STPT01(3)

📦 version 3.12.0, in opensuse-leap 16.0

💅 STPT01(3) — like, the manual page, bestie

okay so this is STPT01, and it lives in the Library Functions Manual (that's the manual name, cute right?). It's a LAPACK testing routine, and honestly? She's a vibe. Let's get into it 🎀

The whole file situation is:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/stpt01.f

That's the path, no cap, copy it exactly if you need it 📁✨

✨ SYNOPSIS ✨

Functions/Subroutines 🦋

  • subroutine STPT01 (uplo, diag, n, ap, ainvp, rcond, work, resid) — yep, that's her. STPT01.

🌸 Function/Subroutine Documentation 🌸

subroutine STPT01 (character uplo, character diag, integer n, real, dimension( * ) ap, real, dimension( * ) ainvp, real rcond, real, dimension( * ) work, real resid)

STPT01 — that's the name again, just so we're all on the same page 💜

🎯 Purpose:

STPT01 computes the residual for a triangular matrix A times its inverse when A is stored in packed format: RESID = norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS ), where EPS is the machine epsilon.

So basically she's the vibe check for A*A⁻¹ ≈ I. If the residual comes back smol, slay. If not… 😭

🫶 Parameters

UPLO

UPLO is CHARACTER*1 Specifies whether the matrix A is upper or lower triangular. - = 'U': Upper triangular - = 'L': Lower triangular

Pick your fighter, bestie. Up or down, no in-between 💅

DIAG

DIAG is CHARACTER*1 Specifies whether or not the matrix A is unit triangular. - = 'N': Non-unit triangular - = 'U': Unit triangular

Unit triangular means the diagonal is all ones — main character energy only 👑

N

N is INTEGER The order of the matrix A. N >= 0.

It's giving "the size of everything." And yes, N >= 0, not negative, we don't do that here 🙈

AP

AP is REAL array, dimension (N*(N+1)/2) The original upper or lower triangular matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: - if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j; - if UPLO = 'L', AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n.

Not me memorizing the packing index formula 😭 fr fr keep those expressions exactly as they are, they're load-bearing 💀

AINVP

AINVP is REAL array, dimension (N*(N+1)/2) On entry, the (triangular) inverse of the matrix A, packed columnwise in a linear array as in AP. On exit, the contents of AINVP are destroyed.
⚠️ Heads up bestie — she does not leave AINVP the way she found it. On exit it's destroyed. Gone. Iconic but ruthless 💀

RCOND

RCOND is REAL The reciprocal condition number of A, computed as 1/(norm(A) * norm(AINV)).

Reciprocal condition number — the way that she's just the inverse of a product, we love a simple queen 🌈

WORK

WORK is REAL array, dimension (N)

Scratch space. Her little workspace. Let her cook 🍓

RESID

RESID is REAL norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS )

The final answer, the moment of truth, the grade on the exam ⭐

👑 Author

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

Absolute legends, all four, no debate 🫶

📍 Definition at line 107 of file stpt01.f.

Like, literally line 107. Go look. We'll wait 🧚

💖 Author

Generated automatically by Doxygen for LAPACK from the source code.

(so nobody hand-wrote this section, it's Doxygen doing its thing, cute for it ✨)

okay bestie that's the whole page 🎀 hand-copied-by-nobody, Doxygen-generated, part of LAPACK Version 3.12.0 and the file lives at /home/abui...IN/stpt01.f(3) — byeee, go test some triangular matrices, mwah 💜🌸

📦 where this page comes from