slaed4.f(3)							      LAPACK							       slaed4.f(3)

NAME

       slaed4.f -

SYNOPSIS

   Functions/Subroutines
       subroutine slaed4 (N, I, D, Z, DELTA, RHO, DLAM, INFO)
	   SLAED4

Function/Subroutine Documentation
   subroutine slaed4 (integerN, integerI, real, dimension( * )D, real, dimension( * )Z, real, dimension( * )DELTA, realRHO, realDLAM, integerINFO)
       SLAED4

       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 .GT. 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.

       Date:
	   November 2011

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

       Definition at line 146 of file slaed4.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.1							  Sun May 26 2013						       slaed4.f(3)