# dlarra.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
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dlarra.f

## SYNOPSIS

### Functions/Subroutines

subroutine dlarra (N, D, E, E2, SPLTOL, TNRM, NSPLIT, ISPLIT, INFO)
DLARRA computes the splitting points with the specified threshold.

## Function/Subroutine 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 "small" 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

NAG Ltd.

Date:

June 2017

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 138 of file dlarra.f.

## Author

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