SLARRB
June 2010
Purpose
Given the relatively robust representation(RRR) L D L^T, SLARRB
does "limited" bisection to refine the eigenvalues of L D L^T,
W( IFIRST-OFFSET ) through W( ILAST-OFFSET ), to more accuracy. Initial
guesses for these eigenvalues are input in W, the corresponding estimate
of the error in these guesses and their gaps are input in WERR
and WGAP, respectively. During bisection, intervals
[left, right] are maintained by storing their mid-points and
semi-widths in the arrays W and WERR respectively.
does "limited" bisection to refine the eigenvalues of L D L^T,
W( IFIRST-OFFSET ) through W( ILAST-OFFSET ), to more accuracy. Initial
guesses for these eigenvalues are input in W, the corresponding estimate
of the error in these guesses and their gaps are input in WERR
and WGAP, respectively. During bisection, intervals
[left, right] are maintained by storing their mid-points and
semi-widths in the arrays W and WERR respectively.
Arguments
| N |
(input) INTEGER
The order of the matrix.
|
| D |
(input) REAL array, dimension (N)
The N diagonal elements of the diagonal matrix D.
|
| LLD |
(input) REAL array, dimension (N-1)
The (N-1) elements L(i)*L(i)*D(i).
|
| IFIRST |
(input) INTEGER
The index of the first eigenvalue to be computed.
|
| ILAST |
(input) INTEGER
The index of the last eigenvalue to be computed.
|
| RTOL1 |
(input) REAL
|
| RTOL2 |
(input) REAL
Tolerance for the convergence of the bisection intervals.
An interval [LEFT,RIGHT] has converged if RIGHT-LEFT.LT.MAX( RTOL1*GAP, RTOL2*MAX(|LEFT|,|RIGHT|) ) where GAP is the (estimated) distance to the nearest eigenvalue. |
| OFFSET |
(input) INTEGER
Offset for the arrays W, WGAP and WERR, i.e., the IFIRST-OFFSET
through ILAST-OFFSET elements of these arrays are to be used. |
| W |
(input/output) REAL array, dimension (N)
On input, W( IFIRST-OFFSET ) through W( ILAST-OFFSET ) are
estimates of the eigenvalues of L D L^T indexed IFIRST throug ILAST. On output, these estimates are refined. |
| WGAP |
(input/output) REAL array, dimension (N-1)
On input, the (estimated) gaps between consecutive
eigenvalues of L D L^T, i.e., WGAP(I-OFFSET) is the gap between eigenvalues I and I+1. Note that if IFIRST.EQ.ILAST then WGAP(IFIRST-OFFSET) must be set to ZERO. On output, these gaps are refined. |
| WERR |
(input/output) REAL array, dimension (N)
On input, WERR( IFIRST-OFFSET ) through WERR( ILAST-OFFSET ) are
the errors in the estimates of the corresponding elements in W. On output, these errors are refined. |
| WORK |
(workspace) REAL array, dimension (2*N)
Workspace.
|
| IWORK |
(workspace) INTEGER array, dimension (2*N)
Workspace.
|
| PIVMIN |
(input) REAL
The minimum pivot in the Sturm sequence.
|
| SPDIAM |
(input) REAL
The spectral diameter of the matrix.
|
| TWIST |
(input) INTEGER
The twist index for the twisted factorization that is used
for the negcount. TWIST = N: Compute negcount from L D L^T - LAMBDA I = L+ D+ L+^T TWIST = 1: Compute negcount from L D L^T - LAMBDA I = U- D- U-^T TWIST = R: Compute negcount from L D L^T - LAMBDA I = N(r) D(r) N(r) |
| INFO |
(output) INTEGER
Error flag.
|
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