ZLA_PORPVGRW(3)

🎀 NAME 🎀

ok so bestie, this whole page is literally just about one file, and its name is a whole journey:

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

that's it. that's the name. it's giving "my professor named the file after his entire life story" 💀 and yes we're in the Library Functions Manual, welcome to the function shelf 🫶

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✨ SYNOPSIS ✨

Functions/Subroutines

• double precision function ZLA_PORPVGRW (uplo, ncols, a, lda, af, ldaf, work) — queen behavior honestly, because ZLA_PORPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric or Hermitian positive-definite matrix. iconic ✨

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💅 FUNCTION/SUBROUTINE DOCUMENTATION 💅

here's the full signature, no cap, copy it exactly:

double precision function ZLA_PORPVGRW (character*1 uplo, integer ncols,
    complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension(
    ldaf, * ) af, integer ldaf, double precision, dimension( * ) work)

and what does she do, you ask? ZLA_PORPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric or Hermitian positive-definite matrix. periodt 💅

Purpose

ok so, in the actual source comments:

!>
!>
!> ZLA_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.
!>

so basically: she gives you norm(A)/norm(U) (and yeah, the norm is used — the source just leaves it blank, we don't make stuff up around here 🙈). if that number comes back much less than 1? 🚨 that means the stability of the LU factorization of the (equilibrated) matrix A could be poor, and the solution X, the estimated condition numbers, and the error bounds could be unreliable. like, do not trust that output, bestie. it's giving red flag city 🔥

Parameters

UPLO

!>          UPLO is CHARACTER*1
!>       = 'U':  Upper triangle of A is stored;
!>       = 'L':  Lower triangle of A is stored.
!>

• UPLO is CHARACTER*1
• = 'U' → the upper triangle of A is stored ✨
• = 'L' → the lower triangle of A is stored ✨

pick your fighter, iykyk

NCOLS

!>          NCOLS is INTEGER
!>     The number of columns of the matrix A. NCOLS >= 0.
!>

NCOLS is INTEGER, and it's literally the number of columns of the matrix A. constraint: NCOLS >= 0. no negatives, we don't do that here 🫶

A

!>          A is COMPLEX*16 array, dimension (LDA,N)
!>     On entry, the N-by-N matrix A.
!>

A is a COMPLEX*16 array with dimension (LDA,N). on entry, it's the N-by-N matrix A. she's the main character of this whole operation 👑

LDA

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

LDA is INTEGER — the leading dimension of the array A, and it's gotta satisfy LDA >= max(1,N). math said respect the bounds 🧚

AF

!>          AF is COMPLEX*16 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 ZPOTRF.
!>

AF is a COMPLEX*16 array with dimension (LDAF,N). it holds the triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T, as computed by ZPOTRF. shoutout to ZPOTRF for doing the actual factorization, we just vibe-check the growth 💜

LDAF

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

LDAF is INTEGER — the leading dimension of the array AF, and LDAF >= max(1,N). again with the bounds. the bounds are non-negotiable 🌸

WORK

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

WORK is a DOUBLE PRECISION array with dimension (2*N). that's her workspace. that's her little scratchpad. slay 🎀

Author

the credit roll, respectfully:

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

also, Definition at line 105 of file zla_porpvgrw.f. — noted, bookmarked, screenshot taken 📸

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🦋 AUTHOR 🦋

(second author section, but make it metadata ✨) — this page was Generated automatically by Doxygen for LAPACK from the source code. the robot did this one, not a human. respect the robot 🤖💖

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ok that's the whole page bestie, you ate, no crumbs left. this was <rainbow>LAPACK, Version 3.12.0</rainbow> and the source file is /home/abui..._porpvgrw.f(3) — mwah, go read some more manpages, ily 🫶💅✨