---
name: "dlarrk.f"
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/dlarrk.f"
---

# dlarrk.f(3)

## NAME

SRC/dlarrk.f

## SYNOPSIS

### Functions/Subroutines

subroutine **dlarrk** (n, iw, gl, gu, d, e2, pivmin, reltol, w, werr, info)\
 **DLARRK** computes one eigenvalue of a symmetric tridiagonal matrix T to suitable accuracy.

## Function/Subroutine Documentation

### subroutine dlarrk (integer n, integer iw, double precision gl, double precision gu, double precision, dimension( \* ) d, double precision, dimension( \* ) e2, double precision pivmin, double precision reltol, double precision w, double precision werr, integer info)

**DLARRK** computes one eigenvalue of a symmetric tridiagonal matrix T to suitable accuracy.

**Purpose:**

```
!>
!> DLARRK computes one eigenvalue of a symmetric tridiagonal
!> matrix T to suitable accuracy. This is an auxiliary code to be
!> called from DSTEMR.
!>
!> To avoid overflow, the matrix must be scaled so that its
!> largest element is no greater than overflow**(1/2) * underflow**(1/4) in absolute value, and for greatest
!> accuracy, it should not be much smaller than that.
!>
!> See W. Kahan , Report CS41, Computer Science Dept., Stanford
!> University, July 21, 1966.
!>
```

**Parameters**

*N*

```
!>          N is INTEGER
!>          The order of the tridiagonal matrix T.  N >= 0.
!>
```

*IW*

```
!>          IW is INTEGER
!>          The index of the eigenvalues to be returned.
!>
```

*GL*

```
!>          GL is DOUBLE PRECISION
!>
```

*GU*

```
!>          GU is DOUBLE PRECISION
!>          An upper and a lower bound on the eigenvalue.
!>
```

*D*

```
!>          D is DOUBLE PRECISION array, dimension (N)
!>          The n diagonal elements of the tridiagonal matrix T.
!>
```

*E2*

```
!>          E2 is DOUBLE PRECISION array, dimension (N-1)
!>          The (n-1) squared off-diagonal elements of the tridiagonal matrix T.
!>
```

*PIVMIN*

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

*RELTOL*

```
!>          RELTOL is DOUBLE PRECISION
!>          The minimum relative width of an interval.  When an interval
!>          is narrower than RELTOL times the larger (in
!>          magnitude) endpoint, then it is considered to be
!>          sufficiently small, i.e., converged.  Note: this should
!>          always be at least radix*machine epsilon.
!>
```

*W*

```
!>          W is DOUBLE PRECISION
!>
```

*WERR*

```
!>          WERR is DOUBLE PRECISION
!>          The error bound on the corresponding eigenvalue approximation
!>          in W.
!>
```

*INFO*

```
!>          INFO is INTEGER
!>          = 0:       Eigenvalue converged
!>          = -1:      Eigenvalue did NOT converge
!>
```

**Internal Parameters:**

```
!>  FUDGE   DOUBLE PRECISION, default = 2
!>          A  to widen the Gershgorin intervals.
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **143** of file **dlarrk.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.