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