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| larrf(3) | LAPACK | larrf(3) |
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
D is DOUBLE PRECISION array, dimension (N)
The N diagonal elements of the diagonal matrix D.
L
L is DOUBLE PRECISION array, dimension (N-1)
The (N-1) subdiagonal elements of the unit bidiagonal
matrix L.
LD
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
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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Contributors:
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 189 of file dlarrf.f.
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.
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 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)
Author
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Contributors:
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 189 of file slarrf.f.
Author
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