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slarrj.f(3) LAPACK slarrj.f(3)

NAME

slarrj.f

SYNOPSIS

Functions/Subroutines


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 (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: 



 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.

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.LT.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.

Date:

June 2017

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 170 of file slarrj.f.

Author

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Tue Nov 14 2017 Version 3.8.0