---
name: "slarra"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/slarra/3lapack"
---

# slarra(3lapack)

the splitting points with threshold SPLTOL

## NAME

SLARRA - 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

## FURTHER DETAILS

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