1SLARRJ(1)           LAPACK auxiliary routine (version 3.1)           SLARRJ(1)
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NAME

6       SLARRJ  - initial eigenvalue approximations of T, SLARRJ does bisection
7       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

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

82       Based on contributions by
83          Beresford Parlett, University of California, Berkeley, USA
84          Jim Demmel, University of California, Berkeley, USA
85          Inderjit Dhillon, University of Texas, Austin, USA
86          Osni Marques, LBNL/NERSC, USA
87          Christof Voemel, University of California, Berkeley, USA
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92 LAPACK auxiliary routine (versionNo3v.e1m)ber 2006                       SLARRJ(1)