dlasd5 man page on Scientific

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DLASD5(1)	    LAPACK auxiliary routine (version 3.2)	     DLASD5(1)

NAME
       DLASD5 - subroutine 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 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) - sigma_I) in its	j-th  component.   The	vector
	      DELTA contains the information necessary to construct the eigen‐
	      vectors.

       RHO    (input) DOUBLE PRECISION
	      The scalar in the symmetric updating formula.   DSIGMA  (output)
	      DOUBLE  PRECISION	 The computed sigma_I, the I-th updated eigen‐
	      value.

       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

 LAPACK auxiliary routine (versioNovember 2008			     DLASD5(1)
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