---
name: "slarrj"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/slarrj/3lapack"
---

# slarrj(3lapack)

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 by\
\
    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