# dlarrf.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
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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

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