man dlasd5 (Fonctions bibliothèques) - 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)
NAME
DLASD5 - 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)
SYNOPSIS
- SUBROUTINE DLASD5(
- I, D, Z, DELTA, RHO, DSIGMA, WORK )
- INTEGER I
- DOUBLE PRECISION DSIGMA, RHO
- DOUBLE PRECISION 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 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) - lambda_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 lambda_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