DLARRF
June 2010
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.
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.
Arguments
| N |
(input) INTEGER
The order of the matrix (subblock, if the matrix splitted).
|
| D |
(input) DOUBLE PRECISION array, dimension (N)
The N diagonal elements of the diagonal matrix D.
|
| L |
(input) DOUBLE PRECISION array, dimension (N-1)
The (N-1) subdiagonal elements of the unit bidiagonal
matrix L. |
| LD |
(input) DOUBLE PRECISION array, dimension (N-1)
The (N-1) elements L(i)*D(i).
|
| CLSTRT |
(input) INTEGER
The index of the first eigenvalue in the cluster.
|
| CLEND |
(input) INTEGER
The index of the last eigenvalue in the cluster.
|
| W |
(input) 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 |
(input/output) DOUBLE PRECISION array, dimension
dimension is >= (CLEND-CLSTRT+1)
The separation from the right neighbor eigenvalue in W. |
| WERR |
(input) 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 |
(input) DOUBLE PRECISION
estimate of the spectral diameter obtained from the
Gerschgorin intervals |
| CLGAPL |
(input) DOUBLE PRECISION
|
| CLGAPR |
(input) 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 |
(input) DOUBLE PRECISION
The minimum pivot allowed in the Sturm sequence.
|
| SIGMA |
(output) DOUBLE PRECISION
The shift used to form L(+) D(+) L(+)^T.
|
| DPLUS |
(output) DOUBLE PRECISION array, dimension (N)
The N diagonal elements of the diagonal matrix D(+).
|
| LPLUS |
(output) DOUBLE PRECISION array, dimension (N-1)
The first (N-1) elements of LPLUS contain the subdiagonal
elements of the unit bidiagonal matrix L(+). |
| WORK |
(workspace) DOUBLE PRECISION array, dimension (2*N)
Workspace.
|
| INFO |
(output) INTEGER
Signals processing OK (=0) or failure (=1)
|
Further Details
Based on contributions by
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
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