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

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

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

23       DLANEG 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.
28       This routine is called from DLARRB.
29       The current routine does  not  use  the  PIVMIN  parameter  but  rather
30       requires  IEEE-754  propagation  of  Infinities and NaNs.  This routine
31       also has no input range restrictions but does require default exception
32       handling  such  that  x/0  produces Inf when x is non-zero, and Inf/Inf
33       produces NaN.  For more information, see:
34         Marques, Riedy, and Voemel, "Benefits of IEEE-754 Features in
35         Modern Symmetric Tridiagonal Eigensolvers," SIAM Journal on
36         Scientific Computing, v28, n5, 2006.  DOI 10.1137/050641624
37         (Tech report version in LAWN 172 with the same title.)
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ARGUMENTS

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

61       Based on contributions by
62          Osni Marques, LBNL/NERSC, USA
63          Christof Voemel, University of California, Berkeley, USA
64          Jason Riedy, University of California, Berkeley, USA
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68 LAPACK auxiliary routine (versionNo3v.e2m)ber 2008                       DLANEG(1)
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