# slaneg.f man page

slaneg.f —

## Synopsis

### Functions/Subroutines

INTEGER functionslaneg(N, D, LLD, SIGMA, PIVMIN, R)SLANEGcomputes the Sturm count.

## Function/Subroutine Documentation

### INTEGER function slaneg (integerN, real, dimension( * )D, real, dimension( * )LLD, realSIGMA, realPIVMIN, integerR)

**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
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 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

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 slaneg.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

slaneg(3) is an alias of slaneg.f(3).