dlasd5()

subroutine dlasd5	(	integer	i,
		double precision, dimension( 2 )	d,
		double precision, dimension( 2 )	z,
		double precision, dimension( 2 )	delta,
		double precision	rho,
		double precision	dsigma,
		double precision, dimension( 2 )	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.

Download DLASD5 + dependencies [TGZ] [ZIP] [TXT]

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

[in]	I	!> I is INTEGER !> The index of the eigenvalue to be computed. I = 1 or I = 2. !>
[in]	D	!> D is DOUBLE PRECISION array, dimension ( 2 ) !> The original eigenvalues. We assume 0 <= D(1) < D(2). !>
[in]	Z	!> Z is DOUBLE PRECISION array, dimension ( 2 ) !> The components of the updating vector. !>
[out]	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. !>
[in]	RHO	!> RHO is DOUBLE PRECISION !> The scalar in the symmetric updating formula. !>
[out]	DSIGMA	!> DSIGMA is DOUBLE PRECISION !> The computed sigma_I, the I-th updated eigenvalue. !>
[out]	WORK	!> WORK is DOUBLE PRECISION array, dimension ( 2 ) !> WORK contains (D(j) + sigma_I) in its j-th component. !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

Ren-Cang Li, Computer Science Division, University of California at Berkeley, USA