TESTING/LIN/dpot03.f(3)

💅 NAME

TESTING/LIN/dpot03.f — okay bestie, this is the source file for dpot03, and it's literally the vibe-check routine for a symmetric matrix times its inverse 🦋

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✨ SYNOPSIS ✨

🌸 Functions/Subroutines

• subroutine dpot03 (uplo, n, a, lda, ainv, ldainv, work, ldwork, rwork, rcond, resid) — DPOT03, the main character 👑

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🎀 Function/Subroutine Documentation

subroutine dpot03 (character uplo, integer n, double precision, dimension(
    lda, * ) a, integer lda, double precision, dimension( ldainv, * ) ainv,
    integer ldainv, double precision, dimension( ldwork, * ) work, integer
    ldwork, double precision, dimension( * ) rwork, double precision rcond,
    double precision resid)

DPOT03 🫶

💜 Purpose:

!>
!> DPOT03 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.
!>

So like, it's checking how well AINV actually works as an inverse of A — residual energy, no cap ✨

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🌈 Parameters

UPLO

!>          UPLO is CHARACTER*1
!>          Specifies whether the upper or lower triangular part of the
!>          symmetric matrix A is stored:
!>          = 'U':  Upper triangular
!>          = 'L':  Lower triangular
!>

Which triangle of A you're storing, bestie — 'U' for upper, 'L' for lower, pick your fighter 💅

N

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

Rows and columns of A (it's symmetric, she's square, she's iconic). Gotta be N >= 0.

A

!>          A is DOUBLE PRECISION array, dimension (LDA,N)
!>          The original symmetric matrix A.
!>

The original symmetric A herself 🌸

LDA

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

Leading dimension of A, and yes LDA >= max(1,N) — don't test me 🙈

AINV

!>          AINV is DOUBLE PRECISION array, dimension (LDAINV,N)
!>          On entry, the inverse of the matrix A, stored as a symmetric
!>          matrix in the same format as A.
!>          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.
!>

⚠️ Heads up bestie: on entry this holds the inverse of A, stored symmetric in the same format as A. But in this version, AINV gets expanded into a full matrix and multiplied by A, so the opposing triangle of AINV will be changed 😭 Like, if the upper triangle of AINV is stored, the lower triangle gets used as work space. She's not coming back the same, fr.

LDAINV

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

Leading dimension of AINV — LDAINV >= max(1,N), periodt.

WORK

!>          WORK is DOUBLE PRECISION array, dimension (LDWORK,N)
!>

Scratch space, dimension (LDWORK,N) 🧚

LDWORK

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

Leading dimension of WORK, and yep, LDWORK >= max(1,N) 🎀

RWORK

!>          RWORK is DOUBLE PRECISION array, dimension (N)
!>

Real workspace, dimension (N) — tiny but mighty ⭐

RCOND

!>          RCOND is DOUBLE PRECISION
!>          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) — literally just that 🦋

RESID

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

The residual itself: norm(I - A*AINV) / ( N * norm(A) * norm(AINV) * EPS ) 🔥 That's the whole point of the routine, iykyk.

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👑 Author

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

Definition at line 123 of file dpot03.f. 📍

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🍓 Author

Generated automatically by Doxygen for LAPACK from the source code. Not me writing my own lore, the robots did it 💀

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LAPACK · Version 3.12.0 — and that's the page, bestie!! TESTING/LIN/dpot03.f(3) out 💖✨🎀🫶