TESTING/LIN/cget03.f(3)

💅 TESTING/LIN/cget03.f(3)

okay so this is a page out of the Library Functions Manual for TESTING/LIN/cget03.f and bestie, it's giving "LAPACK test routine that checks whether your matrix inverse is actually slaying or lowkey flopping" ✨

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🌸 NAME 🌸

TESTING/LIN/cget03.f — no cap, that's the whole name, that's the file 🫶

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✨ SYNOPSIS ✨

Functions/Subroutines

• subroutine cget03 (n, a, lda, ainv, ldainv, work, ldwork, rwork, rcond, resid) — the one and only, she's the main character 💅
  • CGET03

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🎀 Function/Subroutine Documentation 🎀

subroutine cget03 — the full glow-up signature, verbatim, don't @ me:

subroutine cget03 (integer n, complex, dimension( lda, * ) a, integer lda,
    complex, dimension( ldainv, * ) ainv, integer ldainv, complex,
    dimension( ldwork, * ) work, integer ldwork, real, dimension( * ) rwork,
    real rcond, real resid)

CGET03 🦋

💖 Purpose 💖

ok so here's the vibe: CGET03 computes the residual for a general matrix times its inverse. Literally the receipts on your inversion, fr fr:

!> CGET03 computes the residual for a general matrix times its inverse:
!>    norm( I - AINV*A ) / ( N * norm(A) * norm(AINV) * EPS ),
!> where EPS is the machine epsilon.

where EPS is the machine epsilon — yes queen, the tiny one 🌸

🌈 Parameters 🌈

• N

!>          N is INTEGER
!>          The number of rows and columns of the matrix A.  N >= 0.

so like, rows AND columns, she's square, and N >= 0 obviously 💅

• A

!>          A is COMPLEX array, dimension (LDA,N)
!>          The original N x N matrix A.

the OG matrix, the before picture 📸

• LDA

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

leading dimension of A, and LDA >= max(1,N) — rules are rules 🎀

• AINV

!>          AINV is COMPLEX array, dimension (LDAINV,N)
!>          The inverse of the matrix A.

the after picture, aka A's inverse 🦋

• LDAINV

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

leading dimension of AINV and yes LDAINV >= max(1,N), same energy ✨

• WORK

!>          WORK is COMPLEX array, dimension (LDWORK,N)

it's the workspace bestie, she's just out here helping 🙈

• LDWORK

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

leading dimension of WORK, LDWORK >= max(1,N), consistent icon behavior 💅

• RWORK

!>          RWORK is REAL array, dimension (N)

the REAL one, dimension (N) — not like the others, she's REAL and that's iconic 🌸

• RCOND

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

the reciprocal of the condition number of A, computed as ( 1/norm(A) ) / norm(AINV). write that down 📝

• RESID

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

the residual itself, the whole point, the moment 🔥

👑 Author 👑

these absolute legends:

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

⭐ Definition ⭐

Definition at line 108 of file cget03.f — yes, line 108, don't forget it 🫶

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💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code. (so nobody hand-wrote this, the robot did it, and honestly? she ate 🤖✨)

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heads up bestie: RESID and RCOND are both REAL and the residual formula divides by EPS, so this is very much "let the numbers speak" territory — no vibes-based math here, periodt 💀

ok bye ily, this page came from LAPACK, Version 3.12.0 and is dated TESTING/LIN/cget03.f(3) — go compute that residual and slay 🎀💖🌈