SRC/dlarrb.f(3)

💖 SRC/dlarrb.f 💖

okay bestie, this is the SRC/dlarrb.f(3) page from the Library Functions Manual, and it's giving limited bisection but make it precise energy ✨. No preamble, just vibes and eigenvalues 💅.

💖 NAME 💖

SRC/dlarrb.f — that's the whole name, no cap.

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

subroutine dlarrb (n, d, lld, ifirst, ilast, rtol1, rtol2, offset, w,
    wgap, werr, work, iwork, pivmin, spdiam, twist, info)

DLARRB provides limited bisection to locate eigenvalues for more accuracy. periodt.

🦋 Function/Subroutine Documentation 🦋

subroutine dlarrb (integer n, double precision, dimension( * ) d, double
    precision, dimension( * ) lld, integer ifirst, integer ilast, double
    precision rtol1, double precision rtol2, integer offset, double
    precision, dimension( * ) w, double precision, dimension( * ) wgap,
    double precision, dimension( * ) werr, double precision, dimension( * )
    work, integer, dimension( * ) iwork, double precision pivmin, double
    precision spdiam, integer twist, integer info)

DLARRB provides limited bisection to locate eigenvalues for more accuracy.

🌸 Purpose: 🌸

so here's the vibe: given the relatively robust representation(RRR) L D L^T, DLARRB does bisection to refine the eigenvalues of L D L^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 and their gaps are input in WERR and WGAP, respectively. During bisection, intervals [left, right] are maintained by storing their mid-points and semi-widths in the arrays W and WERR respectively. iconic behavior 💜.

🍓 Parameters 🍓

• N — N is INTEGER. The order of the matrix.
• D — D is DOUBLE PRECISION array, dimension (N). The N diagonal elements of the diagonal matrix D.
• LLD — LLD is DOUBLE PRECISION array, dimension (N-1). The (N-1) elements L(i)*L(i)*D(i).
• 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.
• RTOL1 — RTOL1 is DOUBLE PRECISION. That's literally all it says here, bestie.
• RTOL2 — RTOL2 is DOUBLE PRECISION. Tolerance for the convergence of the bisection intervals. An interval [LEFT,RIGHT] has converged if RIGHT-LEFT < MAX( RTOL1*GAP, RTOL2*MAX(|LEFT|,|RIGHT|) ) where GAP is the (estimated) distance to the nearest eigenvalue.
• OFFSET — OFFSET is INTEGER. Offset for the arrays W, WGAP 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.
• WGAP — WGAP is DOUBLE PRECISION array, dimension (N-1). On input, the (estimated) gaps between consecutive eigenvalues of L D L^T, i.e., WGAP(I-OFFSET) is the gap between eigenvalues I and I+1. Note that if IFIRST = ILAST then WGAP(IFIRST-OFFSET) must be set to ZERO. On output, these gaps 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.
• SPDIAM — SPDIAM is DOUBLE PRECISION. The spectral diameter of the matrix.
• TWIST — TWIST is INTEGER. The twist index for the twisted factorization that is used for the negcount.
  • TWIST = N: Compute negcount from L D L^T - LAMBDA I = L+ D+ L+^T
  • TWIST = 1: Compute negcount from L D L^T - LAMBDA I = U- D- U-^T
  • TWIST = R: Compute negcount from L D L^T - LAMBDA I = N(r) D(r) N(r)
• 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 193 of file dlarrb.f.

🌟 Author 🌟

Generated automatically by Doxygen for LAPACK from the source code.

and that's the tea 🍓: source/version is LAPACK Version 3.12.0, and the page is SRC/dlarrb.f(3). The footer doesn't list a date, so we're not inventing one — no cap, bestie 💖💅.