slaneg (l)  Linux Man Pages
slaneg: computes the Sturm count, the number of negative pivots encountered while factoring tridiagonal T  sigma I = L D L^T
Command to display slaneg
manual in Linux: $ man l slaneg
NAME
SLANEG  computes the Sturm count, the number of negative pivots encountered while factoring tridiagonal T  sigma I = L D L^T
SYNOPSIS
 FUNCTION SLANEG(

N, D, LLD, SIGMA, PIVMIN, R )

IMPLICIT
NONE

INTEGER
SLANEG

INTEGER
N, R

REAL
PIVMIN, SIGMA

REAL
D( * ), LLD( * )
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 IEEE754 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
nonzero, and Inf/Inf produces NaN. For more information, see:
Marques, Riedy, and Voemel, "Benefits of IEEE754 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.)
ARGUMENTS
 N (input) INTEGER

The order of the matrix.
 D (input) REAL array, dimension (N)

The N diagonal elements of the diagonal matrix D.
 LLD (input) REAL array, dimension (N1)

The (N1) elements L(i)*L(i)*D(i).
 SIGMA (input) REAL

Shift amount in T  sigma I = L D L^T.
 PIVMIN (input) REAL

The minimum pivot in the Sturm sequence. May be used
when zero pivots are encountered on nonIEEE754
architectures.
 R (input) INTEGER

The twist index for the twisted factorization that is used
for the negcount.
FURTHER DETAILS
Based on contributions by
Osni Marques, LBNL/NERSC, USA
Christof Voemel, University of California, Berkeley, USA
Jason Riedy, University of California, Berkeley, USA
Pages related to slaneg
 slaneg (3)
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 slange (l)  returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real matrix A
 slangt (l)  returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real tridiagonal matrix A
 slanhs (l)  returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hessenberg matrix A
 slansb (l)  returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n symmetric band matrix A, with k superdiagonals
 slansf (l)  returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix A in RFP format
 slansp (l)  returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix A, supplied in packed form
 slanst (l)  returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric tridiagonal matrix A
 slansy (l)  returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix A