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.