ZLA_SYRPVGRW(3)

💅 NAME

okay bestie so this page is zla_syrpvgrw.f — and the full glow-up path is right here so you can find it on disk:

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

it lives in the Library Functions Manual, section (3). iykyk 💖

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✨ SYNOPSIS

Functions/Subroutines

it's giving:

double precision function ZLA_SYRPVGRW (uplo, n, info, a, lda, af, ldaf,
    ipiv, work)

and here's the whole vibe of what it does: ZLA_SYRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric indefinite matrix. slay. 🫶

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🦋 FUNCTION/SUBROUTINE DOCUMENTATION

the full signature, character for character, no edits, no notes:

double precision function ZLA_SYRPVGRW (character*1 uplo, integer n, integer
    info, complex*16, dimension( lda, * ) a, integer lda, complex*16,
    dimension( ldaf, * ) af, integer ldaf, integer, dimension( * ) ipiv,
    double precision, dimension( * ) work)

ZLA_SYRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric indefinite matrix.

🎀 Purpose

literally the main character of this function: it computes the reciprocal pivot growth factor norm(A)/norm(U).

about that norm — the source says, verbatim, The norm is used. there's a little gap in there where the norm symbol is supposed to be, bestie 🙈 that's just how it shipped, not me being messy.

so: if this thing comes back much less than 1, the stability of the LU factorization of the (equilibrated) matrix A could be poor. 🚨 and it gets worse — that also means the solution X, the estimated condition numbers, and the error bounds could all be unreliable. not them being shady, just literally not trustworthy. 😭

🌸 Parameters

• UPLO — UPLO is CHARACTER*1
  • = 'U': the upper triangle of A is stored;
  • = 'L': the lower triangle of A is stored.
• N — N is INTEGER the number of linear equations, i.e., the order of the matrix A. constraint: N >= 0. 🔥
• INFO — INFO is INTEGER the value of INFO returned from ZSYTRF, .i.e., the pivot in column INFO is exactly 0. (that .i.e. is the source's own typing, bestie, i'm just the messenger 🫶)
• A — A is COMPLEX*16 array, dimension (LDA,N) on entry, the N-by-N matrix A.
• LDA — LDA is INTEGER the leading dimension of the array A. LDA >= max(1,N).
• AF — AF is COMPLEX*16 array, dimension (LDAF,N) the block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by ZSYTRF. 👑
• LDAF — LDAF is INTEGER the leading dimension of the array AF. LDAF >= max(1,N).
• IPIV — IPIV is INTEGER array, dimension (N) details of the interchanges and the block structure of D as determined by ZSYTRF.
• WORK — WORK is DOUBLE PRECISION array, dimension (2*N) that's it, that's the whole note. two N. periodt. ✨

⭐ Author

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

💖 Definition at line 121 of file zla_syrpvgrw.f.

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👑 Author

Generated automatically by Doxygen for LAPACK from the source code. (not a human, just a very caffeinated doc generator ☕✨)

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and that's the whole page, bestie — go forth and check your pivot growth 🌈

this gorgeous little artifact is from LAPACK, Version 3.12.0, and the original footer stamp reads /home/abui..._syrpvgrw.f(3) — mwah, bye 💋🎀🦋