# dlarrf.f man page

dlarrf.f

## Synopsis

### Functions/Subroutines

subroutine dlarrf (N, D, L, LD, CLSTRT, CLEND, W, WGAP, WERR, SPDIAM, CLGAPL, CLGAPR, PIVMIN, SIGMA, DPLUS, LPLUS, WORK, INFO)
DLARRF finds a new relatively robust representation such that at least one of the eigenvalues is relatively isolated.

## Function/Subroutine Documentation

### subroutine dlarrf (integer N, double precision, dimension( * ) D, double precision, dimension( * ) L, double precision, dimension( * ) LD, integer CLSTRT, integer CLEND, double precision, dimension( * ) W, double precision, dimension( * ) WGAP, double precision, dimension( * ) WERR, double precision SPDIAM, double precision CLGAPL, double precision CLGAPR, double precision PIVMIN, double precision SIGMA, double precision, dimension( * ) DPLUS, double precision, dimension( * ) LPLUS, double precision, dimension( * ) WORK, integer INFO)

DLARRF finds a new relatively robust representation such that at least one of the eigenvalues is relatively isolated.

Purpose:

``` Given the initial representation L D L^T and its cluster of close
eigenvalues (in a relative measure), W( CLSTRT ), W( CLSTRT+1 ), ...
W( CLEND ), DLARRF finds a new relatively robust representation
L D L^T - SIGMA I = L(+) D(+) L(+)^T such that at least one of the
eigenvalues of L(+) D(+) L(+)^T is relatively isolated.```
Parameters:

N

```          N is INTEGER
The order of the matrix (subblock, if the matrix split).```

D

```          D is DOUBLE PRECISION array, dimension (N)
The N diagonal elements of the diagonal matrix D.```

L

```          L is DOUBLE PRECISION array, dimension (N-1)
The (N-1) subdiagonal elements of the unit bidiagonal
matrix L.```

LD

```          LD is DOUBLE PRECISION array, dimension (N-1)
The (N-1) elements L(i)*D(i).```

CLSTRT

```          CLSTRT is INTEGER
The index of the first eigenvalue in the cluster.```

CLEND

```          CLEND is INTEGER
The index of the last eigenvalue in the cluster.```

W

```          W is DOUBLE PRECISION array, dimension
dimension is >=  (CLEND-CLSTRT+1)
The eigenvalue APPROXIMATIONS of L D L^T in ascending order.
W( CLSTRT ) through W( CLEND ) form the cluster of relatively
close eigenalues.```

WGAP

```          WGAP is DOUBLE PRECISION array, dimension
dimension is >=  (CLEND-CLSTRT+1)
The separation from the right neighbor eigenvalue in W.```

WERR

```          WERR is DOUBLE PRECISION array, dimension
dimension is  >=  (CLEND-CLSTRT+1)
WERR contain the semiwidth of the uncertainty
interval of the corresponding eigenvalue APPROXIMATION in W```

SPDIAM

```          SPDIAM is DOUBLE PRECISION
estimate of the spectral diameter obtained from the
Gerschgorin intervals```

CLGAPL

`          CLGAPL is DOUBLE PRECISION`

CLGAPR

```          CLGAPR is DOUBLE PRECISION
absolute gap on each end of the cluster.
Set by the calling routine to protect against shifts too close
to eigenvalues outside the cluster.```

PIVMIN

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

SIGMA

```          SIGMA is DOUBLE PRECISION
The shift used to form L(+) D(+) L(+)^T.```

DPLUS

```          DPLUS is DOUBLE PRECISION array, dimension (N)
The N diagonal elements of the diagonal matrix D(+).```

LPLUS

```          LPLUS is DOUBLE PRECISION array, dimension (N-1)
The first (N-1) elements of LPLUS contain the subdiagonal
elements of the unit bidiagonal matrix L(+).```

WORK

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

INFO

```          INFO is INTEGER
Signals processing OK (=0) or failure (=1)```
Author:

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date:

June 2016

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 195 of file dlarrf.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page dlarrf(3) is an alias of dlarrf.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK