Provided by: liblapack-doc_3.3.1-1_all #### NAME

```       LAPACK-3 - the splitting points with threshold SPLTOL

```

#### SYNOPSIS

```       SUBROUTINE SLARRA( N, D, E, E2, SPLTOL, TNRM, NSPLIT, ISPLIT, INFO )

IMPLICIT       NONE

INTEGER        INFO, N, NSPLIT

REAL           SPLTOL, TNRM

INTEGER        ISPLIT( * )

REAL           D( * ), E( * ), E2( * )

```

#### PURPOSE

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

```

#### ARGUMENTS

```        N       (input) INTEGER
The order of the matrix. N > 0.

D       (input) REAL             array, dimension (N)
On entry, the N diagonal elements of the tridiagonal
matrix T.

E       (input/output) 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      (input/output) 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 (input) 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 (input) REAL
The norm of the matrix.

NSPLIT  (output) INTEGER
The number of blocks T splits into. 1 <= NSPLIT <= N.

ISPLIT  (output) 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    (output) INTEGER
= 0:  successful exit

```

#### FURTHERDETAILS

```        Based on contributions by
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

LAPACK auxiliary routine (version 3.2)     April 2011                            SLARRA(3lapack)
```