---
name: "larra"
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/larra"
---

# larra(3)

larra: step in stemr

## NAME

larra - larra: step in stemr

## SYNOPSIS

### Functions

subroutine **dlarra** (n, d, e, e2, spltol, tnrm, nsplit, isplit, info)\
 **DLARRA** computes the splitting points with the specified threshold.  subroutine **slarra** (n, d, e, e2, spltol, tnrm, nsplit, isplit, info)\
 **SLARRA** computes the splitting points with the specified threshold.

## Detailed Description

## Function Documentation

### subroutine dlarra (integer n, double precision, dimension( \* ) d, double precision, dimension( \* ) e, double precision, dimension( \* ) e2, double precision spltol, double precision tnrm, integer nsplit, integer, dimension( \* ) isplit, integer info)

**DLARRA** computes the splitting points with the specified threshold.

**Purpose:**

```
!>
!> Compute the splitting points with threshold SPLTOL.
!> DLARRA sets any  off-diagonal elements to zero.
!>
```

**Parameters**

*N*

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

*D*

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

*E*

```
!>          E is DOUBLE PRECISION array, dimension (N)
!>          On entry, the first (N-1) entries contain the subdiagonal
!>          elements of the tridiagonal matrix T; E(N) need not be set.
!>          On exit, the entries E( ISPLIT( I ) ), 1 <= I <= NSPLIT,
!>          are set to zero, the other entries of E are untouched.
!>
```

*E2*

```
!>          E2 is DOUBLE PRECISION array, dimension (N)
!>          On entry, the first (N-1) entries contain the SQUARES of the
!>          subdiagonal elements of the tridiagonal matrix T;
!>          E2(N) need not be set.
!>          On exit, the entries E2( ISPLIT( I ) ),
!>          1 <= I <= NSPLIT, have been set to zero
!>
```

*SPLTOL*

```
!>          SPLTOL is DOUBLE PRECISION
!>          The threshold for splitting. Two criteria can be used:
!>          SPLTOL<0 : criterion based on absolute off-diagonal value
!>          SPLTOL>0 : criterion that preserves relative accuracy
!>
```

*TNRM*

```
!>          TNRM is DOUBLE PRECISION
!>          The norm of the matrix.
!>
```

*NSPLIT*

```
!>          NSPLIT is INTEGER
!>          The number of blocks T splits into. 1 <= NSPLIT <= N.
!>
```

*ISPLIT*

```
!>          ISPLIT is INTEGER array, dimension (N)
!>          The splitting points, at which T breaks up into blocks.
!>          The first block consists of rows/columns 1 to ISPLIT(1),
!>          the second of rows/columns ISPLIT(1)+1 through ISPLIT(2),
!>          etc., and the NSPLIT-th consists of rows/columns
!>          ISPLIT(NSPLIT-1)+1 through ISPLIT(NSPLIT)=N.
!>
```

*INFO*

```
!>          INFO is INTEGER
!>          = 0:  successful exit
!>
```

**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 **134** of file **dlarra.f**.

### subroutine slarra (integer n, real, dimension( \* ) d, real, dimension( \* ) e, real, dimension( \* ) e2, real spltol, real tnrm, integer nsplit, integer, dimension( \* ) isplit, integer info)

**SLARRA** computes the splitting points with the specified threshold.

**Purpose:**

```
!>
!> Compute the splitting points with threshold SPLTOL.
!> SLARRA sets any  off-diagonal elements to zero.
!>
```

**Parameters**

*N*

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

*D*

```
!>          D is REAL array, dimension (N)
!>          On entry, the N diagonal elements of the tridiagonal
!>          matrix T.
!>
```

*E*

```
!>          E is REAL array, dimension (N)
!>          On entry, the first (N-1) entries contain the subdiagonal
!>          elements of the tridiagonal matrix T; E(N) need not be set.
!>          On exit, the entries E( ISPLIT( I ) ), 1 <= I <= NSPLIT,
!>          are set to zero, the other entries of E are untouched.
!>
```

*E2*

```
!>          E2 is REAL array, dimension (N)
!>          On entry, the first (N-1) entries contain the SQUARES of the
!>          subdiagonal elements of the tridiagonal matrix T;
!>          E2(N) need not be set.
!>          On exit, the entries E2( ISPLIT( I ) ),
!>          1 <= I <= NSPLIT, have been set to zero
!>
```

*SPLTOL*

```
!>          SPLTOL is REAL
!>          The threshold for splitting. Two criteria can be used:
!>          SPLTOL<0 : criterion based on absolute off-diagonal value
!>          SPLTOL>0 : criterion that preserves relative accuracy
!>
```

*TNRM*

```
!>          TNRM is REAL
!>          The norm of the matrix.
!>
```

*NSPLIT*

```
!>          NSPLIT is INTEGER
!>          The number of blocks T splits into. 1 <= NSPLIT <= N.
!>
```

*ISPLIT*

```
!>          ISPLIT is INTEGER array, dimension (N)
!>          The splitting points, at which T breaks up into blocks.
!>          The first block consists of rows/columns 1 to ISPLIT(1),
!>          the second of rows/columns ISPLIT(1)+1 through ISPLIT(2),
!>          etc., and the NSPLIT-th consists of rows/columns
!>          ISPLIT(NSPLIT-1)+1 through ISPLIT(NSPLIT)=N.
!>
```

*INFO*

```
!>          INFO is INTEGER
!>          = 0:  successful exit
!>
```

**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 **134** of file **slarra.f**.

## Author

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