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

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

10       SUBROUTINE DLARRJ( 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           DOUBLE         PRECISION PIVMIN, RTOL, SPDIAM
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17           INTEGER        IWORK( * )
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19           DOUBLE         PRECISION  D( * ), E2( * ), W( * ), WERR( * ), WORK(
20                          * )
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PURPOSE

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

32       N       (input) INTEGER
33               The order of the matrix.
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35       D       (input) DOUBLE PRECISION array, dimension (N)
36               The N diagonal elements of T.
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38       E2      (input) DOUBLE PRECISION 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) DOUBLE PRECISION
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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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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91 LAPACK auxiliary routine (versionNo3v.e2m)ber 2008                       DLARRJ(1)