LAPACK

NAME¶

laed4 - laed4: D&C step: secular equation nonlinear solver

SYNOPSIS¶

Functions¶

subroutine dlaed4 (n, i, d, z, delta, rho, dlam, info)
DLAED4 used by DSTEDC. Finds a single root of the secular equation. subroutine slaed4 (n, i, d, z, delta, rho, dlam, info)
SLAED4 used by SSTEDC. Finds a single root of the secular equation.

Detailed Description¶

Function Documentation¶

subroutine dlaed4 (integer n, integer i, double precision, dimension( * ) d, double precision, dimension( * ) z, double precision, dimension( * ) delta, double precision rho, double precision dlam, integer info)¶

DLAED4 used by DSTEDC. Finds a single root of the secular equation.

Purpose:

!>
!> This subroutine computes the I-th updated eigenvalue of a symmetric
!> rank-one modification to a diagonal matrix whose elements are
!> given in the array d, and that
!>
!>            D(i) < D(j)  for  i < j
!>
!> and that RHO > 0.  This is arranged by the calling routine, and is
!> no loss in generality.  The rank-one modified system is thus
!>
!>            diag( D )  +  RHO * Z * Z_transpose.
!>
!> where we assume the Euclidean norm of Z is 1.
!>
!> The method consists of approximating the rational functions in the
!> secular equation by simpler interpolating rational functions.
!>

Parameters

!>          N is INTEGER
!>         The length of all arrays.
!>

!>          I is INTEGER
!>         The index of the eigenvalue to be computed.  1 <= I <= N.
!>

!>          D is DOUBLE PRECISION array, dimension (N)
!>         The original eigenvalues.  It is assumed that they are in
!>         order, D(I) < D(J)  for I < J.
!>

!>          Z is DOUBLE PRECISION array, dimension (N)
!>         The components of the updating vector.
!>

DELTA

!>          DELTA is DOUBLE PRECISION array, dimension (N)
!>         If N > 2, DELTA contains (D(j) - lambda_I) in its  j-th
!>         component.  If N = 1, then DELTA(1) = 1. If N = 2, see DLAED5
!>         for detail. The vector DELTA contains the information necessary
!>         to construct the eigenvectors by DLAED3 and DLAED9.
!>

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.
!>

INFO

!>          INFO is INTEGER
!>         = 0:  successful exit
!>         > 0:  if INFO = 1, the updating process failed.
!>

Internal Parameters:

!>  Logical variable ORGATI (origin-at-i?) is used for distinguishing
!>  whether D(i) or D(i+1) is treated as the origin.
!>
!>            ORGATI = .true.    origin at i
!>            ORGATI = .false.   origin at i+1
!>
!>   Logical variable SWTCH3 (switch-for-3-poles?) is for noting
!>   if we are working with THREE poles!
!>
!>   MAXIT is the maximum number of iterations allowed for each
!>   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 slaed4 (integer n, integer i, real, dimension( * ) d, real, dimension( * ) z, real, dimension( * ) delta, real rho, real dlam, integer info)¶

SLAED4 used by SSTEDC. Finds a single root of the secular equation.