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slasd4.f(3)				      LAPACK				      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:
	   September 2012

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

       Definition at line 154 of file slasd4.f.

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

Version 3.4.2				 Tue Sep 25 2012			      slasd4.f(3)
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