LAPACK

NAME¶

larrj - larrj: step in stemr, refine eigval estimates

SYNOPSIS¶

Functions¶

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

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.