ZPOCON(3)

💅 ZPOCON (3) — the condition-number girlie of the LAPACK library functions manual ✨

okay so, bestie, you found her 🫶 this is a page out of the Library Functions Manual — specifically the zpocon.f(3) situation — and she is here to tell you how sketchy (or not) your Hermitian positive definite matrix is. no cap, this one's a glow-up of a routine.

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🌸 NAME 🌸

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

like, that's literally her whole address. that's the file. she lives there. 💅

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✨ SYNOPSIS ✨

Functions/Subroutines 🎀

subroutine ZPOCON (uplo, n, a, lda, anorm, rcond, work, rwork, info)

ZPOCON

(yes, the subroutine is named ZPOCON. we been knew. 😌)

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🦋 Function/Subroutine Documentation 🦋

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

ZPOCON

💖 Purpose 💖

ZPOCON estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPOTRF.

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 basically she takes your Cholesky factorization (the one ZPOTRF already did for you, mwah) and she's like "how close to singular are we tho 👀" and hands you back RCOND. iconic behavior, truly. the closer to 1, the more your matrix is thriving; the closer to 0, the more she's giving danger. ⭐

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🌈 Parameters 🌈

• UPLO — CHARACTER*1

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

so like, which triangle are we working with, bestie? pick one. 🙈

• N — INTEGER

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

how big is she. the order. N >= 0, no zero-negativity slander allowed. 💀

• A — COMPLEX*16 array, dimension (LDA,N)

A is COMPLEX*16 array, dimension (LDA,N) The triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, as computed by ZPOTRF.

this is the actual factor, the one ZPOTRF already produced. don't come in here with a raw matrix and expect her to understand the assignment. 🎀

• LDA — INTEGER

LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).

the leading dimension of the array A. LDA >= max(1,N). periodt.

• ANORM — DOUBLE PRECISION

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

the 1-norm (or infinity-norm) of the Hermitian matrix A. yes, either one, she's flexible like that. 💅

• RCOND — DOUBLE PRECISION

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.

this is the moment. the main character. she's the output, she's the whole point, she's 1/(ANORM * AINVNM) where AINVNM is an estimate of the 1-norm of inv(A) computed right here in this routine. 👑

• WORK — COMPLEX*16 array, dimension (2*N)

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

scratch space, 2*N of it. she needs room to think. 🧚

• RWORK — DOUBLE PRECISION array, dimension (N)

RWORK is DOUBLE PRECISION array, dimension (N)

more scratch space, this time N and double precision flavored. 🍓

• INFO — INTEGER

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

the vibe check at the end. 0 means we slayed. negative means someone passed an illegal value and the i-th argument is getting called out by name. 😭

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👑 Author 👑

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

the whole squad really said "we made this" and honestly? deserved. 🫶

Definition at line 119 of file zpocon.f.

go look, she's right there. line 119. iykyk. ✨

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💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code.

(not a human, a whole robot, and yet she ate. 🔥)

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LAPACK — Version 3.12.0 🌈⭐ and that's the whole page bestie, signed off from /home/abui...RC/zpocon.f(3) — go forth and check those condition numbers, mwah 💋💖