subroutine slasd5 (I, D, Z, DELTA, RHO, DSIGMA, WORK)
SLASD5 computes the square root of the i-th eigenvalue of a positive symmetric rank-one modification of a 2-by-2 diagonal matrix. Used by sbdsdc.
SLASD5 computes the square root of the i-th eigenvalue of a positive symmetric rank-one modification of a 2-by-2 diagonal matrix. Used by sbdsdc.
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.
Parameters:
I is INTEGER
The index of the eigenvalue to be computed. I = 1 or I = 2.
D
D is REAL array, dimension (2)
The original eigenvalues. We assume 0 <= D(1) < D(2).
Z
Z is REAL array, dimension (2)
The components of the updating vector.
DELTA
DELTA is 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
RHO is REAL
The scalar in the symmetric updating formula.
DSIGMA
DSIGMA is REAL
The computed sigma_I, the I-th updated eigenvalue.
WORK
WORK is REAL array, dimension (2)
WORK contains (D(j) + sigma_I) in its j-th component.
Author:
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
Contributors:
Definition at line 118 of file slasd5.f.
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