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.

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)

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

June 2016

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