TESTING/LIN/dget04.f(3)

💅 TESTING/LIN/dget04.f 💅

okay bestie, welcome to the glow-up of TESTING/LIN/dget04.f — this is a page from the LAPACK testing library, and honestly? it's a little legend. it lives to answer one iconic question: "how far off is my computed answer from the real one?" 🎯

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✨ NAME ✨

TESTING/LIN/dget04.f — the file, the myth, the moment. periodt. 💖

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🦋 SYNOPSIS 🦋

Functions/Subroutines

• subroutine dget04 (n, nrhs, x, ldx, xact, ldxact, rcond, resid) — the one and only DGET04, serving looks and residuals. 👑

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🌸 Function/Subroutine Documentation 🌸

subroutine dget04 (integer n, integer nrhs, double precision, dimension(
    ldx, * ) x, integer ldx, double precision, dimension( ldxact, * ) xact,
    integer ldxact, double precision rcond, double precision resid)

DGET04 🫶

Purpose:

!>
!> DGET04 computes the difference between a computed solution and the
!> true solution to a system of linear equations.
!>
!> RESID =  ( norm(X-XACT) * RCOND ) / ( norm(XACT) * EPS ),
!> where RCOND is the reciprocal of the condition number and EPS is the
!> machine epsilon.
!>

so basically it's the vibe check between your computed solution and the actual truth 💀 — it spits out RESID, which is that whole formula up there. no cap, it's just measuring how much your answer is giving "close enough" vs "not me". ✨

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🎀 Parameters 🎀

• N

!>          N is INTEGER
!>          The number of rows of the matrices X and XACT.  N >= 0.
!>

the row count of X and XACT. and yes, N >= 0. 🙈

• NRHS

!>          NRHS is INTEGER
!>          The number of columns of the matrices X and XACT.  NRHS >= 0.
!>

the column count of X and XACT. also gotta be NRHS >= 0. 💜

• X

!>          X is DOUBLE PRECISION array, dimension (LDX,NRHS)
!>          The computed solution vectors.  Each vector is stored as a
!>          column of the matrix X.
!>

your computed solution vectors, each one chilling as a column of X. main character energy. 🌟

• LDX

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

the leading dimension of X, and it must be LDX >= max(1,N). don't try it any other way bestie. 🚫

• XACT

!>          XACT is DOUBLE PRECISION array, dimension( LDX, NRHS )
!>          The exact solution vectors.  Each vector is stored as a
!>          column of the matrix XACT.
!>

the exact solution vectors — the truth, the whole truth, nothing but the truth. each is a column of XACT. 🎯

• LDXACT

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

leading dimension of XACT, requiring LDXACT >= max(1,N). slay. 💅

• RCOND

!>          RCOND is DOUBLE PRECISION
!>          The reciprocal of the condition number of the coefficient
!>          matrix in the system of equations.
!>

the reciprocal of the condition number of the coefficient matrix in the system. iconic reciprocal behavior. 🔥

• RESID

!>          RESID is DOUBLE PRECISION
!>          The maximum over the NRHS solution vectors of
!>          ( norm(X-XACT) * RCOND ) / ( norm(XACT) * EPS )
!>

the output! it's the max over all the NRHS solution vectors of that formula. this is the moment. 👑

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👑 Author 👑

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

absolute legends, all of them. 🫶

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Definition at line 101 of file dget04.f.

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💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code. (so this page literally wrote itself, we love an independent queen 💅✨)

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and that's the whole thing! this little page is from LAPACK, Version 3.12.0, and it's the TESTING/LIN/dget04.f(3) manual page. go forth and compute your residuals, bestie — you're gonna eat. 🍓💖🎀