SRC/cla_porpvgrw.f(3)

🫶 SRC/cla_porpvgrw.f — from the LAPACK manual pages, bestie

okay so this one is a function page from the LAPACK library docs, and it's genuinely iconic in a quiet, math-girl way. pull up a chair 💅

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✨ SYNOPSIS ✨

Functions/Subroutines

real function cla_porpvgrw (uplo, ncols, a, lda, af, ldaf, work)

CLA_PORPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric or Hermitian positive-definite matrix. like, that's the whole vibe of it 🎀

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🌸 Function/Subroutine Documentation 🌸

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

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

💜 Purpose:

!>
!>
!> CLA_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.
!>

no cap, that last part is the important tea — if this factor comes back wayyy less than 1, everything downstream is sus. the solution X, the estimated condition numbers, and the error bounds could all be unreliable. 🫠

👑 Parameters

• UPLO — is CHARACTER*1.
  • = 'U': Upper triangle of A is stored;
  • = 'L': Lower triangle of A is stored.
• NCOLS — is INTEGER. The number of columns of the matrix A. NCOLS >= 0.
• A — is COMPLEX array, dimension (LDA,N). On entry, the N-by-N matrix A. main character energy fr 🦋
• LDA — is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
• AF — is COMPLEX 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 CPOTRF. (yes, the **T is there exactly like that, iykyk)
• LDAF — is INTEGER. The leading dimension of the array AF. LDAF >= max(1,N).
• WORK — is REAL array, dimension (2*N). literally just scratch space, she's doing her job 💅

⭐ Author

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

📌 Definition at line 104 of file cla_porpvgrw.f.

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🌈 Author

Generated automatically by Doxygen for LAPACK from the source code.

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okay that's the whole page, mwah 💖 and for the cute little sign-off: this gorgeous thing came from the LAPACK manual, Version 3.12.0, for the file SRC/cla_porpvgrw.f(3) — go forth and check your pivot growth, bestie 🎀✨