slaed5(3S)

NAME
     SLAED5 - subroutine computes the I-th eigenvalue of a symmetric rank-one
     modification of a 2-by-2 diagonal matrix  diag( D ) + RHO * Z *
     transpose(Z)

SYNOPSIS
     SUBROUTINE SLAED5( I, D, Z, DELTA, RHO, DLAM )

         INTEGER        I

         REAL           DLAM, RHO

         REAL           D( 2 ), DELTA( 2 ), Z( 2 )

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 I-th eigenvalue of a symmetric rank-one
     modification of a 2-by-2 diagonal matrix diag( D ) + RHO * Z *
     transpose(Z) . The diagonal elements in the array D are assumed to
     satisfy

                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) REAL array, dimension (2)
            The original eigenvalues.  We assume D(1) < D(2).

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

     DELTA  (output) REAL array, dimension (2)
            The vector DELTA contains the information necessary to construct
            the eigenvectors.
     RHO    (input) REAL
            The scalar in the symmetric updating formula.

     DLAM   (output) REAL
            The computed lambda_I, the I-th updated 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)

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