dlarrj-f(3)

dlarrj.f –

Synopsis

Functions/Subroutines

subroutine dlarrj (N, D, E2, IFIRST, ILAST, RTOL, OFFSET, W, WERR, WORK, IWORK, PIVMIN, SPDIAM, INFO)
DLARRJ performs refinement of the initial estimates of the eigenvalues of the matrix T.

Function/Subroutine Documentation

subroutine dlarrj (integerN, double precision, dimension( * )D, double precision, dimension( * )E2, integerIFIRST, integerILAST, double precisionRTOL, integerOFFSET, double precision, dimension( * )W, double precision, dimension( * )WERR, double precision, dimension( * )WORK, integer, dimension( * )IWORK, double precisionPIVMIN, double precisionSPDIAM, integerINFO)

DLARRJ performs refinement of the initial estimates of the eigenvalues of the matrix T.

Purpose:

 Given the initial eigenvalue approximations of T, DLARRJ
 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 is INTEGER
 The order of the matrix.

 D is DOUBLE PRECISION array, dimension (N)
 The N diagonal elements of T.

 E2 is DOUBLE PRECISION 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 DOUBLE PRECISION
 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 is 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.

WERR

 WERR is 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

 WORK is DOUBLE PRECISION array, dimension (2*N)
 Workspace.

IWORK

 IWORK is INTEGER array, dimension (2*N)
 Workspace.

PIVMIN

 PIVMIN is DOUBLE PRECISION
 The minimum pivot in the Sturm sequence for T.

SPDIAM

 SPDIAM is DOUBLE PRECISION
 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:

September 2012

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 167 of file dlarrj.f.

Author

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