SRC/cla_syrpvgrw.f(3)

📦
version 3.12.1 · 7 versions
, in arch rolling

✨ NAME ✨

okay so this page is SRC/cla_syrpvgrw.f(3) from the LAPACK Library Functions Manual, bestie. It’s giving “tiny but important linear algebra helper,” and we’re gonna understand it together 💅

🌸 SYNOPSIS 🌸

Functions/Subroutines

  • real function cla_syrpvgrw (uplo, n, info, a, lda, af, ldaf, ipiv, work) — CLA_SYRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric indefinite matrix. ✨

💅 Function/Subroutine Documentation 💅

real function cla_syrpvgrw (character*1 uplo, integer n, integer info,
    complex, dimension( lda, * ) a, integer lda, complex, dimension( ldaf, *
    ) af, integer ldaf, integer, dimension( * ) ipiv, real, dimension( * )
    work)

CLA_SYRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric indefinite matrix. No cap, that’s the whole glow-up of this routine. 💖

🎯 Purpose

Okay so here’s the tea: CLA_SYRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U). The source literally says The norm is used — double space included, bestie, I’m not editing the facts 🙈.

If that thing is much less than 1, the stability of the LU factorization of the (equilibrated) matrix A could be poor 😭. That also means the solution X, estimated condition numbers, and error bounds could be unreliable. So yeah, this is one of those “pay attention to the ratio” situations. 🔥

🧾 Parameters

UPLO

UPLO is CHARACTER*1:

  • = 'U': Upper triangle of A is stored;
  • = 'L': Lower triangle of A is stored.

Pick your triangle, bestie 🎀

N

N is INTEGER.

The number of linear equations, i.e., the order of the matrix A. N >= 0. 🌸

INFO

INFO is INTEGER.

The value of INFO returned from CSYTRF, .i.e., the pivot in column INFO is exactly 0. Yes, that’s the exact .i.e. spelling from the page — we keep the lore intact. 💀

A

A is COMPLEX 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 array, dimension (LDAF,N).

The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by CSYTRF. 🫶

LDAF

LDAF is INTEGER.

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

IPIV

IPIV is INTEGER array, dimension (N).

Details of the interchanges and the block structure of D as determined by CSYTRF. 🔥

WORK

WORK is REAL array, dimension (2*N). 🍓

👑 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

📍 Definition at line 121 of file cla_syrpvgrw.f.

🫶 Author

Generated automatically by Doxygen for LAPACK from the source code.

and that’s the whole page, bestie — LAPACK Version 3.12.0, SRC/cla_syrpvgrw.f(3), mwah 💖🎀✨

📦 where this page comes from