1SLARRA(1)           LAPACK auxiliary routine (version 3.1)           SLARRA(1)
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NAME

6       SLARRA - splitting points with threshold SPLTOL
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SYNOPSIS

9       SUBROUTINE SLARRA( N, D, E, E2, SPLTOL, TNRM, NSPLIT, ISPLIT, INFO )
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11           IMPLICIT       NONE
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13           INTEGER        INFO, N, NSPLIT
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15           REAL           SPLTOL, TNRM
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17           INTEGER        ISPLIT( * )
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19           REAL           D( * ), E( * ), E2( * )
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PURPOSE

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

27       N       (input) INTEGER
28               The order of the matrix. N > 0.
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30       D       (input) REAL             array, dimension (N)
31               On entry, the N diagonal elements of the tridiagonal matrix T.
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33       E       (input/output) REAL             array, dimension (N)
34               On entry, the first (N-1) entries contain the subdiagonal  ele‐
35               ments  of  the  tridiagonal matrix T; E(N) need not be set.  On
36               exit, the entries E( ISPLIT( I ) ), 1 <= I <= NSPLIT,  are  set
37               to zero, the other entries of E are untouched.
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39       E2      (input/output) REAL             array, dimension (N)
40               On  entry,  the  first (N-1) entries contain the SQUARES of the
41               subdiagonal elements of the tridiagonal matrix  T;  E2(N)  need
42               not  be set.  On exit, the entries E2( ISPLIT( I ) ), 1 <= I <=
43               NSPLIT, have been set to zero
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45               SPLTOL (input) REAL The threshold for splitting.  Two  criteria
46               can be used:
47               SPLTOL<0 : criterion based on absolute off-diagonal value
48               SPLTOL>0 : criterion that preserves relative accuracy
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50               TNRM (input) REAL The norm of the matrix.
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52       NSPLIT  (output) INTEGER
53               The number of blocks T splits into. 1 <= NSPLIT <= N.
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55       ISPLIT  (output) INTEGER array, dimension (N)
56               The  splitting  points,  at which T breaks up into blocks.  The
57               first block consists of rows/columns 1 to ISPLIT(1), the second
58               of  rows/columns  ISPLIT(1)+1  through ISPLIT(2), etc., and the
59               NSPLIT-th consists of rows/columns  ISPLIT(NSPLIT-1)+1  through
60               ISPLIT(NSPLIT)=N.
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62       INFO    (output) INTEGER
63               = 0:  successful exit
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FURTHER DETAILS

66       Based on contributions by
67          Beresford Parlett, University of California, Berkeley, USA
68          Jim Demmel, University of California, Berkeley, USA
69          Inderjit Dhillon, University of Texas, Austin, USA
70          Osni Marques, LBNL/NERSC, USA
71          Christof Voemel, University of California, Berkeley, USA
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76 LAPACK auxiliary routine (versionNo3v.e1m)ber 2006                       SLARRA(1)