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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