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dlasd5 examples
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Man Page Details
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NAME
       DLASD5  -  compute the square root of the I-th eigenvalue of a positive
       symmetric rank-one modification of a 2-by-2 diagonal matrix   diag( D )
       *  diag(  D ) + RHO  The diagonal entries in the array D are assumed to
       satisfy   0 <= D(i) < D(j) for i < j

SYNOPSIS
       SUBROUTINE DLASD5( I, D, Z, DELTA, RHO, DSIGMA, WORK )

           INTEGER        I

           DOUBLE         PRECISION DSIGMA, RHO

           DOUBLE         PRECISION D( 2 ), DELTA( 2 ), WORK( 2 ), Z( 2 )

  Purpose
  =======

  This subroutine computes the square root of the I-th eigenvalue
  of a positive symmetric rank-one modification of a 2-by-2 diagonal
  matrix

             diag( D ) * diag( D ) +  RHO *  Z * transpose(Z) .

  The diagonal entries in the array D are assumed to satisfy

             0 <= D(i) < D(j)  for  i < j .

  We also assume RHO > 0 and that the Euclidean norm of the vector
  Z is one.

  Arguments
  =========

  I      (input) INTEGER
         The index of the eigenvalue to be computed.  I = 1 or I = 2.

  D      (input) DOUBLE PRECISION array, dimension ( 2 )
         The original eigenvalues.  We assume 0 <= D(1) < D(2).

  Z      (input) DOUBLE PRECISION array, dimension ( 2 )
         The components of the updating vector.

  DELTA  (output) DOUBLE PRECISION array, dimension ( 2 )
         Contains (D(j) - lambda_I) in its  j-th component.
         The vector DELTA contains the information necessary
         to construct the eigenvectors.

  RHO    (input) DOUBLE PRECISION
         The scalar in the symmetric updating formula.

  DSIGMA (output) DOUBLE PRECISION
         The computed lambda_I, the I-th updated eigenvalue.

  WORK   (workspace) DOUBLE PRECISION array, dimension ( 2 )
         WORK contains (D(j) + sigma_I) in its  j-th component.

  Further Details
  ===============

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

