# slarrb.f man page

slarrb.f —

## Synopsis

### Functions/Subroutines

subroutineslarrb(N, D, LLD, IFIRST, ILAST, RTOL1, RTOL2, OFFSET, W, WGAP, WERR, WORK, IWORK, PIVMIN, SPDIAM, TWIST, INFO)SLARRBprovides limited bisection to locate eigenvalues for more accuracy.

## Function/Subroutine Documentation

### subroutine slarrb (integerN, real, dimension( * )D, real, dimension( * )LLD, integerIFIRST, integerILAST, realRTOL1, realRTOL2, integerOFFSET, real, dimension( * )W, real, dimension( * )WGAP, real, dimension( * )WERR, real, dimension( * )WORK, integer, dimension( * )IWORK, realPIVMIN, realSPDIAM, integerTWIST, integerINFO)

**SLARRB** provides limited bisection to locate eigenvalues for more accuracy.

**Purpose:**

```
Given the relatively robust representation(RRR) L D L^T, SLARRB
does "limited" bisection to refine the eigenvalues of L D L^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 and their gaps are input in WERR
and WGAP, respectively. 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 the diagonal matrix D.
```

*LLD*

```
LLD is REAL array, dimension (N-1)
The (N-1) elements L(i)*L(i)*D(i).
```

*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.
```

*RTOL1*

`RTOL1 is REAL`

*RTOL2*

```
RTOL2 is REAL
Tolerance for the convergence of the bisection intervals.
An interval [LEFT,RIGHT] has converged if
RIGHT-LEFT.LT.MAX( RTOL1*GAP, RTOL2*MAX(|LEFT|,|RIGHT|) )
where GAP is the (estimated) distance to the nearest
eigenvalue.
```

*OFFSET*

```
OFFSET is INTEGER
Offset for the arrays W, WGAP 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 throug
ILAST.
On output, these estimates are refined.
```

*WGAP*

```
WGAP is REAL array, dimension (N-1)
On input, the (estimated) gaps between consecutive
eigenvalues of L D L^T, i.e., WGAP(I-OFFSET) is the gap between
eigenvalues I and I+1. Note that if IFIRST.EQ.ILAST
then WGAP(IFIRST-OFFSET) must be set to ZERO.
On output, these gaps 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.
```

*SPDIAM*

```
SPDIAM is REAL
The spectral diameter of the matrix.
```

*TWIST*

```
TWIST is INTEGER
The twist index for the twisted factorization that is used
for the negcount.
TWIST = N: Compute negcount from L D L^T - LAMBDA I = L+ D+ L+^T
TWIST = 1: Compute negcount from L D L^T - LAMBDA I = U- D- U-^T
TWIST = R: Compute negcount from L D L^T - LAMBDA I = N(r) D(r) N(r)
```

*INFO*

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

**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 195 of file slarrb.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

Sat Nov 16 2013 Version 3.4.2 LAPACK