SRC/sla_porpvgrw.f(3)

💖 SRC/sla_porpvgrw.f(3) 💖

okay so bestie, this page comes straight out of the Library Functions Manual and it's all about one very specific little Fortran function. no cap, she's niche but she's iconic. let's get into it 🫶

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✨ SYNOPSIS ✨

Functions/Subroutines

• real function sla_porpvgrw (uplo, ncols, a, lda, af, ldaf, work) — SLA_PORPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric or Hermitian positive-definite matrix. that's the whole vibe 💅

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🌸 Function/Subroutine Documentation 🌸

real function sla_porpvgrw (character*1 uplo, integer ncols, real, dimension( lda, * ) a, integer lda, real, dimension( ldaf, * ) af, integer ldaf, real, dimension( * ) work)

k so what does she do? SLA_PORPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric or Hermitian positive-definite matrix. that's it, that's the function ✨

🎀 Purpose 🎀

!> !> SLA_PORPVGRW 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. !>

(and yes, the original really does just say The norm is used. with a lil gap in there — not me, that's literally what it says, i'm just the messenger 😭)

okay so translating that from math-speak: if this number comes back much less than 1, the stability of the LU factorization of the (equilibrated) matrix A could be poor, and that means the solution X, the estimated condition numbers, and the error bounds could all be unreliable. so like… don't trust the vibes if this number is tiny 💀

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🦋 Parameters 🦋

• UPLO — UPLO is CHARACTER*1
  • = 'U': Upper triangle of A is stored;
  • = 'L': Lower triangle of A is stored.
• NCOLS — NCOLS is INTEGER
  • The number of columns of the matrix A. NCOLS >= 0.
• A — A is REAL 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 REAL array, dimension (LDAF,N)
  • The triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T, as computed by SPOTRF.
• LDAF — LDAF is INTEGER
  • The leading dimension of the array AF. LDAF >= max(1,N).
• WORK — WORK is REAL array, dimension (2*N)
  • literally just workspace, bestie. give her (2*N) and she's happy 🍓

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👑 Author 👑

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

⭐ Definition at line 103 of file sla_porpvgrw.f. ⭐

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💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code. (so nobody hand-wrote this one, the robots did it 🤖✨)

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and that's the whole page, bestie! this lil guy is SRC/sla_porpvgrw.f(3) from LAPACK Version 3.12.0 — slay, go compute some pivot growth factors responsibly 💖🎀🦋