LAPACK

NAME¶

laed5 - laed5: D&C step: secular equation, 2x2

SYNOPSIS¶

Functions¶

subroutine dlaed5 (i, d, z, delta, rho, dlam)
DLAED5 used by DSTEDC. Solves the 2-by-2 secular equation. subroutine slaed5 (i, d, z, delta, rho, dlam)
SLAED5 used by SSTEDC. Solves the 2-by-2 secular equation.

Detailed Description¶

Function Documentation¶

subroutine dlaed5 (integer i, double precision, dimension( 2 ) d, double precision, dimension( 2 ) z, double precision, dimension( 2 ) delta, double precision rho, double precision dlam)¶

DLAED5 used by DSTEDC. Solves the 2-by-2 secular equation.

Purpose:

!>
!> This subroutine computes the I-th eigenvalue of a symmetric rank-one
!> modification of a 2-by-2 diagonal matrix
!>
!>            diag( D )  +  RHO * Z * transpose(Z) .
!>
!> The diagonal elements in the array D are assumed to satisfy
!>
!>            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 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)
!>         The vector DELTA contains the information necessary
!>         to construct the eigenvectors.
!>

RHO

!>          RHO is DOUBLE PRECISION
!>         The scalar in the symmetric updating formula.
!>

DLAM

!>          DLAM is DOUBLE PRECISION
!>         The computed lambda_I, the I-th updated eigenvalue.
!>

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 slaed5 (integer i, real, dimension( 2 ) d, real, dimension( 2 ) z, real, dimension( 2 ) delta, real rho, real dlam)¶

SLAED5 used by SSTEDC. Solves the 2-by-2 secular equation.