dlaneg.f(3) [centos man page]

dlaneg.f(3)							      LAPACK							       dlaneg.f(3)

NAME

       dlaneg.f -

SYNOPSIS

   Functions/Subroutines
       INTEGER function dlaneg (N, D, LLD, SIGMA, PIVMIN, R)
	   DLANEG computes the Sturm count.

Function/Subroutine Documentation
   INTEGER function dlaneg (integerN, double precision, dimension( * )D, double precision, dimension( * )LLD, double precisionSIGMA, double
       precisionPIVMIN, integerR)
       DLANEG computes the Sturm count.

       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:
	   N

		     N is INTEGER
		     The order of the matrix.

	   D

		     D is DOUBLE PRECISION array, dimension (N)
		     The N diagonal elements of the diagonal matrix D.

	   LLD

		     LLD is DOUBLE PRECISION array, dimension (N-1)
		     The (N-1) elements L(i)*L(i)*D(i).

	   SIGMA

		     SIGMA is DOUBLE PRECISION
		     Shift amount in T - sigma I = L D L^T.

	   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.

	   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 119 of file dlaneg.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2							  Tue Sep 25 2012						       dlaneg.f(3)

Check Out this Related Man Page

dlarrc.f(3)							      LAPACK							       dlarrc.f(3)

NAME

       dlarrc.f -

SYNOPSIS

   Functions/Subroutines
       subroutine dlarrc (JOBT, N, VL, VU, D, E, PIVMIN, EIGCNT, LCNT, RCNT, INFO)
	   DLARRC computes the number of eigenvalues of the symmetric tridiagonal matrix.

Function/Subroutine Documentation
   subroutine dlarrc (characterJOBT, integerN, double precisionVL, double precisionVU, double precision, dimension( * )D, double precision,
       dimension( * )E, double precisionPIVMIN, integerEIGCNT, integerLCNT, integerRCNT, integerINFO)
       DLARRC computes the number of eigenvalues of the symmetric tridiagonal matrix.

       Purpose:

	    Find the number of eigenvalues of the symmetric tridiagonal matrix T
	    that are in the interval (VL,VU] if JOBT = 'T', and of L D L^T
	    if JOBT = 'L'.

       Parameters:
	   JOBT

		     JOBT is CHARACTER*1
		     = 'T':  Compute Sturm count for matrix T.
		     = 'L':  Compute Sturm count for matrix L D L^T.

	   N

		     N is INTEGER
		     The order of the matrix. N > 0.

	   VL

		     VL is DOUBLE PRECISION

	   VU

		     VU is DOUBLE PRECISION
		     The lower and upper bounds for the eigenvalues.

	   D

		     D is DOUBLE PRECISION array, dimension (N)
		     JOBT = 'T': The N diagonal elements of the tridiagonal matrix T.
		     JOBT = 'L': The N diagonal elements of the diagonal matrix D.

	   E

		     E is DOUBLE PRECISION array, dimension (N)
		     JOBT = 'T': The N-1 offdiagonal elements of the matrix T.
		     JOBT = 'L': The N-1 offdiagonal elements of the matrix L.

	   PIVMIN

		     PIVMIN is DOUBLE PRECISION
		     The minimum pivot in the Sturm sequence for T.

	   EIGCNT

		     EIGCNT is INTEGER
		     The number of eigenvalues of the symmetric tridiagonal matrix T
		     that are in the interval (VL,VU]

	   LCNT

		     LCNT is INTEGER

	   RCNT

		     RCNT is INTEGER
		     The left and right negcounts of the interval.

	   INFO

		     INFO is INTEGER

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   September 2012

       Contributors:
	   Beresford Parlett, University of California, Berkeley, USA
	    Jim Demmel, University of California, Berkeley, USA
	    Inderjit Dhillon, University of Texas, Austin, USA
	    Osni Marques, LBNL/NERSC, USA
	    Christof Voemel, University of California, Berkeley, USA

       Definition at line 136 of file dlarrc.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2							  Tue Sep 25 2012						       dlarrc.f(3)

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dlaneg.f(3) [centos man page]

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