integer function dlaneg	(	integer	N,
		double precision, dimension( * )	D,
		double precision, dimension( * )	LLD,
		double precision	SIGMA,
		double precision	PIVMIN,
		integer	R
	)

DLANEG computes the Sturm count.

Download DLANEG + dependencies [TGZ] [ZIP] [TXT]

Purpose:

 DLANEG computes the Sturm count, the number of negative pivots
 encountered while factoring tridiagonal T - sigma I = L D L^T.
 This implementation works directly on the factors without forming
 the tridiagonal matrix T.  The Sturm count is also the number of
 eigenvalues of T less than sigma.

 This routine is called from DLARRB.

 The current routine does not use the PIVMIN parameter but rather
 requires IEEE-754 propagation of Infinities and NaNs.  This
 routine also has no input range restrictions but does require
 default exception handling such that x/0 produces Inf when x is
 non-zero, and Inf/Inf produces NaN.  For more information, see:

   Marques, Riedy, and Voemel, "Benefits of IEEE-754 Features in
   Modern Symmetric Tridiagonal Eigensolvers," SIAM Journal on
   Scientific Computing, v28, n5, 2006.  DOI 10.1137/050641624
   (Tech report version in LAWN 172 with the same title.)

Parameters

[in]	N	N is INTEGER The order of the matrix.
[in]	D	D is DOUBLE PRECISION array, dimension (N) The N diagonal elements of the diagonal matrix D.
[in]	LLD	LLD is DOUBLE PRECISION array, dimension (N-1) The (N-1) elements L(i)*L(i)*D(i).
[in]	SIGMA	SIGMA is DOUBLE PRECISION Shift amount in T - sigma I = L D L^T.
[in]	PIVMIN	PIVMIN is DOUBLE PRECISION The minimum pivot in the Sturm sequence. May be used when zero pivots are encountered on non-IEEE-754 architectures.
[in]	R	R is INTEGER The twist index for the twisted factorization that is used for the negcount.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date

September 2012

Contributors:

Osni Marques, LBNL/NERSC, USA
Christof Voemel, University of California, Berkeley, USA
Jason Riedy, University of California, Berkeley, USA

Definition at line 120 of file dlaneg.f.

*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      INTEGER            n, r
      DOUBLE PRECISION   pivmin, sigma
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   d( * ), lld( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   zero, one
      parameter            ( zero = 0.0d0, one = 1.0d0 )
*     Some architectures propagate Infinities and NaNs very slowly, so
*     the code computes counts in BLKLEN chunks.  Then a NaN can
*     propagate at most BLKLEN columns before being detected.  This is
*     not a general tuning parameter; it needs only to be just large
*     enough that the overhead is tiny in common cases.
      INTEGER blklen
      parameter( blklen = 128 )
*     ..
*     .. Local Scalars ..
      INTEGER            bj, j, neg1, neg2, negcnt
      DOUBLE PRECISION   bsav, dminus, dplus, gamma, p, t, tmp
      LOGICAL sawnan
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC min, max
*     ..
*     .. External Functions ..
      LOGICAL disnan
      EXTERNAL disnan
*     ..
*     .. Executable Statements ..

      negcnt = 0

*     I) upper part: L D L^T - SIGMA I = L+ D+ L+^T
      t = -sigma
      DO 210 bj = 1, r-1, blklen
         neg1 = 0
         bsav = t
         DO 21 j = bj, min(bj+blklen-1, r-1)
            dplus = d( j ) + t
            IF( dplus.LT.zero ) neg1 = neg1 + 1
            tmp = t / dplus
            t = tmp * lld( j ) - sigma
 21      CONTINUE
         sawnan = disnan( t )
*     Run a slower version of the above loop if a NaN is detected.
*     A NaN should occur only with a zero pivot after an infinite
*     pivot.  In that case, substituting 1 for T/DPLUS is the
*     correct limit.
         IF( sawnan ) THEN
            neg1 = 0
            t = bsav
            DO 22 j = bj, min(bj+blklen-1, r-1)
               dplus = d( j ) + t
               IF( dplus.LT.zero ) neg1 = neg1 + 1
               tmp = t / dplus
               IF (disnan(tmp)) tmp = one
               t = tmp * lld(j) - sigma
 22         CONTINUE
         END IF
         negcnt = negcnt + neg1
 210  CONTINUE
*
*     II) lower part: L D L^T - SIGMA I = U- D- U-^T
      p = d( n ) - sigma
      DO 230 bj = n-1, r, -blklen
         neg2 = 0
         bsav = p
         DO 23 j = bj, max(bj-blklen+1, r), -1
            dminus = lld( j ) + p
            IF( dminus.LT.zero ) neg2 = neg2 + 1
            tmp = p / dminus
            p = tmp * d( j ) - sigma
 23      CONTINUE
         sawnan = disnan( p )
*     As above, run a slower version that substitutes 1 for Inf/Inf.
*
         IF( sawnan ) THEN
            neg2 = 0
            p = bsav
            DO 24 j = bj, max(bj-blklen+1, r), -1
               dminus = lld( j ) + p
               IF( dminus.LT.zero ) neg2 = neg2 + 1
               tmp = p / dminus
               IF (disnan(tmp)) tmp = one
               p = tmp * d(j) - sigma
 24         CONTINUE
         END IF
         negcnt = negcnt + neg2
 230  CONTINUE
*
*     III) Twist index
*       T was shifted by SIGMA initially.
      gamma = (t + sigma) + p
      IF( gamma.LT.zero ) negcnt = negcnt+1

      dlaneg = negcnt