TESTING/LIN/spot02.f(3)

📦
version 3.12.1 · 3 versions
, in arch rolling

💅 TESTING/LIN/spot02.f(3) — the spot02 era

ok so bestie, welcome to the manual page for TESTING/LIN/spot02.f(3), aka the LAPACK library functions manual entry for a lil testing subroutine that has ONE job and does it gorgeously. come sit, i'll walk you through it 💖

✨ NAME ✨

TESTING/LIN/spot02.f — like, literally that. that's the name. it's the file, it's the vibe, it's giving "i live in the TESTING/LIN directory and i'm proud" 🎀

✨ SYNOPSIS ✨

Functions/Subroutines

  • subroutine spot02 (uplo, n, nrhs, a, lda, x, ldx, b, ldb, rwork, resid) — SPOT02. yes she's a subroutine, yes she takes eleven arguments, yes she ate 🔥

✨ Function/Subroutine Documentation ✨

subroutine spot02 (character uplo, integer n, integer nrhs, real, dimension( lda, * ) a, integer lda, real, dimension( ldx, * ) x, integer ldx, real, dimension( ldb, * ) b, integer ldb, real, dimension( * ) rwork, real resid)

SPOT02 🫶 (the full signature in all its character/integer/real glory, dimension( lda, * ), dimension( ldx, * ), dimension( ldb, * ), dimension( * ) and all — no cap, that's the whole thing)

🦋 Purpose 🦋

!> !> SPOT02 computes the residual for the solution of a symmetric system !> of linear equations A*x = b: !> !> RESID = norm(B - A*X) / ( norm(A) * norm(X) * EPS ), !> !> where EPS is the machine epsilon. !>

so basically she computes the residual for solving a symmetric system of linear equations A*x = b, and the formula is literally:

RESID = norm(B - A*X) / ( norm(A) * norm(X) * EPS )

where EPS is the machine epsilon, obviously 💅 it's giving "how wrong is my answer, scaled so the number actually means something" and honestly? iconic.

🎀 Parameters 🎀

  • UPLO — ok so UPLO is CHARACTER*1 and it tells us whether the upper or lower triangular part of the symmetric matrix A is the one being stored:
    • = 'U': Upper triangular
    • = 'L': Lower triangular
  • N — N is INTEGER, and it's the number of rows and columns of the matrix A. constraint era: N >= 0. 🙈
  • NRHS — NRHS is INTEGER, the number of columns of B, the matrix of right hand sides. also constrained: NRHS >= 0. ✨
  • A — A is REAL array, dimension (LDA,N) — and it's the original symmetric matrix A. the main character, lowkey 👑
  • LDA — LDA is INTEGER, the leading dimension of the array A. rule of the land: LDA >= max(1,N) 🧚
  • X — X is REAL array, dimension (LDX,NRHS) — the computed solution vectors for the system of linear equations. bestie did her math and here's the receipts 💖
  • LDX — LDX is INTEGER, the leading dimension of the array X. requirement: LDX >= max(1,N). note the double space in the original, we love a careless space 🌸
  • B — B is REAL array, dimension (LDB,NRHS). on entry, it's the right hand side vectors for the system of linear equations. on exit, B is overwritten with the difference B - A*X. ⚠️ girly gets DESTROYED — she comes in as the RHS and leaves as the difference. know that before you hand her over 😭
  • LDB — LDB is INTEGER, the leading dimension of the array B. requirement: LDB >= max(1,N) 💜
  • RWORK — RWORK is REAL array, dimension (N). that's it. that's the whole description. she's a workspace and she's mysterious 🍓
  • RESID — RESID is REAL, and it's the maximum over the number of right hand sides of:
norm(B - A*X) / ( norm(A) * norm(X) * EPS )

so like, the worst-case residual across all your right hand sides. the final score. the vibe check result ⭐

👑 Author 👑

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

a whole committee of legends, fr fr 🫶

Definition at line 125 of file spot02.f. 📍

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code. (so nobody wrote this prose, a robot did, and honestly? she tried her best 💀)

ok that's the whole page bestie, no details left behind, periodt. this came to you straight from TESTING/LIN/spot02.f(3) in LAPACK Version 3.12.0 — go forth and check those residuals, and remember: B gets overwritten, so don't come crying to me 😭💖✨

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