DLA_PORPVGRW(3)

💅 DLA_PORPVGRW(3) — like, the LAPACK Library Functions Manual, bestie 🎀

okay so real talk, this page lives in the LAPACK Library Functions Manual (it's in section 3, the library-functions girlypop section) and the whole file it's documenting is /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dla_porpvgrw.f. yes that's the whole path, don't @ me, the build machine chose violence 😭

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✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dla_porpvgrw.f — no cap, that IS the name section, it's literally just the file path and honestly? iconic of it.

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🌸 SYNOPSIS 🌸

Functions/Subroutines 🦋

• double precision function DLA_PORPVGRW (uplo, ncols, a, lda, af, ldaf, work) — DLA_PORPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric or Hermitian positive-definite matrix. she's giving math, she's giving structure, she's giving "trust me bestie the norm matters" 💖

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👑 Function/Subroutine Documentation 👑

double precision function DLA_PORPVGRW (character*1 uplo, integer ncols,
    double precision, dimension( lda, * ) a, integer lda, double precision,
    dimension( ldaf, * ) af, integer ldaf, double precision, dimension( * )
    work)

DLA_PORPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric or Hermitian positive-definite matrix. that's the whole gig. she's a one-job queen and she does it well ⭐

💜 Purpose 💜

!>
!>
!> DLA_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.
!>

🚨 okay so lowkey important: if that value comes back much less than 1, the stability of the LU factorization of the (equilibrated) matrix A could be poor. and that means your solution X, your estimated condition numbers, and your error bounds could be unreliable. so like… do not ignore her. she is warning you fr fr 💀

(and yes, the doc block literally says "The norm is used." with a double space and no norm named in between — that's just how the source shipped it, I'm not about to invent one, iykyk 🙈)

🍓 Parameters 🍓

• UPLO — hiiii so UPLO is CHARACTER*1:
  • = 'U': Upper triangle of A is stored;
  • = 'L': Lower triangle of A is stored. pick your fighter, bestie 🫶
• NCOLS — NCOLS is INTEGER. The number of columns of the matrix A. Constraint: NCOLS >= 0. zero is fine, negative is not 💅
• A — A is DOUBLE PRECISION array, dimension (LDA,N). On entry, the N-by-N matrix A. she's the main character of this whole situation 👑
• LDA — LDA is INTEGER. The leading dimension of the array A. Constraint: LDA >= max(1,N). respect the constraint or perish 🧚
• AF — AF is DOUBLE PRECISION 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 DPOTRF. so like, AF is the glow-up result of DPOTRF doing its thing ✨
• LDAF — LDAF is INTEGER. The leading dimension of the array AF. Constraint: LDAF >= max(1,N). same energy, different array 🌈
• WORK — WORK is DOUBLE PRECISION array, dimension (2*N). that's it, that's the whole note. she's the scratch space, she's doing her best, give her 2*N 🎀

🌟 Author 🌟

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

all four of them, together, a whole collaborative slay 🔥

Definition at line 104 of file dla_porpvgrw.f. (line one hundred and four, for the people keeping score 💖)

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⭐ Author (yes, again) ⭐

Generated automatically by Doxygen for LAPACK from the source code. so nobody hand-wrote this page, a robot did it, and the robot ate, ngl 🤖✨

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🫶 also a tiny heads-up: the Author section shows up twice on this page — once inside the function documentation and once at the bottom. that's not me being extra, that's genuinely how the page is built. iykyk 💀

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okay bye bestie, go compute that reciprocal pivot growth factor and stay stable out there 💜🦋 periodt 💅

LAPACK, Version 3.12.0 — and the page footer's file tag is /home/abui..._porpvgrw.f(3), which we're folding in right here at the very end with a lil curtsy 🎀