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

6       SLANEG  -  the  Sturm  count, the number of negative pivots encountered
7       while factoring tridiagonal T - sigma I = L D L^T
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SYNOPSIS

10       FUNCTION SLANEG( N, D, LLD, SIGMA, PIVMIN, R )
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12           IMPLICIT     NONE
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14           INTEGER      SLANEG
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16           INTEGER      N, R
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18           REAL         PIVMIN, SIGMA
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20           REAL         D( * ), LLD( * )
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PURPOSE

23       SLANEG computes the Sturm count, the number of negative pivots  encoun‐
24       tered  while  factoring tridiagonal T - sigma I = L D L^T.  This imple‐
25       mentation works directly on the factors without forming the tridiagonal
26       matrix  T.  The Sturm count is also the number of eigenvalues of T less
27       than sigma.
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29       This routine is called from SLARRB.
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31       The current routine does  not  use  the  PIVMIN  parameter  but  rather
32       requires  IEEE-754  propagation  of  Infinities and NaNs.  This routine
33       also has no input range restrictions but does require default exception
34       handling  such  that  x/0  produces Inf when x is non-zero, and Inf/Inf
35       produces NaN.  For more information, see:
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37         Marques, Riedy, and Voemel, "Benefits of IEEE-754 Features in
38         Modern Symmetric Tridiagonal Eigensolvers," SIAM Journal on
39         Scientific Computing, v28, n5, 2006.  DOI 10.1137/050641624
40         (Tech report version in LAWN 172 with the same title.)
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ARGUMENTS

44       N       (input) INTEGER
45               The order of the matrix.
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47       D       (input) REAL             array, dimension (N)
48               The N diagonal elements of the diagonal matrix D.
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50       LLD     (input) REAL             array, dimension (N-1)
51               The (N-1) elements L(i)*L(i)*D(i).
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53       SIGMA   (input) REAL
54               Shift amount in T - sigma I = L D L^T.
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56       PIVMIN  (input) REAL
57               The minimum pivot in the Sturm sequence.  May be used when zero
58               pivots are encountered on non-IEEE-754 architectures.
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60       R       (input) INTEGER
61               The  twist index for the twisted factorization that is used for
62               the negcount.
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FURTHER DETAILS

65       Based on contributions by
66          Osni Marques, LBNL/NERSC, USA
67          Christof Voemel, University of California, Berkeley, USA
68          Jason Riedy, University of California, Berkeley, USA
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73 LAPACK auxiliary routine (versionNo3v.e1m)ber 2006                       SLANEG(1)
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