SRC/zla_porpvgrw.f(3)

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💖 SRC/zla_porpvgrw.f(3) 💖

Library Functions Manual — bestie edition, obviously. We’re folding the manual name in right here so you know the vibe: this is a LAPACK manual page, and it’s about to explain zla_porpvgrw like your favorite group chat would.

✨ NAME ✨

SRC/zla_porpvgrw.f — that’s the file, bestie. The function living inside it is zla_porpvgrw.

🦋 SYNOPSIS 🦋

📚 Functions/Subroutines

       double precision function zla_porpvgrw (uplo, ncols, a, lda, af, ldaf,
           work)
  • Okay so this is the main-character function: zla_porpvgrw — ZLA_PORPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric or Hermitian positive-definite matrix.

🎀 Function/Subroutine Documentation 🎀

       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)

ZLA_PORPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric or Hermitian positive-definite matrix.

🎯 Purpose

Okay, purpose time — this is the actual plot:

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.

Lowkey important: if that reciprocal pivot growth factor is much less than 1, the stability of the LU factorization of the (equilibrated) matrix A could be poor, and that also means the solution X, estimated condition numbers, and error bounds could be unreliable. Not a cute look. 😭

🧚 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 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 triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T, as computed by ZPOTRF.
  • LDAF — LDAF is INTEGER. The leading dimension of the array AF. LDAF >= max(1,N).
  • WORK — WORK is DOUBLE PRECISION array, dimension (2*N). That’s the whole work situation, bestie.

👑 Author 👑

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

Definition at line 105 of file zla_porpvgrw.f.

💌 Author 💌

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