SLARRJ(3)

📦 version 3.12.0, in opensuse-leap 16.0

💖 NAME 💖

okay so bestie, this manual page is SLARRJ(3) — Library Functions Manual energy, no cap. The file path for it is:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/slarrj.f

That's the whole name situation 🫶

🌸 SYNOPSIS 🌸

Functions/Subroutines

Here's the subroutine in all its main-character glory:

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. ✨

✨ 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 here's the tea: given the initial eigenvalue approximations of T, SLARRJ does bisection to refine the eigenvalues of T — specifically W( IFIRST-OFFSET ) through W( ILAST-OFFSET ) — to more accuracy. Initial guesses for these eigenvalues are input in W, and the corresponding estimate of the error in these guesses is input 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.

👑 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.

📜 Author 📜

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💖 Sign-off / footer tea: LAPACK Version 3.12.0, source path /home/abui...RC/slarrj.f(3). That's the footer moment, bestie — periodt. 🫶

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