SRC/dlarrj.f(3)

🌸 SRC/dlarrj.f 🌸

Manual name: Library Functions Manual — folded in right here, bestie, because we are not copying the header line like a boring NPC. This is the SRC/dlarrj.f page, and it is lowkey iconic if you're into eigenvalue refinement.

✨ NAME ✨

SRC/dlarrj.f — the page name, periodt. The manual it lives in is Library Functions Manual.

💅 SYNOPSIS 💅

Functions/Subroutines

• subroutine dlarrj (n, d, e2, ifirst, ilast, rtol, offset, w, werr, work, iwork, pivmin, spdiam, info) — DLARRJ performs refinement of the initial estimates of the eigenvalues of the matrix T.

🦋 Function/Subroutine Documentation 🦋

💖 subroutine dlarrj 💖

subroutine dlarrj (integer n, double precision, dimension( * ) d, double
    precision, dimension( * ) e2, integer ifirst, integer ilast, double
    precision rtol, integer offset, double precision, dimension( * ) w,
    double precision, dimension( * ) werr, double precision, dimension( * )
    work, integer, dimension( * ) iwork, double precision pivmin, double
    precision spdiam, integer info)

DLARRJ performs refinement of the initial estimates of the eigenvalues of the matrix T. slay. No cap.

🔥 Purpose:

Okay so here's the tea: given the initial eigenvalue approximations of T, DLARRJ does bisection to refine the eigenvalues of T, W( IFIRST-OFFSET ) through W( ILAST-OFFSET ), to more accuracy. Initial guesses for these eigenvalues are input in W, and the corresponding estimate of the error in these guesses is input in WERR. During bisection, intervals [left, right] are maintained by storing their mid-points and semi-widths in the arrays W and WERR respectively. That's the whole vibe.

🌈 Parameters

• N — N is INTEGER; the order of the matrix.
• D — D is DOUBLE PRECISION array, dimension (N); the N diagonal elements of T.
• E2 — E2 is DOUBLE PRECISION array, dimension (N-1); the Squares of the (N-1) subdiagonal elements of T.
• IFIRST — IFIRST is INTEGER; the index of the first eigenvalue to be computed.
• ILAST — ILAST is INTEGER; the index of the last eigenvalue to be computed.
• RTOL — RTOL is DOUBLE PRECISION; tolerance for the convergence of the bisection intervals. An interval [LEFT,RIGHT] has converged if RIGHT-LEFT < RTOL*MAX(|LEFT|,|RIGHT|).
• OFFSET — OFFSET is INTEGER; offset for the arrays W and WERR, i.e., the IFIRST-OFFSET through ILAST-OFFSET elements of these arrays are to be used.
• W — W is DOUBLE PRECISION array, dimension (N). On input, W( IFIRST-OFFSET ) through W( ILAST-OFFSET ) are estimates of the eigenvalues of L D L^T indexed IFIRST through ILAST. On output, these estimates are refined.
• WERR — WERR is DOUBLE PRECISION array, dimension (N). On input, WERR( IFIRST-OFFSET ) through WERR( ILAST-OFFSET ) are the errors in the estimates of the corresponding elements in W. On output, these errors are refined.
• WORK — WORK is DOUBLE PRECISION array, dimension (2*N); workspace.
• IWORK — IWORK is INTEGER array, dimension (2*N); workspace.
• PIVMIN — PIVMIN is DOUBLE PRECISION; the minimum pivot in the Sturm sequence for T.
• SPDIAM — SPDIAM is DOUBLE PRECISION; the spectral diameter of T.
• INFO — INFO is INTEGER; error flag.

👑 Author

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

🎀 Contributors:

• Beresford Parlett, University of California, Berkeley, USA
• Jim Demmel, University of California, Berkeley, USA
• Inderjit Dhillon, University of Texas, Austin, USA
• Osni Marques, LBNL/NERSC, USA
• Christof Voemel, University of California, Berkeley, USA

📌 Definition at line 165 of file dlarrj.f.

🧚 Author

Generated automatically by Doxygen for LAPACK from the source code.

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Sign-off: LAPACK Version 3.12.0 · source SRC/dlarrj.f(3). The footer doesn't hand us a date, just those two, bestie. 💅✨