TESTING/LIN/zget07.f(3)

🌸 NAME 🌸

TESTING/LIN/zget07.f — okay bestie, this is the page for that file, and it lives in the Library Functions Manual. It’s giving “library functions manual” energy from the very first line, periodt. 💅

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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 is the routine, and yes, that’s its whole name. 💖

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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 — that’s the main character of this whole page, no cap. 👑

💖 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.

The purpose block is literally this:

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 )

So yeah, it’s checking whether the error-bound ratios are slaying or lowkey sus. 💀

🦋 Parameters 🦋

• TRANS — TRANS is CHARACTER*1. 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).
• N — N is INTEGER. This is the number of rows of the matrices X and XACT. N >= 0.
• NRHS — NRHS is INTEGER. This is the number of columns of the matrices X and XACT. NRHS >= 0.
• A — A is COMPLEX*16 array, dimension (LDA,N). It’s the original n by n matrix A.
• LDA — LDA is INTEGER. This is 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. This is 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. Each vector is stored as a column of the matrix X.
• LDX — LDX is INTEGER. This is 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. Each vector is stored as a column of the matrix XACT.
• LDXACT — LDXACT is INTEGER. This is 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, .FALSE. not to check FERR. When the test system is ill-conditioned, the solution in XACT may be incorrect. This is important, bestie — ill-conditioned systems can be messy. 🙈
• 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 + (*) )

👑 Author 👑

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

Definition at line 164 of file zget07.f. 💜

🌈 Author (the auto-generated one) 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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source/version sign-off, bestie: this iconic little page is LAPACK, Version 3.12.0, and the page is TESTING/LIN/zget07.f(3). That’s the footer vibe, and it ate. 💋✨