# laneg - Man Page

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, double precision 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 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.)

**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 L^T.

*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

Definition at line **117** of file **dlaneg.f**.

### 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 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.

**Contributors:**Osni Marques, LBNL/NERSC, USA

Christof Voemel, University of California, Berkeley, USA

Jason Riedy, University of California, Berkeley, USA

Definition at line **117** of file **slaneg.f**.

## Author

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