SRC/slarrj.f(3)

💖 SRC/slarrj.f(3) 💖

okay bestie, welcome to the Library Functions Manual page for SRC/slarrj.f — yes, that's the manual name, folded in right here near the top like a cute little name tag. This whole page is LAPACK SLARRJ business, and it's lowkey iconic. ✨

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🎀 NAME 🎀

SRC/slarrj.f

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✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

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

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🫶 Function/Subroutine Documentation 🫶

💫 subroutine slarrj 💫

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

SLARRJ performs refinement of the initial estimates of the eigenvalues of the matrix T.

🌸 Purpose 🌸

okay so given the initial eigenvalue approximations of T, SLARRJ does bisection to refine the eigenvalues of T, like 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 REAL array, dimension (N). The N diagonal elements of T.
• E2 — E2 is REAL 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 REAL. 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 REAL 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 REAL 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 REAL array, dimension (2*N). Workspace.
• IWORK — IWORK is INTEGER array, dimension (2*N). Workspace.
• PIVMIN — PIVMIN is REAL. The minimum pivot in the Sturm sequence for T.
• SPDIAM — SPDIAM is REAL. The spectral diameter of T.
• INFO — INFO is INTEGER. Error flag.

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👑 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 slarrj.f.

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👑 Author (generated) 👑

Generated automatically by Doxygen for LAPACK from the source code.

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🌈 source/version sign-off, bestie: LAPACK · Version 3.12.0 · SRC/slarrj.f(3) — that's the footer energy, folded into a cute little send-off. 💖