dlarrj man page on Scientific

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

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

SYNOPSIS
SUBROUTINE DLARRJ( N, D, E2, IFIRST,  ILAST,  RTOL,  OFFSET,  W,	 WERR,
WORK, IWORK, PIVMIN, SPDIAM, INFO )

INTEGER	  IFIRST, ILAST, INFO, N, OFFSET

DOUBLE	  PRECISION PIVMIN, RTOL, SPDIAM

INTEGER	  IWORK( * )

DOUBLE	  PRECISION  D( * ), E2( * ), W( * ), WERR( * ), WORK(
* )

PURPOSE
Given the initial eigenvalue approximations of T, DLARRJ	 does	bisec‐
tion  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	 main‐
tained  by storing their mid-points and semi-widths in the arrays W and
WERR respectively.

ARGUMENTS
N       (input) INTEGER
The order of the matrix.

D       (input) DOUBLE PRECISION array, dimension (N)
The N diagonal elements of T.

E2      (input) DOUBLE PRECISION array, dimension (N-1)
The Squares of the (N-1) subdiagonal elements of T.

IFIRST  (input) INTEGER
The index of the first eigenvalue to be computed.

ILAST   (input) INTEGER
The index of the last eigenvalue to be computed.

RTOL   (input) DOUBLE PRECISION
Tolerance for the convergence of the  bisection  intervals.   An
interval	   [LEFT,RIGHT]	    has	    converged	  if	RIGHT-
LEFT.LT.RTOL*MAX(|LEFT|,|RIGHT|).

OFFSET  (input) 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       (input/output) 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.

WERR    (input/output) 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.

WORK    (workspace) DOUBLE PRECISION array, dimension (2*N)
Workspace.

IWORK   (workspace) INTEGER array, dimension (2*N)
Workspace.

PIVMIN  (input) DOUBLE PRECISION
The minimum pivot in the Sturm sequence for T.

SPDIAM  (input) DOUBLE PRECISION
The spectral diameter of T.

INFO    (output) INTEGER
Error flag.

FURTHER DETAILS
Based on contributions by
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

LAPACK auxiliary routine (versioNovember 2008			     DLARRJ(1)
```
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