Library Functions Manual

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

Definition at line 115 of file dlasd5.f.

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.