ZGET07(3)

💅 ZGET07(3) 💅

okay bestie, this is the ZGET07(3) page from the Library Functions Manual, and the header path is literally /home/abui...IN/zget07.f(3). We're about to vibe-check LAPACK's error-bound tester, no cap. ✨

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🎀 NAME 🎀

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/zget07.f

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✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

subroutine ZGET07 (trans, n, nrhs, a, lda, b, ldb, x, ldx, xact, ldxact,
    ferr, chkferr, berr, reslts)

ZGET07

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💖 Function/Subroutine Documentation 💖

subroutine ZGET07 (character trans, integer n, integer nrhs, complex*16,
    dimension( lda, * ) a, integer lda, complex*16, dimension( ldb, * ) b,
    integer ldb, complex*16, dimension( ldx, * ) x, integer ldx, complex*16,
    dimension( ldxact, * ) xact, integer ldxact, double precision,
    dimension( * ) ferr, logical chkferr, double precision, dimension( * )
    berr, double precision, dimension( * ) reslts)

ZGET07

🦋 Purpose 🦋

okay so ZGET07 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. 💫

RESLTS(1) is the test of the error bound:

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) is the residual from the iterative refinement routine:

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 — it's a CHARACTER*1, and it 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). pick your fighter ✨
• N — N is INTEGER, and it's the number of rows of the matrices X and XACT. N >= 0.
• NRHS — NRHS is INTEGER, and it's the number of columns of the matrices X and XACT. NRHS >= 0.
• A — A is COMPLEX*16 array, dimension (LDA,N). This is 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 COMPLEX*16 array, dimension (LDB,NRHS). These are 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 COMPLEX*16 array, dimension (LDX,NRHS). These are the computed solution vectors, and 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 COMPLEX*16 array, dimension (LDX,NRHS). These are the exact solution vectors, and 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 DOUBLE PRECISION array, dimension (NRHS). These are 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 it to .TRUE. to check FERR, and .FALSE. not to check FERR.
• BERR — BERR is DOUBLE PRECISION array, dimension (NRHS). This is 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 DOUBLE PRECISION array, dimension (2). This is the maximum over the NRHS solution vectors of the ratios:

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

⚠️ real talk: when the test system is ill-conditioned, the solution in XACT may be incorrect. CHKFERR is literally the switch for whether you check FERR, bestie. don't ignore that. 💀

👑 Author 👑

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

Definition at line 164 of file zget07.f.

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👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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mwah 💋 this little tour was brought to you by LAPACK Version 3.12.0, from /home/abui...IN/zget07.f(3). bye bestie, go test those bounds! 🫶🎀