laed4(3)

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

              N is INTEGER
             The length of all arrays.

    I

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

    D

              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

              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

Definition at line 144 of file dlaed4.f.

  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.

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

              N is INTEGER
             The length of all arrays.

    I

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

    D

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

    Z

              Z is REAL array, dimension (N)
             The components of the updating vector.

    DELTA

              DELTA is REAL 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 SLAED5
             for detail. The vector DELTA contains the information necessary
             to construct the eigenvectors by SLAED3 and SLAED9.

    RHO

              RHO is REAL
             The scalar in the symmetric updating formula.

    DLAM

              DLAM is REAL
             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

Definition at line 144 of file slaed4.f.

Author

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