TESTING/LIN/zget04.f(3)

💅 TESTING/LIN/zget04.f — bestie's fave little residual checker ✨

okay so picture this: it's a Fortran file in TESTING/LIN, and it's the one that stares at your computed answer and your exact answer and goes "hmm. bestie. how far off are we, actually?" 🎀 Folding the manual name in right here so you know what you're looking at: zget04.f(3), straight out of the LAPACK library functions manual.

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✨ SYNOPSIS ✨

Functions/Subroutines 🦋

• subroutine zget04 (n, nrhs, x, ldx, xact, ldxact, rcond, resid) — literally just ZGET04, living its best life, doing one job and doing it well 💅

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🫶 Function/Subroutine Documentation 🫶

subroutine zget04 (integer n, integer nrhs, complex*16, dimension( ldx, * )
    x, integer ldx, complex*16, dimension( ldxact, * ) xact, integer ldxact,
    double precision rcond, double precision resid)

ZGET04 👑 — that's the name, no cap.

🍓 Purpose 🍓

!> ZGET04 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 like… it takes your computed solution, compares it to the true one, and spits out a residual scaled by the condition number and machine epsilon. It's giving "who are you really, mathematically speaking" energy 🔥 note that RESID is scaled by RCOND and EPS in exactly that formula — keep it, memorize it, it's iconic.

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🌈 Parameters 🌈

• N — INTEGER, obvi 💖 The number of rows of the matrices X and XACT. Constraint: N >= 0.

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

• NRHS — INTEGER, the right-hand-side count, the column count, the whole vibe 🦋 The number of columns of the matrices X and XACT. Constraint: NRHS >= 0.

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

• X — COMPLEX*16 array, dimension (LDX,NRHS) ✨ The computed solution vectors — and each vector is stored as a column of the matrix X.

!> X is COMPLEX*16 array, dimension (LDX,NRHS) !> The computed solution vectors. Each vector is stored as a !> column of the matrix X.

• LDX — INTEGER, the leading dimension flex 💅 The leading dimension of the array X. Constraint: LDX >= max(1,N).

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

• XACT — COMPLEX*16 array, dimension (LDX,NRHS) — wait, bestie, read it exactly as written in the source: it's documented as dimension (LDX,NRHS) with leading dimension described below as LDXACT 🎀 The exact solution vectors, each stored as a column of the matrix XACT.

!> XACT is COMPLEX*16 array, dimension (LDX,NRHS) !> The exact solution vectors. Each vector is stored as a !> column of the matrix XACT.

• LDXACT — INTEGER 🌸 The leading dimension of the array XACT. Constraint: LDXACT >= max(1,N).

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

• RCOND — DOUBLE PRECISION ⭐ The reciprocal of the condition number of the coefficient matrix in the system of equations. (Yes, the reciprocal. Don't come for me, that's what it says.)

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

• RESID — DOUBLE PRECISION 💀 The output, the moment of truth: the maximum over the NRHS solution vectors of ( norm(X-XACT) * RCOND ) / ( norm(XACT) * EPS )

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

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👑 Author 👑

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

(Group project, but make it Fortran 🫶)

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🧚 Definition 🧚

Definition at line 101 of file zget04.f.

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💜 Author (the meta one) 💜

Generated automatically by Doxygen for LAPACK from the source code. Not a human, just vibes and a parser 🌸

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okay that's the whole page, no details left behind, periodt 💅 and for the cute sign-off: this little masterpiece is from LAPACK, Version 3.12.0, page TESTING/LIN/zget04.f(3) — go forth and compute your residuals, bestie, you're gonna slay 🎀✨🦋