slaneg (3) - Linux Manuals

slaneg.f -

SYNOPSIS

Functions/Subroutines

INTEGER function slaneg (N, D, LLD, SIGMA, PIVMIN, R)
SLANEG computes 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

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.

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

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