# slarrf.f man page

slarrf.f —

## Synopsis

### Functions/Subroutines

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

## Function/Subroutine Documentation

### subroutine slarrf (integerN, real, dimension( * )D, real, dimension( * )L, real, dimension( * )LD, integerCLSTRT, integerCLEND, real, dimension( * )W, real, dimension( * )WGAP, real, dimension( * )WERR, realSPDIAM, realCLGAPL, realCLGAPR, realPIVMIN, realSIGMA, real, dimension( * )DPLUS, real, dimension( * )LPLUS, real, dimension( * )WORK, integerINFO)

**SLARRF** 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 ), SLARRF 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 splitted).
```

*D*

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

*L*

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

*LD*

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

*WERR*

```
WERR is REAL 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 REAL
estimate of the spectral diameter obtained from the
Gerschgorin intervals
```

*CLGAPL*

`CLGAPL is REAL`

*CLGAPR*

```
CLGAPR is REAL
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 REAL
The minimum pivot allowed in the Sturm sequence.
```

*SIGMA*

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

*DPLUS*

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

*LPLUS*

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

*WORK*

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

*INFO*

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

**Author:**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date:**

September 2012

**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 191 of file slarrf.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

slarrf(3) is an alias of slarrf.f(3).