LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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◆ dlarrj()

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.

Download DLARRJ + dependencies [TGZ] [ZIP] [TXT]

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
[in]N
          N is INTEGER
          The order of the matrix.
[in]D
          D is DOUBLE PRECISION array, dimension (N)
          The N diagonal elements of T.
[in]E2
          E2 is DOUBLE PRECISION array, dimension (N-1)
          The Squares of the (N-1) subdiagonal elements of T.
[in]IFIRST
          IFIRST is INTEGER
          The index of the first eigenvalue to be computed.
[in]ILAST
          ILAST is INTEGER
          The index of the last eigenvalue to be computed.
[in]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|).
[in]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.
[in,out]W
          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.
[in,out]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.
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (2*N)
          Workspace.
[out]IWORK
          IWORK is INTEGER array, dimension (2*N)
          Workspace.
[in]PIVMIN
          PIVMIN is DOUBLE PRECISION
          The minimum pivot in the Sturm sequence for T.
[in]SPDIAM
          SPDIAM is DOUBLE PRECISION
          The spectral diameter of T.
[out]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