---
name: "dlarrj"
section: "3"
platform: "linux"
package: "lapack-doc"
version: "3.12.1-2"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/dlarrj.f"
---

# dlarrj(3)

Part of [dlarrj.f(3)](/dlarrj.f/3.md).

## NAME

SRC/dlarrj.f

## SYNOPSIS

### Functions/Subroutines

subroutine **dlarrj** (n, d, e2, ifirst, ilast, rtol, offset, w, werr, work, iwork, pivmin, spdiam, info)\
 **DLARRJ** performs refinement of the initial estimates of the eigenvalues of the matrix T.

## Function/Subroutine Documentation

### subroutine dlarrj (integer n, double precision, dimension( \* ) d, double precision, dimension( \* ) e2, integer ifirst, integer ilast, double precision rtol, integer offset, double precision, dimension( \* ) w, double precision, dimension( \* ) werr, double precision, dimension( \* ) work, integer, dimension( \* ) iwork, double precision pivmin, double precision spdiam, integer info)

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

**Purpose:**

```
!>
!> Given the initial eigenvalue approximations of T, DLARRJ
!> 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 DOUBLE PRECISION array, dimension (N)
!>          The N diagonal elements of T.
!>
```

*E2*

```
!>          E2 is DOUBLE PRECISION 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 DOUBLE PRECISION
!>          Tolerance for the convergence of the bisection intervals.
!>          An interval [LEFT,RIGHT] has converged if
!>          RIGHT-LEFT < 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (2*N)
!>          Workspace.
!>
```

*IWORK*

```
!>          IWORK is INTEGER array, dimension (2*N)
!>          Workspace.
!>
```

*PIVMIN*

```
!>          PIVMIN is DOUBLE PRECISION
!>          The minimum pivot in the Sturm sequence for T.
!>
```

*SPDIAM*

```
!>          SPDIAM is DOUBLE PRECISION
!>          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.

**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 **165** of file **dlarrj.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.