SGET07(3)

💅 SGET07(3) — LAPACK's error-bound vibe check ✨

Okay so this is from the Library Functions Manual, and we're talking about SGET07 — a LAPACK subroutine that is literally a vibe check for error bounds. No cap. 🫶

🌸 NAME

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/sget07.f

That's the file path, periodt. 💖

✨ SYNOPSIS

🧚 Functions/Subroutines

subroutine SGET07 (trans, n, nrhs, a, lda, b, ldb, x, ldx, xact, ldxact,
    ferr, chkferr, berr, reslts)
    SGET07

🔥 Function/Subroutine Documentation

subroutine SGET07 (character trans, integer n, integer nrhs, real,
    dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b, integer
    ldb, real, dimension( ldx, * ) x, integer ldx, real, dimension( ldxact,
    * ) xact, integer ldxact, real, dimension( * ) ferr, logical chkferr,
    real, dimension( * ) berr, real, dimension( * ) reslts)
    SGET07

SGET07

🎯 Purpose:

Okay so SGET07 tests the error bounds from iterative refinement for the computed solution to a system of equations op(A)*X = B, where A is a general n by n matrix and op(A) = A or A**T, depending on TRANS. It's giving very main-character numerical-validation energy. 👑

• RESLTS(1) = test of the error bound
  • = norm(X - XACT) / ( norm(X) * FERR )
• A large value is returned if this ratio is not less than one. So yeah, if that ratio isn't less than one, bestie, expect a large value. 😭
• RESLTS(2) = residual from the iterative refinement routine
  • = the maximum of BERR / ( (n+1)*EPS + (*) ), where
  • (*) = (n+1)*UNFL / (min_i (abs(op(A))*abs(X) +abs(b))_i )

🧸 Parameters

• TRANS — TRANS is CHARACTER*1. It specifies the form of the system of equations, and it's literally choosing the solver vibe:
  • 'N': A * X = B (No transpose)
  • 'T': A**T * X = B (Transpose)
  • 'C': A**H * X = B (Conjugate transpose = Transpose)
• N — N is INTEGER. The number of rows of the matrices X and XACT. N >= 0. Slay, non-negative. ✨
• NRHS — NRHS is INTEGER. The number of columns of the matrices X and XACT. NRHS >= 0. Also non-negative, we love that.
• A — A is REAL array, dimension (LDA,N). The original n by n matrix A. Iconic.
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N). Respect the leading dimension, fr fr.
• B — B is REAL array, dimension (LDB,NRHS). The right hand side vectors for the system of linear equations. The B in the equation, bestie. 💅
• LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,N).
• X — X is REAL array, dimension (LDX,NRHS). The computed solution vectors. Each vector is stored as a column of the matrix X. It's giving column storage. 🦋
• LDX — LDX is INTEGER. The leading dimension of the array X. LDX >= max(1,N).
• XACT — XACT is REAL array, dimension (LDX,NRHS). The exact solution vectors. Each vector is stored as a column of the matrix XACT. Exact-solution energy. 🎀
• LDXACT — LDXACT is INTEGER. The leading dimension of the array XACT. LDXACT >= max(1,N).
• FERR — FERR is REAL array, dimension (NRHS). The estimated forward error bounds for each solution vector X. If XTRUE is the true solution, FERR bounds the magnitude of the largest entry in (X - XTRUE) divided by the magnitude of the largest entry in X. Big important error-bound math, no cap. 🔥
• CHKFERR — CHKFERR is LOGICAL. Set to .TRUE. to check FERR, .FALSE. not to check FERR. Heads up: When the test system is ill-conditioned, the solution in XACT may be incorrect. So yeah, ill-conditioned systems can make XACT sus. 🙈
• BERR — BERR is REAL array, dimension (NRHS). The componentwise relative backward error of each solution vector (i.e., the smallest relative change in any entry of A or B that makes X an exact solution). Literally the smallest change that makes it exact. 💅
• RESLTS — RESLTS is REAL array, dimension (2). The maximum over the NRHS solution vectors of the ratios:

RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
RESLTS(2) = BERR / ( (n+1)*EPS + (*) )

That's the whole results vibe. Good. 🌈

👑 Author

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

Definition at line 163 of file sget07.f.

💌 Author

Generated automatically by Doxygen for LAPACK from the source code.

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Cute sign-off 🌈: LAPACK Version 3.12.0, page source /home/abui...IN/sget07.f(3). Date? Not shown in this footer, bestie — so we're not inventing one. That's the deets, and that's periodt. 💖