# slarrj.f man page

slarrj.f —

## Synopsis

### Functions/Subroutines

subroutineslarrj(N, D, E2, IFIRST, ILAST, RTOL, OFFSET, W, WERR, WORK, IWORK, PIVMIN, SPDIAM, INFO)SLARRJperforms refinement of the initial estimates of the eigenvalues of the matrix T.

## Function/Subroutine Documentation

### subroutine slarrj (integerN, real, dimension( * )D, real, dimension( * )E2, integerIFIRST, integerILAST, realRTOL, integerOFFSET, real, dimension( * )W, real, dimension( * )WERR, real, dimension( * )WORK, integer, dimension( * )IWORK, realPIVMIN, realSPDIAM, integerINFO)

**SLARRJ** performs refinement of the initial estimates of the eigenvalues of the matrix T.

**Purpose:**

```
Given the initial eigenvalue approximations of T, SLARRJ
does bisection to refine the eigenvalues of 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 in WERR. 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 T.
```

*E2*

```
E2 is REAL array, dimension (N-1)
The Squares of the (N-1) subdiagonal elements of T.
```

*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.
```

*RTOL*

```
RTOL is REAL
Tolerance for the convergence of the bisection intervals.
An interval [LEFT,RIGHT] has converged if
RIGHT-LEFT.LT.RTOL*MAX(|LEFT|,|RIGHT|).
```

*OFFSET*

```
OFFSET is INTEGER
Offset for the arrays W 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 through
ILAST.
On output, these estimates 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 for T.
```

*SPDIAM*

```
SPDIAM is REAL
The spectral diameter of T.
```

*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 167 of file slarrj.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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