# slarrf.f - Man Page

## Synopsis

### Functions/Subroutines

subroutine **slarrf** (**N**, D, L, LD, CLSTRT, CLEND, W, WGAP, WERR, SPDIAM, CLGAPL, CLGAPR, PIVMIN, SIGMA, DPLUS, LPLUS, WORK, INFO)**SLARRF** finds a new relatively robust representation such that at least one of the eigenvalues is relatively isolated.

## Function/Subroutine Documentation

### subroutine slarrf (integer N, real, dimension( * ) D, real, dimension( * ) L, real, dimension( * ) LD, integer CLSTRT, integer CLEND, real, dimension( * ) W, real, dimension( * ) WGAP, real, dimension( * ) WERR, real SPDIAM, real CLGAPL, real CLGAPR, real PIVMIN, real SIGMA, real, dimension( * ) DPLUS, real, dimension( * ) LPLUS, real, dimension( * ) WORK, integer INFO)

**SLARRF** finds a new relatively robust representation such that at least one of the eigenvalues is relatively isolated.

**Purpose:**

Given the initial representation L D L^T and its cluster of close eigenvalues (in a relative measure), W( CLSTRT ), W( CLSTRT+1 ), ... W( CLEND ), SLARRF finds a new relatively robust representation L D L^T - SIGMA I = L(+) D(+) L(+)^T such that at least one of the eigenvalues of L(+) D(+) L(+)^T is relatively isolated.

**Parameters:***N*N is INTEGER The order of the matrix (subblock, if the matrix split).

*D*D is REAL array, dimension (N) The N diagonal elements of the diagonal matrix D.

*L*L is REAL array, dimension (N-1) The (N-1) subdiagonal elements of the unit bidiagonal matrix L.

*LD*LD is REAL array, dimension (N-1) The (N-1) elements L(i)*D(i).

*CLSTRT*CLSTRT is INTEGER The index of the first eigenvalue in the cluster.

*CLEND*CLEND is INTEGER The index of the last eigenvalue in the cluster.

*W*W is REAL array, dimension dimension is >= (CLEND-CLSTRT+1) The eigenvalue APPROXIMATIONS of L D L^T in ascending order. W( CLSTRT ) through W( CLEND ) form the cluster of relatively close eigenalues.

*WGAP*WGAP is REAL array, dimension dimension is >= (CLEND-CLSTRT+1) The separation from the right neighbor eigenvalue in W.

*WERR*WERR is REAL array, dimension dimension is >= (CLEND-CLSTRT+1) WERR contain the semiwidth of the uncertainty interval of the corresponding eigenvalue APPROXIMATION in W

*SPDIAM*SPDIAM is REAL estimate of the spectral diameter obtained from the Gerschgorin intervals

*CLGAPL*CLGAPL is REAL

*CLGAPR*CLGAPR is REAL absolute gap on each end of the cluster. Set by the calling routine to protect against shifts too close to eigenvalues outside the cluster.

*PIVMIN*PIVMIN is REAL The minimum pivot allowed in the Sturm sequence.

*SIGMA*SIGMA is REAL The shift used to form L(+) D(+) L(+)^T.

*DPLUS*DPLUS is REAL array, dimension (N) The N diagonal elements of the diagonal matrix D(+).

*LPLUS*LPLUS is REAL array, dimension (N-1) The first (N-1) elements of LPLUS contain the subdiagonal elements of the unit bidiagonal matrix L(+).

*WORK*WORK is REAL array, dimension (2*N) Workspace.

*INFO*INFO is INTEGER Signals processing OK (=0) or failure (=1)

**Author:**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date:**June 2016

**Contributors:**Beresford Parlett, University of California, Berkeley, USA

Jim Demmel, University of California, Berkeley, USA

Inderjit Dhillon, University of Texas, Austin, USA

Osni Marques, LBNL/NERSC, USA

Christof Voemel, University of California, Berkeley, USA

Definition at line 195 of file slarrf.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page slarrf(3) is an alias of slarrf.f(3).