DLARRB(3)

💖 DLARRB(3) — Library Functions Manual 💖

okay so bestie, welcome to DLARRB(3) — a Library Functions Manual page. The source file for this whole situation is /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dlarrb.f. This routine is giving “limited bisection to locate eigenvalues for more accuracy” energy, and we’re gonna go through every single detail together. 🫶

💖 NAME 💖

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dlarrb.f — that’s the source file path, and this is the page for DLARRB(3) from the Library Functions Manual. 💅

✨ 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.

🦋 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: 🌸

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.

🎀 Parameters 🎀

• N — INTEGER. The order of the matrix.
• D — DOUBLE PRECISION array, dimension (N). The N diagonal elements of the diagonal matrix D.
• LLD — DOUBLE PRECISION array, dimension (N-1). The (N-1) elements L(i)*L(i)*D(i).
• IFIRST — INTEGER. The index of the first eigenvalue to be computed.
• ILAST — INTEGER. The index of the last eigenvalue to be computed.
• RTOL1 — DOUBLE PRECISION. No extra note in the original — just the type, bestie.
• RTOL2 — 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 — 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 — 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 — 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 — 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 — DOUBLE PRECISION array, dimension (2*N). Workspace.
• IWORK — INTEGER array, dimension (2*N). Workspace.
• PIVMIN — DOUBLE PRECISION. The minimum pivot in the Sturm sequence.
• SPDIAM — DOUBLE PRECISION. The spectral diameter of the matrix.
• TWIST — 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 — 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

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okay that’s literally the whole page, bestie. Generated automatically by Doxygen for LAPACK from the source code, LAPACK Version 3.12.0, footer path /home/abui...RC/dlarrb.f(3). Stay iconic 💅✨