Man page - laneg(3)

Packages contains this manual

Manual

laneg

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
integer function dlaneg (integer n, double precision, dimension( * ) d,double precision, dimension( * ) lld, double precision sigma, doubleprecision pivmin, integer r)
integer function slaneg (integer n, real, dimension( * ) d, real,dimension( * ) lld, real sigma, real pivmin, integer r)
Author

NAME

laneg - 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.

Detailed Description

Function Documentation

integer function dlaneg (integer n, double precision, dimension( * ) d,double precision, dimension( * ) lld, double precision sigma, doubleprecision 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 LˆT.
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
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 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 LˆT.

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

Univ. of Colorado Denver

NAG Ltd.

Contributors:

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

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 LˆT.
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 LˆT.

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.

Contributors:

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

Author

Generated automatically by Doxygen for LAPACK from the source code.