slasd53lapack
Subroutine compute 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 the diagonal entries in the array d are assumed to satisfy 0 <= d(i) < d(j) for i < j
Usage
- SUBROUTINE SLASD5(
-
I, D, Z, DELTA, RHO, DSIGMA, WORK )
- INTEGER
-
I
- REAL
-
DSIGMA, RHO
- REAL
-
D( 2 ), DELTA( 2 ), WORK( 2 ), Z( 2 )
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 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) REAL array, dimension (2)
-
The original eigenvalues. We assume 0 <= D(1) < D(2).
- Z (input) REAL array, dimension (2)
-
The components of the updating vector.
- DELTA (output) REAL 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) REAL
-
The scalar in the symmetric updating formula. DSIGMA (output) REAL The computed sigma_I, the I-th updated eigenvalue.
- WORK (workspace) REAL 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