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slarrf.f(3) LAPACK slarrf.f(3)

NAME

slarrf.f -

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 (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.

Author

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