---
name: "dlaneg"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/dlaneg/3lapack"
---

# dlaneg(3lapack)

computes the Sturm count, the number of negative pivots encountered while factoring tridiagonal T - sigma I = L D L^T

## NAME

DLANEG - computes the Sturm count, the number of negative pivots encountered while factoring tridiagonal T - sigma I = L D L^T

## SYNOPSIS

- FUNCTION DLANEG(

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

- IMPLICIT

  NONE

- INTEGER

  DLANEG

- INTEGER

  N, R

- DOUBLE

  PRECISION PIVMIN, SIGMA

- DOUBLE

  PRECISION D( \* ), LLD( \* )

## 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 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.)\

## ARGUMENTS

- N (input) INTEGER

  The order of the matrix.

- D (input) DOUBLE PRECISION array, dimension (N)

  The N diagonal elements of the diagonal matrix D.

- LLD (input) DOUBLE PRECISION array, dimension (N-1)

  The (N-1) elements L(i)\*L(i)\*D(i).

- SIGMA (input) DOUBLE PRECISION

  Shift amount in T - sigma I = L D L^T.

- PIVMIN (input) DOUBLE PRECISION

  The minimum pivot in the Sturm sequence.  May be used when zero pivots are encountered on non-IEEE-754 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\