CPOCON(3)

💅 CPOCON 💅

ok so this is a page from the Library Functions Manual, and honestly? it's giving math-girlie excellence. we're looking at cpocon.f(3) — yes, that whole path is literally the name, don't come for me:

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

bestie, it's a LAPACK routine and it's lowkey iconic. let's get into it 🫶

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✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/cpocon.f — that's the file, that's the whole name, that's the vibe. periodt.

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🌸 SYNOPSIS 🌸

Functions/Subroutines

• subroutine CPOCON (uplo, n, a, lda, anorm, rcond, work, rwork, info) — CPOCON. that's it, that's the function. she's here, she's ready 💅

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🦋 Function/Subroutine Documentation 🦋

subroutine CPOCON (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, real anorm, real rcond, complex, dimension( * ) work, real, dimension( * ) rwork, integer info)

CPOCON

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🎀 Purpose 🎀

!> !> CPOCON 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 CPOTRF. !> !> An estimate is obtained for norm(inv(A)), and the reciprocal of the !> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). !>

ok so real talk: she takes your Cholesky factorization (the A = U**H*U or A = L*L**H situation that CPOTRF already did for you) and she's like "how sketchy is this matrix, actually?" she estimates norm(inv(A)), then flips it into RCOND = 1 / (ANORM * norm(inv(A))). math girlie behavior, no cap 🔥

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💖 Parameters 💖

• UPLO

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

which triangle of A we're keeping. 'U' = upper, 'L' = lower. pick your fighter 🎀

• N

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

the order of the matrix A, and she's gotta be N >= 0. negative? absolutely not, blocked 🙈

• A

!> A is COMPLEX 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 CPOTRF.

the triangular factor U or L from that Cholesky factorization (A = U**H*U or A = L*L**H), straight outta CPOTRF. she's the main character, dimension (LDA,N) 💅

• LDA

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

leading dimension of A. rule is LDA >= max(1,N). don't test her ⭐

• ANORM

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

the 1-norm (or infinity-norm, either one bestie) of the Hermitian matrix A. literally the size of the problem 🦋

• 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 output glow-up ✨ it's the reciprocal of A's condition number, computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is the estimate of the 1-norm of inv(A) that she cooks up in this very routine. iykyk 💜

• WORK

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

scratch space, complex, dimension (2*N). she works hard so you don't have to 💀

• RWORK

!> RWORK is REAL array, dimension (N)

more scratch space, but real this time, dimension (N). equal opportunity workspace 🌈

• INFO

!> 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 successful exit, slay. < 0 means INFO = -i and the i-th argument had an illegal value — somebody did NOT read the parameter list, and it shows.

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👑 Author 👑

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

the whole squad came together for this one, we love a collab 🫶💖

Definition at line 119 of file cpocon.f.

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🌟 Author 🌟

Generated automatically by Doxygen for LAPACK from the source code. (yes, the robots did the paperwork, we're just here for the vibes 🧚)

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and that's the whole page, bestie! this doc came to you courtesy of LAPACK, Version 3.12.0, straight from /home/abui...RC/cpocon.f(3) — stay conditioned, stay positive definite, and remember: RCOND is just a girl estimating reciprocals 💅💖✨