1SLARRJ(1)           LAPACK auxiliary routine (version 3.2)           SLARRJ(1)
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NAME

6       SLARRJ - the initial eigenvalue approximations of T, SLARRJ does bisec‐
7       tion to refine the eigenvalues of T,
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SYNOPSIS

10       SUBROUTINE SLARRJ( N, D, E2, IFIRST,  ILAST,  RTOL,  OFFSET,  W,  WERR,
11                          WORK, IWORK, PIVMIN, SPDIAM, INFO )
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13           INTEGER        IFIRST, ILAST, INFO, N, OFFSET
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15           REAL           PIVMIN, RTOL, SPDIAM
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17           INTEGER        IWORK( * )
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19           REAL           D( * ), E2( * ), W( * ), WERR( * ), WORK( * )
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PURPOSE

22       Given  the  initial eigenvalue approximations of T, SLARRJ does  bisec‐
23       tion to refine the eigenvalues of T,  W(  IFIRST-OFFSET  )  through  W(
24       ILAST-OFFSET ), to more accuracy. Initial guesses for these eigenvalues
25       are input in W, the  corresponding  estimate  of  the  error  in  these
26       guesses  in  WERR.  During bisection, intervals [left, right] are main‐
27       tained by storing their mid-points and semi-widths in the arrays W  and
28       WERR respectively.
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ARGUMENTS

31       N       (input) INTEGER
32               The order of the matrix.
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34       D       (input) REAL             array, dimension (N)
35               The N diagonal elements of T.
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37       E2      (input) REAL             array, dimension (N-1)
38               The Squares of the (N-1) subdiagonal elements of T.
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40       IFIRST  (input) INTEGER
41               The index of the first eigenvalue to be computed.
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43       ILAST   (input) INTEGER
44               The index of the last eigenvalue to be computed.
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46       RTOL   (input) REAL
47              Tolerance  for  the  convergence of the bisection intervals.  An
48              interval    [LEFT,RIGHT]     has     converged     if     RIGHT-
49              LEFT.LT.RTOL*MAX(|LEFT|,|RIGHT|).
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51       OFFSET  (input) INTEGER
52               Offset  for  the  arrays  W  and  WERR, i.e., the IFIRST-OFFSET
53               through ILAST-OFFSET elements of these arrays are to be used.
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55       W       (input/output) REAL             array, dimension (N)
56               On input, W( IFIRST-OFFSET )  through  W(  ILAST-OFFSET  )  are
57               estimates  of the eigenvalues of L D L^T indexed IFIRST through
58               ILAST.  On output, these estimates are refined.
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60       WERR    (input/output) REAL             array, dimension (N)
61               On input, WERR( IFIRST-OFFSET ) through  WERR(  ILAST-OFFSET  )
62               are  the  errors in the estimates of the corresponding elements
63               in W.  On output, these errors are refined.
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65       WORK    (workspace) REAL             array, dimension (2*N)
66               Workspace.
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68       IWORK   (workspace) INTEGER array, dimension (2*N)
69               Workspace.
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71       PIVMIN  (input) DOUBLE PRECISION
72               The minimum pivot in the Sturm sequence for T.
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74       SPDIAM  (input) DOUBLE PRECISION
75               The spectral diameter of T.
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77       INFO    (output) INTEGER
78               Error flag.
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FURTHER DETAILS

81       Based on contributions by
82          Beresford Parlett, University of California, Berkeley, USA
83          Jim Demmel, University of California, Berkeley, USA
84          Inderjit Dhillon, University of Texas, Austin, USA
85          Osni Marques, LBNL/NERSC, USA
86          Christof Voemel, University of California, Berkeley, USA
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90 LAPACK auxiliary routine (versionNo3v.e2m)ber 2008                       SLARRJ(1)