TESTING/LIN/dget07.f(3)

💅 TESTING/LIN/dget07.f(3) — Library Functions Manual 💅

okay bestie, welcome to the TESTING/LIN/dget07.f(3) page from the Library Functions Manual ✨. This one is all about DGET07, its error-bound testing era, and every parameter you need to know. Let’s go 🫶

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🌸 NAME 🌸

TESTING/LIN/dget07.f — that’s the file/page name, no cap 💖

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✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

subroutine dget07 (trans, n, nrhs, a, lda, b, ldb, x, ldx, xact, ldxact,
    ferr, chkferr, berr, reslts)
    DGET07

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💖 Function/Subroutine Documentation 💖

subroutine dget07 (character trans, integer n, integer nrhs, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldb, * ) b, integer ldb, double precision, dimension( ldx, * ) x, integer ldx, double precision, dimension( ldxact, * ) xact, integer ldxact, double precision, dimension( * ) ferr, logical chkferr, double precision, dimension( * ) berr, double precision, dimension( * ) reslts)

DGET07 is the subroutine we’re documenting, and yes it’s giving main character energy 👑.

🔥 Purpose 🔥

DGET07 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) = 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 )

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🍓 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 + (*) )

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👑 Author 👑

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 163 of file dget07.f 💖

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🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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💖 cute little sign-off tea: the footer says LAPACK Version 3.12.0 and the page is TESTING/LIN/dget07.f(3) 🌸. There isn’t a separate date line shown here, so we’re not inventing one, bestie — periodt 🫶✨