# dlaneg.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
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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 (integer N, double precision, dimension( * ) D, double precision, dimension( * ) LLD, double precision SIGMA, double precision PIVMIN, integer R)

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:

December 2016

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.

## Author

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