ZGECON(3)

💅 ZGECON(3) — the girlies' guide to estimating condition numbers ✨

okay so bestie, welcome to the ZGECON page, from the LAPACK library functions manual — the file lives at /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zgecon.f and honestly it's giving very "let me tell you about your matrix's health" energy 🫶

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✨ SYNOPSIS ✨

Functions/Subroutines:

subroutine ZGECON (norm, n, a, lda, anorm, rcond, work, rwork, info)

ZGECON. that's her. that's the icon. 👑

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🦋 Function/Subroutine Documentation 🦋

subroutine ZGECON (character norm, 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)

ZGECON 💖

🌸 Purpose:

!> !> ZGECON estimates the reciprocal of the condition number of a general !> complex matrix A, in either the 1-norm or the infinity-norm, using !> the LU factorization computed by ZGETRF. !> !> An estimate is obtained for norm(inv(A)), and the reciprocal of the !> condition number is computed as !> RCOND = 1 / ( norm(A) * norm(inv(A)) ). !>

so basically it's like a vibe check for your matrix — it tells you how close to ✨trouble✨ inverting A is gonna be. no cap. 🔥

🎀 Parameters 🎀

• NORM — ok so NORM is CHARACTER*1 and it's literally the main character here, it decides which condition number you want:

!> NORM is CHARACTER*1 !> Specifies whether the 1-norm condition number or the !> infinity-norm condition number is required: !> = '1' or 'O': 1-norm; !> = 'I': Infinity-norm. !>

• N — N is INTEGER, the order of the matrix A. and bestie, N >= 0. periodt.

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

• A — A is a COMPLEX*16 array, dimension (LDA,N) — it's holding the factors L and U from the factorization A = P*L*U as computed by ZGETRF. like she already did the work, we're just checking her vibe 💅

!> A is COMPLEX*16 array, dimension (LDA,N) !> The factors L and U from the factorization A = P*L*U !> as computed by ZGETRF. !>

• LDA — LDA is INTEGER, the leading dimension of the array A. and it better be LDA >= max(1,N). no exceptions, babes.

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

• ANORM — ANORM is DOUBLE PRECISION. if NORM = '1' or 'O', it's the 1-norm of the original matrix A. if NORM = 'I', it's the infinity-norm of the original matrix A. pick your fighter 💀

!> ANORM is DOUBLE PRECISION !> If NORM = '1' or 'O', the 1-norm of the original matrix A. !> If NORM = 'I', the infinity-norm of the original matrix A. !>

• RCOND — RCOND is DOUBLE PRECISION and this is the payoff, the moment we've all been waiting for 😭 it's the reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))).

!> RCOND is DOUBLE PRECISION !> The reciprocal of the condition number of the matrix A, !> computed as RCOND = 1/(norm(A) * norm(inv(A))). !>

• WORK — WORK is a COMPLEX*16 array, dimension (2*N). do not forget the 2, bestie. 🫶

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

• RWORK — RWORK is a DOUBLE PRECISION array, dimension (2*N). same energy, different type. 🌈

!> RWORK is DOUBLE PRECISION array, dimension (2*N) !>

• INFO — INFO is INTEGER and it's the one who tells you if everything slayed or if it flopped:

!> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value. !> NaNs are illegal values for ANORM, and they propagate to !> the output parameter RCOND. !> Infinity is illegal for ANORM, and it propagates to the output !> parameter RCOND as 0. !> = 1: if RCOND = NaN, or !> RCOND = Inf, or !> the computed norm of the inverse of A is 0. !> In the latter, RCOND = 0 is returned. !>

🚨 lowkey important: NaN is an illegal value for ANORM and it propagates to the output parameter RCOND. Infinity is also illegal for ANORM and it propagates to RCOND as 0. and if INFO = 1 because the computed norm of the inverse of A is 0, then RCOND = 0 gets returned. know the lore, iykyk 💀

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👑 Author 👑

absolute icons, the whole squad:

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

Definition at line 130 of file zgecon.f.

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💜 Author (the meta one) 💜

Generated automatically by Doxygen for LAPACK from the source code. she's auto-generated, she's cunty, she's doing her best 🌸

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LAPACK, Version 3.12.0 — mwah, that's the tea, thanks for coming to my ted talk, go forth and estimate those condition numbers responsibly 💖✨🎀🦋