DLASD4 man page on IRIX

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DLASD4(3S)							    DLASD4(3S)

NAME
     DLASD4 - 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

SYNOPSIS
     SUBROUTINE DLASD4( N, I, D, Z, DELTA, RHO, SIGMA, WORK, INFO )

	 INTEGER	I, INFO, N

	 DOUBLE		PRECISION RHO, SIGMA

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

IMPLEMENTATION
     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, the default integer size is
     4 bytes (32 bits). Another version of SCSL is available in which integers
     are 8 bytes (64 bits).  This version allows the user access to larger
     memory sizes and helps when porting legacy Cray codes.  It can be loaded
     by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
     only one of the two versions; 4-byte integer and 8-byte integer library
     calls cannot be mixed.

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.

ARGUMENTS
     N	    (input) INTEGER
	    The length of all arrays.

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

									Page 1

DLASD4(3S)							    DLASD4(3S)

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

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

     DELTA  (output) DOUBLE PRECISION 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) DOUBLE PRECISION
	    The scalar in the symmetric updating formula.

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

     WORK   (workspace) DOUBLE PRECISION 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

SEE ALSO
     INTRO_LAPACK(3S), INTRO_SCSL(3S)

     This man page is available only online.

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