SRC/sla_gerpvgrw.f(3)

💅 SRC/sla_gerpvgrw.f — from the LAPACK Library Functions Manual, bestie

okay so real talk, this page is about one tiny but iconic Fortran function. buckle up 🎀

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✨ NAME ✨

SRC/sla_gerpvgrw.f — that's the file, that's the vibe. it's the home of SLA_GERPVGRW, and honestly? she's doing the most important quiet work. 🫶

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🌸 SYNOPSIS 🌸

Functions/Subroutines

• real function sla_gerpvgrw (n, ncols, a, lda, af, ldaf) — the one and only SLA_GERPVGRW, showing up to do her little pivot-growth check 💖

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🦋 Function/Subroutine Documentation 🦋

real function sla_gerpvgrw (integer n, integer ncols, real, dimension( lda,
    * ) a, integer lda, real, dimension( ldaf, * ) af, integer ldaf)

SLA_GERPVGRW — she's literally the main character of this page 👑

💜 Purpose:

!>
!> SLA_GERPVGRW computes the reciprocal pivot growth factor
!> norm(A)/norm(U). The  norm is used. If this is
!> much less than 1, the stability of the LU factorization of the
!> (equilibrated) matrix A could be poor. This also means that the
!> solution X, estimated condition numbers, and error bounds could be
!> unreliable.
!>

so basically: she computes the reciprocal pivot growth factor, which is norm(A)/norm(U), and the norm in question is the norm (yes, the doc literally has that blank spot right there in "The norm is used." — we're keeping it exactly as written, no cap 🙈). if that factor is much less than 1, then the stability of the LU factorization of the (equilibrated) matrix A could be poor. and that's not a fun time, bestie — it also means the solution X, the estimated condition numbers, and the error bounds could all be unreliable. 😭 so like... listen to her, she's warning you.

🧚 Parameters

• N — N is INTEGER. it's the number of linear equations, i.e. the order of the matrix A. constraint: N >= 0. ✨
• NCOLS — NCOLS is INTEGER. the number of columns of the matrix A. constraint: NCOLS >= 0. 🌸
• A — A is REAL array, dimension (LDA,N). on entry, this is the N-by-N matrix A. she's the star of the show 💅
• LDA — LDA is INTEGER. the leading dimension of the array A. constraint: LDA >= max(1,N). 🔥
• AF — AF is REAL array, dimension (LDAF,N). the factors L and U from the factorization A = P*L*U, as computed by SGETRF. iconic duo energy 👑
• LDAF — LDAF is INTEGER. the leading dimension of the array AF. constraint: LDAF >= max(1,N). ⭐

🎀 Author

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

Definition at line 96 of file sla_gerpvgrw.f. 📍 like, go look, it's right there.

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💖 Author (the meta one)

Generated automatically by Doxygen for LAPACK from the source code. so nobody hand-wrote this footer, the robot did it for us 🤖✨

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and that's the whole page, bestie! 🎉 LAPACK, Version 3.12.0, SRC/sla_gerpvgrw.f(3) — drink some water, go check your pivot growth, and slay the rest of your day 💅🌈🦋