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slarrj.f(3) LAPACK slarrj.f(3)

NAME

slarrj.f -

SYNOPSIS

Functions/Subroutines


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.

Function/Subroutine Documentation

subroutine slarrj (integerN, real, dimension( * )D, real, dimension( * )E2, integerIFIRST, integerILAST, realRTOL, integerOFFSET, real, dimension( * )W, real, dimension( * )WERR, real, dimension( * )WORK, integer, dimension( * )IWORK, realPIVMIN, realSPDIAM, integerINFO)

SLARRJ performs refinement of the initial estimates of the eigenvalues of the matrix T.
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.
Parameters:
N 
          N is INTEGER
          The order of the matrix.
D 
          D is REAL array, dimension (N)
          The N diagonal elements of T.
E2 
          E2 is REAL 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 REAL
          Tolerance for the convergence of the bisection intervals.
          An interval [LEFT,RIGHT] has converged if
          RIGHT-LEFT.LT.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 
          W is 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 
          WERR is 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 
          WORK is REAL array, dimension (2*N)
          Workspace.
IWORK 
          IWORK is INTEGER array, dimension (2*N)
          Workspace.
PIVMIN 
          PIVMIN is REAL
          The minimum pivot in the Sturm sequence for T.
SPDIAM 
          SPDIAM is REAL
          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.
Date:
September 2012
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 167 of file slarrj.f.

Author

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