TESTING/LIN/spot03.f(3)

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🎀 TESTING/LIN/spot03.f(3) 🎀

okay so bestie, welcome to the Library Functions Manual page for TESTING/LIN/spot03.f(3) — it's giving LAPACK testing subroutine, and we're gonna read it together. 💅✨

💖 NAME 💖

TESTING/LIN/spot03.f — literally the name, no cap.

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

  • subroutine spot03 (uplo, n, a, lda, ainv, ldainv, work, ldwork, rwork, rcond, resid) — SPOT03

🦋 Function/Subroutine Documentation 🦋

Here's the actual signature, copied exactly so nobody comes for me:

   subroutine spot03 (character uplo, integer n, real, dimension( lda, * ) a,
       integer lda, real, dimension( ldainv, * ) ainv, integer ldainv, real,
       dimension( ldwork, * ) work, integer ldwork, real, dimension( * ) rwork,
       real rcond, real resid)
       SPOT03

SPOT03 — that's the icon, periodt.

🎯 Purpose 🎯

SPOT03 computes the residual for a symmetric matrix times its inverse:

norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * EPS )

where EPS is the machine epsilon. 💖

🌸 Parameters 🌸

🌟 UPLO

UPLO is CHARACTER*1 — it says whether the upper or lower triangular part of the symmetric matrix A is stored:

  • = 'U': Upper triangular
  • = 'L': Lower triangular

🌟 N

N is INTEGER — the number of rows and columns of the matrix A. N >= 0. 🫶

🌟 A

A is REAL array, dimension (LDA,N) — the original symmetric matrix A. Iconic.

🌟 LDA

LDA is INTEGER — the leading dimension of the array A. LDA >= max(1,N). 🔥

🌟 AINV

AINV is REAL array, dimension (LDAINV,N) — on entry, the inverse of the matrix A, stored as a symmetric matrix in the same format as A.

⚠️ bestie, important: in this version, AINV is expanded into a full matrix and multiplied by A, so the opposing triangle of AINV will be changed; i.e., if the upper triangular part of AINV is stored, the lower triangular part will be used as work space. So yeah, it's not staying exactly as you left it. 💅

🌟 LDAINV

LDAINV is INTEGER — the leading dimension of the array AINV. LDAINV >= max(1,N). ✨

🌟 WORK

WORK is REAL array, dimension (LDWORK,N). 🧚

🌟 LDWORK

LDWORK is INTEGER — the leading dimension of the array WORK. LDWORK >= max(1,N). 🎀

🌟 RWORK

RWORK is REAL array, dimension (N). 🌈

🌟 RCOND

RCOND is REAL — the reciprocal of the condition number of A, computed as ( 1/norm(A) ) / norm(AINV). 💜

🌟 RESID

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

👑 Author 👑

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

Definition at line 123 of file spot03.f. 📍

🌈 Author 🌈

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mwah! This page is from LAPACK, Version 3.12.0, and it's the TESTING/LIN/spot03.f(3) page — bye bestie, go slay your residuals! 🎀💅✨

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