Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

ID 766686
Date 3/22/2024
Public

A newer version of this document is available. Customers should click here to go to the newest version.

Document Table of Contents

?laneg

Computes the Sturm count, the number of negative pivots encountered while factoring tridiagonal T-sigma*I = L*D*LT.

Syntax

value = slaneg( n, d, lld, sigma, pivmin, r )

value = dlaneg( n, d, lld, sigma, pivmin, r )

Include Files

  • mkl.fi

Description

The routine computes the Sturm count, the number of negative pivots encountered while factoring tridiagonal T-sigma*I = L*D*LT. 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 ?larb. The current routine does not use the pivmin parameter but rather requires IEEE-754 propagation of infinities and NaNs (NaN stands for 'Not A Number'). 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 [Marques06]).

Input Parameters

n

INTEGER. The order of the matrix.

d

REAL for slaneg

DOUBLE PRECISION for dlaneg

Array, DIMENSION (n).

Contains n diagonal elements of the matrix D.

lld

REAL for slaneg

DOUBLE PRECISION for dlaneg

Array, DIMENSION (n-1).

Contains (n-1) elements L(i)*L(i)*D(i).

sigma

REAL for slaneg

DOUBLE PRECISION for dlaneg

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

pivmin

REAL for slaneg

DOUBLE PRECISION for dlaneg

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

r

INTEGER.

The twist index for the twisted factorization that is used for the negcount.

Output Parameters

value

INTEGER. The number of negative pivots encountered while factoring.