# laneg - Man Page

laneg: Sturm count

## Synopsis

### Functions

integer function dlaneg (n, d, lld, sigma, pivmin, r)
DLANEG computes the Sturm count.
integer function slaneg (n, d, lld, sigma, pivmin, r)
SLANEG computes the Sturm count.

## Function 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.

Contributors:

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

Definition at line 117 of file dlaneg.f.

### integer function slaneg (integer n, real, dimension( * ) d, real, dimension( * ) lld, real sigma, real pivmin, integer r)

SLANEG computes the Sturm count.

Purpose:

``` SLANEG 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 SLARRB.

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 REAL array, dimension (N)
The N diagonal elements of the diagonal matrix D.```

LLD

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

SIGMA

```          SIGMA is REAL
Shift amount in T - sigma I = L D L^T.```

PIVMIN

```          PIVMIN is REAL
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.

Contributors:

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

Definition at line 117 of file slaneg.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Info

Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK