larrj - Man Page

larrj: step in stemr, refine eigval estimates

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.
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.

Detailed Description

Function Documentation

subroutine dlarrj (integer n, double precision, dimension( * ) d, double precision, dimension( * ) e2, integer ifirst, integer ilast, double precision rtol, integer offset, double precision, dimension( * ) w, double precision, dimension( * ) werr, double precision, dimension( * ) work, integer, dimension( * ) iwork, double precision pivmin, double precision spdiam, integer info)

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 < 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.

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 165 of file dlarrj.f.

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.