Provided by: liblapack-doc_3.3.1-1_all bug

NAME

       LAPACK-3 - subroutine compute 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

SYNOPSIS

       SUBROUTINE SLASD4( N, I, D, Z, DELTA, RHO, SIGMA, WORK, INFO )

           INTEGER        I, INFO, N

           REAL           RHO, SIGMA

           REAL           D( * ), DELTA( * ), WORK( * ), Z( * )

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
        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.

ARGUMENTS

        N      (input) INTEGER
               The length of all arrays.

        I      (input) INTEGER
               The index of the eigenvalue to be computed.  1 <= I <= N.

        D      (input) REAL array, dimension ( N )
               The original eigenvalues.  It is assumed that they are in
               order, 0 <= D(I) < D(J)  for I < J.

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

        DELTA  (output) 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    (input) REAL
               The scalar in the symmetric updating formula.

        SIGMA  (output) REAL
               The computed sigma_I, the I-th updated eigenvalue.

        WORK   (workspace) 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   (output) INTEGER
               = 0:  successful exit
               > 0:  if INFO = 1, the updating process failed.

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.
        Further Details
        ===============
        Based on contributions by
        Ren-Cang Li, Computer Science Division, University of California
        at Berkeley, USA

 LAPACK auxiliary routine (version 3.3.1)   April 2011                            SLASD4(3lapack)