subroutine dlasd5 (I, D, Z, DELTA, RHO, DSIGMA, WORK)
DLASD5 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.
DLASD5 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 DOUBLE PRECISION array, dimension ( 2 )
The original eigenvalues. We assume 0 <= D(1) < D(2).
Z
Z is DOUBLE PRECISION array, dimension ( 2 )
The components of the updating vector.
DELTA
DELTA is 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
RHO is DOUBLE PRECISION
The scalar in the symmetric updating formula.
DSIGMA
DSIGMA is DOUBLE PRECISION
The computed sigma_I, the I-th updated eigenvalue.
WORK
WORK is DOUBLE PRECISION 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 dlasd5.f.
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