TESTING/LIN/sget07.f(3)

💅 TESTING/LIN/sget07.f 💅

from the Library Functions Manual — okay bestie, let's get into it 🫶

✨ NAME ✨

TESTING/LIN/sget07.f

🦋 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

💖 Purpose 💖

Okay so SGET07 is the vibe-check for error bounds from iterative refinement. It looks at 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. 👑

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.

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. Specifies the form of the system of equations. = '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.
• NRHS — NRHS is INTEGER. The number of columns of the matrices X and XACT. NRHS >= 0.
• A — A is REAL array, dimension (LDA,N). The original n by n matrix A.
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
• B — B is REAL array, dimension (LDB,NRHS). The right hand side vectors for the system of linear equations.
• 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.
• 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.
• 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.
• CHKFERR — CHKFERR is LOGICAL. Set to .TRUE. to check FERR, .FALSE. not to check FERR. When the test system is ill-conditioned, the solution in XACT may be incorrect. 🫶
• 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).
• 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 + (*) )

👑 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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💖 and that's the whole glow-up! LAPACK — Version 3.12.0 — TESTING/LIN/sget07.f(3) — periodt. 💖