# larrf - Man Page

larrf: step in stemr, find relative robust representation (RRR)

## Synopsis

### Functions

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.
subroutine slarrf (n, d, l, ld, clstrt, clend, w, wgap, werr, spdiam, clgapl, clgapr, pivmin, sigma, dplus, lplus, work, info)
SLARRF finds a new relatively robust representation such that at least one of the eigenvalues is relatively isolated.

## Function 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.

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 189 of file dlarrf.f.

### subroutine slarrf (integer n, real, dimension( * ) d, real, dimension( * ) l, real, dimension( * ) ld, integer clstrt, integer clend, real, dimension( * ) w, real, dimension( * ) wgap, real, dimension( * ) werr, real spdiam, real clgapl, real clgapr, real pivmin, real sigma, real, dimension( * ) dplus, real, dimension( * ) lplus, real, dimension( * ) work, integer info)

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 split).```

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

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 189 of file slarrf.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Info

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