# dlaneg(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

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

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)```

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```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

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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