# slarrj (l) - Linux Man Pages

## slarrj: the initial eigenvalue approximations of T, SLARRJ does bisection to refine the eigenvalues of T,

## NAME

SLARRJ - the initial eigenvalue approximations of T, SLARRJ does bisection to refine the eigenvalues of T,## SYNOPSIS

- SUBROUTINE SLARRJ(
- N, D, E2, IFIRST, ILAST, RTOL, OFFSET, W, WERR, WORK, IWORK, PIVMIN, SPDIAM, INFO )

- INTEGER IFIRST, ILAST, INFO, N, OFFSET

- REAL PIVMIN, RTOL, SPDIAM

- INTEGER IWORK( * )

- REAL D( * ), E2( * ), W( * ), WERR( * ), WORK( * )

## PURPOSE

Given the initial eigenvalue approximations of T, SLARRJ does bisection to refine the eigenvalues of 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 in WERR. During bisection, intervals [left, right] are maintained by storing their mid-points and semi-widths in the arrays W and WERR respectively.## ARGUMENTS

- N (input) INTEGER
- The order of the matrix.
- D (input) REAL array, dimension (N)
- The N diagonal elements of T.
- E2 (input) REAL array, dimension (N-1)
- The Squares of the (N-1) subdiagonal elements of T.
- IFIRST (input) INTEGER
- The index of the first eigenvalue to be computed.
- ILAST (input) INTEGER
- The index of the last eigenvalue to be computed.
- RTOL (input) REAL
- Tolerance for the convergence of the bisection intervals. An interval [LEFT,RIGHT] has converged if RIGHT-LEFT.LT.RTOL*MAX(|LEFT|,|RIGHT|).
- OFFSET (input) 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 (input/output) 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 (input/output) 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 (workspace) REAL array, dimension (2*N)
- Workspace.
- IWORK (workspace) INTEGER array, dimension (2*N)
- Workspace.
- PIVMIN (input) DOUBLE PRECISION
- The minimum pivot in the Sturm sequence for T.
- SPDIAM (input) DOUBLE PRECISION
- The spectral diameter of T.
- INFO (output) INTEGER
- Error flag.

## FURTHER DETAILS

Based on contributions byBeresford 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