dlasd5.f (3)

Functions/Subroutines

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.

subroutine dlasd5 (integerI, double precision, dimension( 2 )D, double precision, dimension( 2 )Z, double precision, dimension( 2 )DELTA, double precisionRHO, double precisionDSIGMA, 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.

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

          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 Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

September 2012

Contributors:

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

Definition at line 117 of file dlasd5.f.

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