?larrj

Performs refinement of the initial estimates of the eigenvalues of the matrix T.

Syntax

call slarrj( n, d, e2, ifirst, ilast, rtol, offset, w, werr, work, iwork, pivmin, spdiam, info )

call dlarrj( n, d, e2, ifirst, ilast, rtol, offset, w, werr, work, iwork, pivmin, spdiam, info )

Include Files

The FORTRAN 77 interfaces are specified in the mkl_lapack.fi include file (to be used in Fortran programs) and in the mkl_lapack.h include file (to be used in C programs).

Description

Given the initial eigenvalue approximations of T, this routine 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 [a,b] are maintained by storing their mid-points and semi-widths in the arrays w and werr respectively.

Input Parameters

n

INTEGER. The order of the matrix T.

d

REAL for slarrj

DOUBLE PRECISION for dlarrj

Array, DIMENSION (n).

Contains n diagonal elements of the matrix T.

e2

REAL for slarrj

DOUBLE PRECISION for dlarrj

Array, DIMENSION (n-1).

Contains (n-1) squared sub-diagonal elements of the T.

ifirst

INTEGER.

The index of the first eigenvalue to be computed.

ilast

INTEGER.

The index of the last eigenvalue to be computed.

rtol

REAL for slarrj

DOUBLE PRECISION for dlarrj

Tolerance for the convergence of the bisection intervals. An interval [a,b] is considered to be converged if (b-a) ≤ rtol*max(|a|,|b|).

offset

INTEGER.

Offset for the arrays w and werr, that is the ifirst-offset through ilast-offset elements of these arrays are to be used.

w

REAL for slarrj

DOUBLE PRECISION for dlarrj

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.

werr

REAL for slarrj

DOUBLE PRECISION for dlarrj

Array, DIMENSION (n).

On input, werr(ifirst-offset) through werr(ilast-offset) are the errors in the estimates of the corresponding elements in w.

work

REAL for slarrj

DOUBLE PRECISION for dlarrj

Workspace array, DIMENSION (2*n).

iwork

INTEGER.

Workspace array, DIMENSION (2*n).

pivmin

REAL for slarrj

DOUBLE PRECISION for dlarrj

The minimum pivot in the Sturm sequence for the matrix T.

spdiam

REAL for slarrj

DOUBLE PRECISION for dlarrj

The spectral diameter of the matrix T.

Output Parameters

w

On exit, contains the refined estimates of the eigenvalues.

werr

On exit, contains the refined errors in the estimates of the corresponding elements in w.

info

INTEGER.

Now it is not used and always is set to 0.