DLASD5
November 2006
Purpose
This subroutine computes the square root of the I-th eigenvalue
of a positive symmetric rank-one modification of a 2-by-2 diagonal
matrix
diag( D ) * diag( D ) + RHO * Z * transpose(Z) .
The diagonal entries in the array D are assumed to satisfy
0 <= D(i) < D(j) for i < j .
We also assume RHO > 0 and that the Euclidean norm of the vector
Z is one.
of a positive symmetric rank-one modification of a 2-by-2 diagonal
matrix
diag( D ) * diag( D ) + RHO * Z * transpose(Z) .
The diagonal entries in the array D are assumed to satisfy
0 <= D(i) < D(j) for i < j .
We also assume RHO > 0 and that the Euclidean norm of the vector
Z is one.
Arguments
| I |
(input) INTEGER
The index of the eigenvalue to be computed. I = 1 or I = 2.
|
| D |
(input) DOUBLE PRECISION array, dimension ( 2 )
The original eigenvalues. We assume 0 <= D(1) < D(2).
|
| Z |
(input) DOUBLE PRECISION array, dimension ( 2 )
The components of the updating vector.
|
| DELTA |
(output) DOUBLE PRECISION array, dimension ( 2 )
Contains (D(j) - sigma_I) in its j-th component.
The vector DELTA contains the information necessary to construct the eigenvectors. |
| RHO |
(input) DOUBLE PRECISION
The scalar in the symmetric updating formula.
|
| DSIGMA |
(output) DOUBLE PRECISION
The computed sigma_I, the I-th updated eigenvalue.
|
| WORK |
(workspace) DOUBLE PRECISION array, dimension ( 2 )
WORK contains (D(j) + sigma_I) in its j-th component.
|
Further Details
Based on contributions by
Ren-Cang Li, Computer Science Division, University of California
at Berkeley, USA
Ren-Cang Li, Computer Science Division, University of California
at Berkeley, USA