does both, versatile queen 💅

!> ANORM is DOUBLE PRECISION !> The 1-norm (or infinity-norm) of the Hermitian matrix A. !>

• RCOND — 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. so it's an estimate of an estimate, we love layered lore 🦋

!> 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 — COMPLEX*16 array, dimension (2*N). that's it that's the whole description, she's mysterious ✨

!> WORK is COMPLEX*16 array, dimension (2*N) !>

• RWORK — DOUBLE PRECISION array, dimension (N). also mysterious. also iconic.

!> RWORK is DOUBLE PRECISION array, dimension (N) !>

• INFO — INTEGER, the vibe report:
  • = 0: successful exit 🎉
  • < 0: if INFO = -i, the i-th argument had an illegal value 💀

!> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !>

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👑 Author 👑

the legends behind it, all of them:

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

⭐ Definition ⭐

Definition at line 117 of file zppcon.f. noted. bookmarked. screenshot taken.

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🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code. so nobody hand-wrote this page, the robots did it, and honestly? they ate.

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ngl bestie, if you pass a bad argument you get a negative INFO and that's your sign to reread the docs. N >= 0. always. periodt. 🙈

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okay that's the whole page!! mwah 💖 this was LAPACK, Version 3.12.0, and the file was /home/abui...RC/zppcon.f(3) — go be brilliant with your Hermitian positive definite packed matrices, i'm obsessed with you 🫶✨🎀