1SLARRA(1)           LAPACK auxiliary routine (version 3.2)           SLARRA(1)
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NAME

6       SLARRA - the 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

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

62       Based on contributions by
63          Beresford Parlett, University of California, Berkeley, USA
64          Jim Demmel, University of California, Berkeley, USA
65          Inderjit Dhillon, University of Texas, Austin, USA
66          Osni Marques, LBNL/NERSC, USA
67          Christof Voemel, University of California, Berkeley, USA
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71 LAPACK auxiliary routine (versionNo3v.e2m)ber 2008                       SLARRA(1)