LAPACK

NAME¶

larrf - larrf: step in stemr, find relative robust representation (RRR)

SYNOPSIS¶

Functions¶

subroutine dlarrf (n, d, l, ld, clstrt, clend, w, wgap, werr, spdiam, clgapl, clgapr, pivmin, sigma, dplus, lplus, work, info)
DLARRF finds a new relatively robust representation such that at least one of the eigenvalues is relatively isolated. 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.

Detailed Description¶

Function Documentation¶

subroutine dlarrf (integer n, double precision, dimension( * ) d, double precision, dimension( * ) l, double precision, dimension( * ) ld, integer clstrt, integer clend, double precision, dimension( * ) w, double precision, dimension( * ) wgap, double precision, dimension( * ) werr, double precision spdiam, double precision clgapl, double precision clgapr, double precision pivmin, double precision sigma, double precision, dimension( * ) dplus, double precision, dimension( * ) lplus, double precision, dimension( * ) work, integer info)¶

DLARRF 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 ), DLARRF 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 is INTEGER


          The order of the matrix (subblock, if the matrix split).



          D is DOUBLE PRECISION array, dimension (N)


          The N diagonal elements of the diagonal matrix D.



          L is DOUBLE PRECISION array, dimension (N-1)


          The (N-1) subdiagonal elements of the unit bidiagonal


          matrix L.



          LD is DOUBLE PRECISION 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 is DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension


          dimension is >=  (CLEND-CLSTRT+1)


          The separation from the right neighbor eigenvalue in W.

WERR



          WERR is DOUBLE PRECISION 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 DOUBLE PRECISION


          estimate of the spectral diameter obtained from the


          Gerschgorin intervals

CLGAPL



          CLGAPL is DOUBLE PRECISION

CLGAPR



          CLGAPR is DOUBLE PRECISION


          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 DOUBLE PRECISION


          The minimum pivot allowed in the Sturm sequence.

SIGMA



          SIGMA is DOUBLE PRECISION


          The shift used to form L(+) D(+) L(+)^T.

DPLUS



          DPLUS is DOUBLE PRECISION array, dimension (N)


          The N diagonal elements of the diagonal matrix D(+).

LPLUS



          LPLUS is DOUBLE PRECISION array, dimension (N-1)


          The first (N-1) elements of LPLUS contain the subdiagonal


          elements of the unit bidiagonal matrix L(+).

WORK



          WORK is DOUBLE PRECISION 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.

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

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.