# larrj - Man Page

larrj: step in stemr, refine eigval estimates

## Synopsis

### Functions

subroutine dlarrj (n, d, e2, ifirst, ilast, rtol, offset, w, werr, work, iwork, pivmin, spdiam, info)
DLARRJ performs refinement of the initial estimates of the eigenvalues of the matrix T.
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 Documentation

### subroutine dlarrj (integer n, double precision, dimension( * ) d, double precision, dimension( * ) e2, integer ifirst, integer ilast, double precision rtol, integer offset, double precision, dimension( * ) w, double precision, dimension( * ) werr, double precision, dimension( * ) work, integer, dimension( * ) iwork, double precision pivmin, double precision spdiam, integer info)

DLARRJ performs refinement of the initial estimates of the eigenvalues of the matrix T.

Purpose:

``` Given the initial eigenvalue approximations of T, DLARRJ
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 DOUBLE PRECISION array, dimension (N)
The N diagonal elements of T.```

E2

```          E2 is DOUBLE PRECISION 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 DOUBLE PRECISION
Tolerance for the convergence of the bisection intervals.
An interval [LEFT,RIGHT] has converged if
RIGHT-LEFT < 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 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

```          WERR is 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

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

IWORK

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

PIVMIN

```          PIVMIN is DOUBLE PRECISION
The minimum pivot in the Sturm sequence for T.```

SPDIAM

```          SPDIAM is DOUBLE PRECISION
The spectral diameter of T.```

INFO

```          INFO is INTEGER
Error flag.```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

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 165 of file dlarrj.f.

### subroutine slarrj (integer n, real, dimension( * ) d, real, dimension( * ) e2, integer ifirst, integer ilast, real rtol, integer offset, real, dimension( * ) w, real, dimension( * ) werr, real, dimension( * ) work, integer, dimension( * ) iwork, real pivmin, real spdiam, integer info)

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 < 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

NAG Ltd.

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 165 of file slarrj.f.

## Author

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## Info

Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK