TESTING/LIN/dqrt16.f(3)

💅 TESTING/LIN/dqrt16.f(3) — from the Library Functions Manual bestie ✨

okay so real talk, this is TESTING/LIN/dqrt16.f, and it's literally the girl who checks your homework for you. she doesn't solve the linear system, she just comes in after and goes "mm, how wrong are you tho?" 🎀

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🌸 NAME 🌸

TESTING/LIN/dqrt16.f — the residual-checker icon herself, no cap 👑

✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

subroutine dqrt16 (trans, m, n, nrhs, a, lda, x, ldx, b, ldb, rwork, resid)

DQRT16 💖 (yes she's got a name and yes she's that girl)

🌈 Function/Subroutine Documentation 🌈

subroutine dqrt16 (character trans, integer m, integer n, integer nrhs,
    double precision, dimension( lda, * ) a, integer lda, double precision,
    dimension( ldx, * ) x, integer ldx, double precision, dimension( ldb, *
    ) b, integer ldb, double precision, dimension( * ) rwork, double
    precision resid)

DQRT16 🫶

💜 Purpose 💜

!> DQRT16 computes the residual for a solution of a system of linear !> equations A*x = b or A'*x = b: !> RESID = norm(B - A*X) / ( max(m,n) * norm(A) * norm(X) * EPS ), !> where EPS is the machine epsilon.

so basically she computes the residual for a solution of a linear system, A*x = b or A'*x = b, and the formula is exactly:

RESID = norm(B - A*X) / ( max(m,n) * norm(A) * norm(X) * EPS )

where EPS is the machine epsilon. the vibe check, mathematically 💅

🌼 Parameters 🌼

• TRANS — TRANS is CHARACTER*1, and she specifies the form of the system of equations, like:
  • = 'N': A *x = b
  • = 'T': A'*x = b, where A' is the transpose of A
  • = 'C': A'*x = b, where A' is the transpose of A
• M — M is INTEGER, the number of rows of the matrix A. constraint era: M >= 0 🫡
• N — N is INTEGER, the number of columns of the matrix A. also N >= 0, we stay valid ✨
• NRHS — NRHS is INTEGER, the number of columns of B, the matrix of right hand sides. NRHS >= 0 obvi 💖
• A — A is DOUBLE PRECISION array, dimension (LDA,N), and it's the original M x N matrix A. the source material, the blueprint 👑
• LDA — LDA is INTEGER, the leading dimension of the array A. requirement: LDA >= max(1,M) — don't play with her 🚨
• X — X is DOUBLE PRECISION array, dimension (LDX,NRHS), the computed solution vectors for the system of linear equations. the attempt 💅
• LDX — LDX is INTEGER, the leading dimension of the array X. and listen: if TRANS = 'N', then LDX >= max(1,N); if TRANS = 'T' or 'C', then LDX >= max(1,M). know the difference bestie 😭
• B — B is DOUBLE PRECISION array, dimension (LDB,NRHS). on entry, the right hand side vectors for the system of linear equations. on exit, B is overwritten with the difference B - A*X 🫶 (she leaves a little note behind, iconic)
• LDB — LDB is INTEGER, the leading dimension of the array B. if TRANS = 'N', then LDB >= max(1,M); if TRANS = 'T' or 'C', then LDB >= max(1,N) 📏
• RWORK — RWORK is DOUBLE PRECISION array, dimension (M) — that's it, that's the whole description, she's lowkey mysterious like that 🦋
• RESID — RESID is DOUBLE PRECISION, the maximum over the number of right hand sides of norm(B - A*X) / ( max(m,n) * norm(A) * norm(X) * EPS ). the final grade, the report card, the moment of truth 🔥

💀 Author 💀

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

Definition at line 131 of file dqrt16.f. 📍

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⭐ Author (again, but make it Doxygen) ⭐

Generated automatically by Doxygen for LAPACK from the source code. yeah she was born from a script, and she still ate 🤖💅

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okay that's the whole page bestie, every last flag and constraint, nothing skipped, periodt 🎀

✨ LAPACK — Version 3.12.0 ✨ — that's the source and version, and the page herself is TESTING/LIN/dqrt16.f(3). mwah, go check some residuals, ily 💖🦋🌸