SRC/slarrb.f(3)

✨ NAME ✨

SRC/slarrb.f — okay bestie, that's the page name, and it's from the LAPACK Library Functions Manual. This one is all about SLARRB, the limited-bisection eigenvalue-refinement icon. 💅

---

🌸 SYNOPSIS 🌸

Functions/Subroutines

subroutine slarrb (n, d, lld, ifirst, ilast, rtol1, rtol2, offset, w,
    wgap, werr, work, iwork, pivmin, spdiam, twist, info)
    SLARRB provides limited bisection to locate eigenvalues for more
    accuracy.

---

🧚 Function/Subroutine Documentation 🧚

💖 subroutine slarrb 💖

subroutine slarrb (integer n, real, dimension( * ) d, real, dimension( * )
    lld, integer ifirst, integer ilast, real rtol1, real rtol2, integer
    offset, real, dimension( * ) w, real, dimension( * ) wgap, real,
    dimension( * ) werr, real, dimension( * ) work, integer, dimension( * )
    iwork, real pivmin, real spdiam, integer twist, integer info)
    SLARRB provides limited bisection to locate eigenvalues for more
    accuracy.

🎯 Purpose:

Given the relatively robust representation(RRR) L D L^T, SLARRB 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.

🧸 Parameters

• N — N is INTEGER. The order of the matrix.
• D — D is REAL array, dimension (N). The N diagonal elements of the diagonal matrix D.
• LLD — LLD is REAL 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 REAL.
• RTOL2 — RTOL2 is REAL. 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 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.
• WGAP — WGAP is REAL 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 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.
• SPDIAM — SPDIAM is REAL. 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 slarrb.f.

---

🌟 Author 🌟

Generated automatically by Doxygen for LAPACK from the source code.

💖 That's the whole page, bestie. Footer vibes: LAPACK, Version 3.12.0, SRC/slarrb.f(3) — periodt. 💖