LAPACK

NAME¶

lasd5 - lasd5: D&C step: secular equation, 2x2

SYNOPSIS¶

Functions¶

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 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.

Detailed Description¶

Function Documentation¶

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.

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 is DOUBLE PRECISION array, dimension ( 2 )


         The original eigenvalues.  We assume 0 <= D(1) < D(2).



          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.

Contributors:

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

subroutine slasd5 (integer i, real, dimension( 2 ) d, real, dimension( 2 ) z, real, dimension( 2 ) delta, real rho, real dsigma, real, dimension( 2 ) 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.