CLA_HERPVGRW(3)

💅 NAME 💅

Okay so bestie, this page is about a file — literally the source file itself, no cap:

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

That's it, that's the name section. It's giving "the man page is just pointing at its own source file" energy and honestly? Iconic. This lives in the Library Functions Manual, so jot that down 🎀

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✨ SYNOPSIS ✨

Functions/Subroutines

   real function CLA_HERPVGRW (uplo, n, info, a, lda, af, ldaf, ipiv, work)
       CLA_HERPVGRW

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🦋 Function/Subroutine Documentation 🦋

Here's the whole signature in all its glory, bestie — type it exactly, do NOT freestyle:

   real function CLA_HERPVGRW (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_HERPVGRW ✨ (yes it gets its own little encore line, it's the main character)

🧮 Purpose

!> !> !> CLA_HERPVGRW 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 like — the tea ☕ — this routine hands you the reciprocal pivot growth factor norm(A)/norm(U). And ngl, tiny heads-up: the source literally says "The norm is used" with the norm name just… not there 💀 I'm not inventing anything, that's verbatim, don't come for me.

The important bit: if that value is much less than 1, the stability of the LU factorization of the (equilibrated) matrix A could be poor 😭 and that means the solution X, the estimated condition numbers, and the error bounds could all be unreliable. So like, vibe check your results, fr fr.

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🎀 Parameters 🎀

• UPLO — it's CHARACTER*1, and it tells you which triangle is doing the work:
  • = 'U': the upper triangle of A is stored 🔼✨
  • = 'L': the lower triangle of A is stored 💅
• N — INTEGER. The number of linear equations, i.e. the order of the matrix A. Must be N >= 0. No negative orders, babe, that's not a thing 💀
• INFO — INTEGER. The value of INFO returned from SSYTRF, .i.e., the pivot in column INFO is exactly 0. (That .i.e. is verbatim, I would never 🙈)
• A — COMPLEX array, dimension (LDA,N). On entry, the N-by-N matrix A. The whole thing, the star of the show 👑
• LDA — INTEGER. The leading dimension of the array A. LDA >= max(1,N) — that's a hard requirement, not a suggestion 🫶
• AF — COMPLEX array, dimension (LDAF,N). The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by CHETRF. Like, the factorization's whole lewk 💖
• LDAF — INTEGER. The leading dimension of the array AF. LDAF >= max(1,N). Same rules, different array ✨
• IPIV — INTEGER array, dimension (N). Details of the interchanges and the block structure of D as determined by CHETRF. The receipts of who swapped with who 🕵️‍♀️
• WORK — REAL array, dimension (2*N). Scratch space, it's literally just vibing there and helping out 🌸

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🌈 Author 🌈

Absolute legends, all four of them:

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

📍 Where it lives

Definition at line 121 of file cla_herpvgrw.f. Go look, it's right there 💜

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⭐ Author (the auto-generated one) ⭐

Generated automatically by Doxygen for LAPACK from the source code. Not a human, just a very diligent little robot 🤖✨

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And that's the whole page, bestie!! 🫶 This cutie is from LAPACK, Version 3.12.0, and the whole thing is stamped /home/abui..._herpvgrw.f(3) — mwah, slay, periodt 💅🎀