slarrf (3)

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.

subroutine slarrf (integerN, real, dimension( * )D, real, dimension( * )L, real, dimension( * )LD, integerCLSTRT, integerCLEND, real, dimension( * )W, real, dimension( * )WGAP, real, dimension( * )WERR, realSPDIAM, realCLGAPL, realCLGAPR, realPIVMIN, realSIGMA, real, dimension( * )DPLUS, real, dimension( * )LPLUS, real, dimension( * )WORK, integerINFO)

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 splitted).

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:

September 2012

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 191 of file slarrf.f.

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