TESTING/LIN/sppt01.f(3)

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version 3.12.1 · 2 versions
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💖 NAME 💖

Okay so this page is literally the manual for TESTING/LIN/sppt01.f(3), under the Library Functions Manual umbrella, and the main-character subroutine is sppt01. Periodt. 💅

🌈 SYNOPSIS 🌈

✨ Functions/Subroutines ✨

  • subroutine sppt01 (uplo, n, a, afac, rwork, resid) — SPPT01 (that’s the label, bestie).

🦋 Function/Subroutine Documentation 🦋

subroutine sppt01 (character uplo, integer n, real, dimension( * ) a, real,
       dimension( * ) afac, real, dimension( * ) rwork, real resid)

SPPT01

🎯 Purpose 🎯

Bestie, SPPT01 reconstructs a symmetric positive definite packed matrix A from its L*L' or U'*U factorization, then computes the residual. The residual formulas are exactly:

norm( L*L' - A ) / ( N * norm(A) * EPS ) or
norm( U'*U - A ) / ( N * norm(A) * EPS ),

where EPS is the machine epsilon. No cap, that’s the whole mission. 🫶

🧸 Parameters 🧸

  • UPLO — UPLO is CHARACTER*1. It specifies whether the upper or lower triangular part of the symmetric matrix A is stored: = 'U': Upper triangular; = 'L': Lower triangular. Pick your lane, upper or lower. 💜
  • N — N is INTEGER. The number of rows and columns of the matrix A. N >= 0. ✨
  • A — A is REAL array, dimension (N*(N+1)/2). This is the original symmetric matrix A, stored as a packed triangular matrix. Packed and ready. 🎀
  • AFAC — AFAC is REAL array, dimension (N*(N+1)/2). On entry, this is the factor L or U from the L*L' or U'*U factorization of A, stored as a packed triangular matrix. It gets overwritten with the reconstructed matrix, and then with the difference L*L' - A (or U'*U - A). So yeah, it does not stay the same — it’s giving transformation. 🦋
  • RWORK — RWORK is REAL array, dimension (N). That’s it, that’s the whole note. 🌸
  • RESID — RESID is REAL. If UPLO = 'L', it’s norm(L*L' - A) / ( N * norm(A) * EPS ). If UPLO = 'U', it’s norm(U'*U - A) / ( N * norm(A) * EPS ). Residual math, slay. ⭐

👑 Author 👑

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

Definition at line 92 of file sppt01.f.

🎀 Author 🎀

Generated automatically by Doxygen for LAPACK from the source code. Iconic automation behavior, honestly. 💫

Sign-off tea: this page comes from LAPACK, Version 3.12.0, and the footer tags it as TESTING/LIN/sppt01.f(3). Date-wise? The page doesn’t list one, so that’s the whole footer vibe — no extra date, bestie. 💖✨🎀

📦 where this page comes from