◆ 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