slarrj.f −

**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.*

* subroutine SLARRJ (integerN, real, dimension( * )D, real, dimension( * )E2, integerIFIRST, integerILAST, realRTOL, integerOFFSET, real, dimension( * )W, real, dimension( * )WERR, real, dimension( * )WORK, integer, dimension( * )IWORK, realPIVMIN, realSPDIAM, integerINFO)* performs refinement of the initial estimates of the eigenvalues of the matrix T.

SLARRJ

**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:**

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 slarrj.f.

Generated automatically by Doxygen for LAPACK from the source code.