LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ slarrf()

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.

Download SLARRF + dependencies [TGZ] [ZIP] [TXT]

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
[in]N
!>          N is INTEGER
!>          The order of the matrix (subblock, if the matrix split).
!>
[in]D
!>          D is REAL array, dimension (N)
!>          The N diagonal elements of the diagonal matrix D.
!>
[in]L
!>          L is REAL array, dimension (N-1)
!>          The (N-1) subdiagonal elements of the unit bidiagonal
!>          matrix L.
!>
[in]LD
!>          LD is REAL array, dimension (N-1)
!>          The (N-1) elements L(i)*D(i).
!>
[in]CLSTRT
!>          CLSTRT is INTEGER
!>          The index of the first eigenvalue in the cluster.
!>
[in]CLEND
!>          CLEND is INTEGER
!>          The index of the last eigenvalue in the cluster.
!>
[in]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.
!>
[in,out]WGAP
!>          WGAP is REAL array, dimension
!>          dimension is >=  (CLEND-CLSTRT+1)
!>          The separation from the right neighbor eigenvalue in W.
!>
[in]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
!>
[in]SPDIAM
!>          SPDIAM is REAL
!>          estimate of the spectral diameter obtained from the
!>          Gerschgorin intervals
!>
[in]CLGAPL
!>          CLGAPL is REAL
!>
[in]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.
!>
[in]PIVMIN
!>          PIVMIN is REAL
!>          The minimum pivot allowed in the Sturm sequence.
!>
[out]SIGMA
!>          SIGMA is REAL
!>          The shift used to form L(+) D(+) L(+)^T.
!>
[out]DPLUS
!>          DPLUS is REAL array, dimension (N)
!>          The N diagonal elements of the diagonal matrix D(+).
!>
[out]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(+).
!>
[out]WORK
!>          WORK is REAL array, dimension (2*N)
!>          Workspace.
!>
[out]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.
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