DLARRJ(3)

💖 DLARRJ(3) 💖

okay so bestie, welcome to the Library Functions Manual page for DLARRJ(3) — the header path is literally /home/abui...RC/dlarrj.f(3), and this whole thing is a LAPACK glow-up for eigenvalue estimates. no cap, it's giving refinement era ✨

🎀 NAME 🎀

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dlarrj.f — that's the source file this page is repping, bestie. 💅

✨ 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. (periodt, that's the whole vibe.) 🔥

🫶 Function/Subroutine Documentation 🫶

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. 🦋

🎯 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, the corresponding estimate of the error in these guesses in WERR. During bisection, intervals [left, right] are maintained by storing their mid-points and semi-widths in the arrays W and WERR respectively. 🌸

🌸 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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💖 okay bye bestie — this page is LAPACK Version 3.12.0, and the footer path is /home/abui...RC/dlarrj.f(3). slay and stay convergent ✨💅