slasd4.f(3)

NAME
slasd4.f -

SYNOPSIS

  Functions/Subroutines

subroutine slasd4 (N, I, D, Z, DELTA, RHO, SIGMA, WORK, INFO)
SLASD4 computes the square root of the i-th updated eigenvalue of a positive symmetric rank-one modification to a positive diagonal matrix. Used by sbdsdc.

Function/Subroutine Documentation

  subroutine slasd4 (integerN, integerI, real, dimension( * )D, real, dimension( * )Z, real, dimension( * )DELTA, realRHO, realSIGMA, real, dimension( * )WORK, integerINFO)

SLASD4 computes the square root of the i-th updated eigenvalue of a positive symmetric rank-one modification to a positive diagonal matrix. Used by sbdsdc.

Purpose:

     This subroutine computes the square root of the I-th updated
     eigenvalue of a positive symmetric rank-one modification to
     a positive diagonal matrix whose entries are given as the squares
     of the corresponding entries in the array d, and that

            0 <= 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 ) * 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, 0 <= 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 .ne. 1, DELTA contains (D(j) - sigma_I) in its  j-th
             component.  If N = 1, then DELTA(1) = 1.  The vector DELTA
             contains the information necessary to construct the
             (singular) eigenvectors.

    RHO

              RHO is REAL
             The scalar in the symmetric updating formula.

    SIGMA

              SIGMA is REAL
             The computed sigma_I, the I-th updated eigenvalue.

    WORK

              WORK is REAL array, dimension ( N )
             If N .ne. 1, WORK contains (D(j) + sigma_I) in its  j-th
             component.  If N = 1, then WORK( 1 ) = 1.

    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.

Date:
    November 2013

Contributors:
    Ren-Cang Li, Computer Science Division, University of California at Berkeley, USA

Definition at line 154 of file slasd4.f.

Author

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