DPTT05(3)

okay so bestie, this is DPTT05(3) from the Library Functions Manual — yes, the LAPACK test-routine corner of the group chat. The file it documents is right here, and we're gonna walk through every single parameter like we're decoding a crush's text. 💅✨

✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/dptt05.f

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💅 SYNOPSIS 💅

Functions/Subroutines

• subroutine DPTT05 (n, nrhs, d, e, b, ldb, x, ldx, xact, ldxact, ferr, berr, reslts) — DPTT05

subroutine DPTT05 (n, nrhs, d, e, b, ldb, x, ldx, xact, ldxact, ferr, berr, reslts)

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🦋 Function/Subroutine Documentation 🦋

subroutine DPTT05 (integer n, integer nrhs, double precision, dimension( * ) d, double precision, dimension( * ) e, 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, double precision, dimension( * ) berr, double precision, dimension( * ) reslts)

and the routine's name is, say it with me, DPTT05. 👑

🎀 Purpose 🎀

okay so DPTT05 is the vibe check for error bounds from iterative refinement for the computed solution to a system of equations A*X = B, where A is a symmetric tridiagonal matrix of order n. No cap — that's the whole job. 💖

The source comment (Doxygen !> style) lays out the receipts like 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 — that's the red flag in the group chat. 🚩

RESLTS(2) = residual from the iterative refinement routine
          = the maximum of BERR / ( NZ*EPS + (*) ), where
            (*) = NZ*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
            and NZ = max. number of nonzeros in any row of A, plus 1

🌸 Parameters 🌸

• N — INTEGER. The number of rows of the matrices X, B, and XACT, and the order of the matrix A. N >= 0.
• NRHS — INTEGER. The number of columns of the matrices X, B, and XACT. NRHS >= 0.
• D — DOUBLE PRECISION array, dimension (N). The n diagonal elements of the tridiagonal matrix A.
• E — DOUBLE PRECISION array, dimension (N-1). The (n-1) subdiagonal elements of the tridiagonal matrix A.
• B — DOUBLE PRECISION array, dimension (LDB,NRHS). The right hand side vectors for the system of linear equations.
• LDB — INTEGER. The leading dimension of the array B. LDB >= max(1,N).
• X — DOUBLE PRECISION array, dimension (LDX,NRHS). The computed solution vectors. Each vector is stored as a column of the matrix X.
• LDX — INTEGER. The leading dimension of the array X. LDX >= max(1,N).
• XACT — DOUBLE PRECISION array, dimension (LDX,NRHS). The exact solution vectors. Each vector is stored as a column of the matrix XACT.
• LDXACT — INTEGER. The leading dimension of the array XACT. LDXACT >= max(1,N).
• FERR — 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.
• BERR — 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 — 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 / ( NZ*EPS + (*) )

💖 Author 💖

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

Definition at line 148 of file dptt05.f.

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🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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okay that's the whole page, bestie — footer says LAPACK Version 3.12.0 and points at /home/abui...IN/dptt05.f(3); no date is listed on this one. mwah 💋🎀